Welcome to MechanicsArXiv. This repository provides a platform for researchers to share early-stage research, working or completed papers, technical reports, reviews, and tutorials in the broadly defined field of solid mechanics. Our mission is to accelerate the dissemination of scholarly work, foster collaboration, and provide open access to the latest innovations across mechanics.
A non-local constitutive model for the Mullins effect in filled elastomers
Filled rubber-like materials are widely used in engineering applications and are well known to exhibit the Mullins effect. In this work, an established local constitutive model from the literature is extended to a non-local setting to resolve the mesh dependence inherent to the local approach. Non-local effects are incorporated using two separate approaches: (i) a Helmholtz-type equation governing a non-local soft volume fraction, and (ii) a Laplacian term introduced directly into the soft volume fraction local evolution law. In both formulations, an additional governing partial differential equation arises and is solved numerically in Abaqus using an analogy with the heat equation. The two approaches yield different results, leaving the choice between them to be guided by experimental findings. The details of the implementation, along with the code developed in this work are also provided.
Harnessing disorder to decouple extension and shear in kirigami metamaterials
Kirigami transforms stiff sheets into compliant, shape-morphing structures via periodic cut patterns. These repeating motifs rotate with stretch, so that extension in general leads to shear, and anisotropic properties cannot be tuned independently. Biological tissues evade this through controlled disorder, such as graded fiber orientations in skin and hierarchical anisotropy in myocardium. Here, we show that engineered disorder is tunable design degree of freedom: stochastic kirigami accesses a continuous and far broader region of mechanical response than periodic patterns, including programmable anisotropy with near-complete suppression of extension–shear coupling. Because disordered patterns lack a simple parameterization, we navigate this space with a geometry-aware graph neural network (GNN) that maps cut topology to full nonlinear, bidirectional stress–strain response, coupled to a genetic algorithm for inverse design of kirigami patterns that reproduce target stress–strain responses in two perpendicular loading directions. The GNN is trained an order of magnitude faster and more accurately than image-based models. Fabricated elastomer samples reproduce the targeted nonlinear, anisotropic responses, closing the loop from design to physical component. By turning disorder into a control axis for directional stiffness, this work points toward architected materials that stretch without parasitic shear, enabling tissue-interfacing devices matched to the anisotropy of living tissue.
Dendrite-growth resistance in solid state electrolytes
We address dendrite growth resistance in solid electrolytes in all-solid-state Li-ion batteries. First, we introduce a dendrite-growth model in the electrical, ionic-flow, temperature, and stress fields in the solid-state electrolyte. The model analysis shows that the applied electrode potential generates field singularities at the dendrite/crack tip, driven by electrochemical ion-deposition pressure and the thermal-conductivity jump at the dendrite/electrolyte interface. An extended J- integral is introduced to characterize the stress and temperature-gradient singularities and associated driving forces of the dendrite/crack tip in the heat-generating medium. These singularities are then used to construct universal threshold-current-density diagrams of dendrite/crack growth in solid electrolytes. From the universal diagram, the resistance to dendrite/crack growth is defined. This resistance depends on the dendrite/crack length, film thickness, and the properties of the electrochemically active solid-state electrolyte. These properties include ion conductivity, thermal conductivity, thermal expansion coefficient, elastic moduli, and toughness against dendrite/crack growth. The analyses show that the driving force from thermal stresses induced by Joule heating of the ionic current in the electrolyte is particularly significant for short dendrite/crack structures. The polarity of the temperature gradient in the electrolyte is found to be a primary factor in determining the threshold current density for short- dendrite/crack growth. The analysis offers methods for testing the dendrite/crack toughness of the electrochemically active solid-state electrolyte. It also guides the design of battery-cell packing sequences to maximize resistance to dendrite/crack formation and growth along the cooling path.
Joule-heating-induced temperature gradient
Electro-chemo-mechanical embrittlement/toughening
Impedance-Guided Programmable Transmission of Localized Deformation in Modular Soft Metamaterials
Soft metamaterials provide a promising platform for robotics, biomedical devices, and flexible electronics. The localized mechanical responses by nonuniform excitation are ubiquitous in soft materials, yet their controlled transmission across assemblies remains largely overlooked in metamaterial design, which critically constrains nontrivial functionalities with end-to-end and long-range deformation transmission. Here, we introduce an impedance-guided design framework that enables programmable transmission of localized deformation in modular soft metamaterials, achieving behaviors unattainable by intuitive design. By establishing a nonlinear model considering position-dependent interactions and integrating the concept of mechanical impedance within metamaterials, we regulate assembly-level transmission solely through unit-cell topology optimization. The resulting framework enables effective synthesis of module families, allowing both homogeneous and heterogeneous assemblies to be custom-built with markedly enhanced transmission characteristics. Leveraging the highly combinatorial and extensible design space, we physically realize diverse on-demand displacement manipulation architectures, including obstacle-bypassing modular soft-metamaterial assemblies, defect-tolerant soft gripping, and embodied signal processing. Beyond deformation programming, the reconfigurability and reassemblability of these soft modules can embed electric logic signals, enabling energy-efficient and low-latency information processing through compliant-switch-controlled mechanical LED displays and wearable finger-motion-sensing controllers. Our method provides fundamental insights into localized deformation transmission in modular soft metamaterials and establishes a scalable route toward embodied-intelligence material systems, particularly for soft-metamaterial-centric actuation, sensing, and collective computing.
Modeling damage and fracture in additively manufactured polymeric triply periodic minimal surface lattices
Architected triply periodic minimal surface (TPMS) lattices offer superior specific energy absorption, toughness, fatigue strength, and tunability. While recent advancements have established rate-dependent viscoplastic constitutive models to capture the complex nonlinear deformation response of additively manufactured polymeric TPMS structures, predicting fracture and the resulting structural failure remains a significant challenge. We address this by performing systematic experiments on unit cells and lattices of various sizes under tension, compression, and non-monotonic loading. The experiments inform the development of a new constitutive model that captures the damage and fracture behavior of polymeric TPMS lattices. We first implement a high-fidelity viscoplastic deformation constitutive model from Ma et al. (2026) into finite element software Abaqus/Explicit via a user material subroutine. We then propose a damage initiation criterion for amorphous polymers based on stored elastic energy and equivalent plastic strain. The damage model is implemented in Abaqus using gradient-damage framework following Konale and Srivastava (2025). The damage model and numerical simulation capability are quantitatively and qualitatively validated using experimental results for a unit cell under non-monotonic loading and lattices under tension. The proposed damage model and simulation capability enable in silico design of architected polymer structures.
A robust and versatile parallel FFT-based mechanical solver for general non-periodic and periodic boundary conditions
General boundary conditions are implemented within a fast Fourier transform framework for linear and non-linear mechanical problems using small or finite transformation formulations. In the context of parallel computing (distributed memory), we present a framework that enables the combination of periodic and non-periodic (Dirichlet or Neumann) boundary conditions. Taking advantage of the link between non-periodic boundary conditions and the symmetries of the relevant components of the fluctuation displacement and stress fields, discrete trigonometric transforms are employed to adapt the classical Moulinec–Suquet fast Fourier transform approach. The present study employs an original displacement-based fixed-point algorithm in combination with a convergence acceleration method in order to solve boundary value problems. Finite difference approaches are used to build the discrete Green operators associated with a pre-conditioner (reference material), whose choice depends on the loading type and the small or finite transformation frameworks. The newly developed double tetrahedron scheme is employed to investigate non-periodic problems. Outcomes are compared to those of the classical hexahedral scheme. The robustness and computational efficiency of the presented parallel solver is demonstrated through numerical experiments of non-trivial loading scenarios (tension, bending, normal-mixed loading, torsion-bending), complex and densely discretized microstructures and diverse behavior laws (elasticity, isotropic plasticity, crystal plasticity), within small and finite transformation frameworks.
Discrete Trigonometric and Fourier transforms
Morphology-Property Interplay in Chemo-Mechanics of Ion-Intercalation Active Particles
Morphology, material property, and mechanical constraint jointly govern the chemo-mechanical behavior of ion-intercalation particles, yet their coupled effects remain insufficiently understood. Here we establish a thermodynamically consistent single-particle framework and combine analytical solutions with multiphysics simulations to determine how these factors regulate lithiation and stress generation. We study hollow spherical, cylindrical, and ellipsoidal particles with isotropic or transversely isotropic material properties under fully constrained, inner-free, or unconstrained boundary conditions. We show that the transient lithiation pathway and the associated stress and strain fields are governed not by morphology, property, or constraint alone, but by their coupled interaction: isotropic particles are sensitive to the mechanical constraint, whereas transversely isotropic particles exhibit persistent heterogeneous lithiation dominated by anisotropic diffusivity. Flux decomposition analysis reveals that the mechanical contribution to Li flux is negligible in spheres but dominant in ellipsoids. Correlation analysis further shows that Li concentration and volumetric strain exhibit strong anti-correlation in unconstrained particles but weak correlation under full constraints. Bayesian optimization of hollow ellipsoids identifies Pareto-optimal morphologies that balance lithiation capacity against peak tensile stress. These results provide a unified framework for the morphology-property interplay in intercalation particles and offer morphology design principles for chemo-mechanical stability.
Spatial Variation of Stiffness and Edge Beam Participation in RC Box Culverts
Reinforced concrete (RC) box culverts exhibit a non-uniform structural response under two patch localized loading due to plate action and boundary elements at the opening that are not accounted for in conventional 2-D models for design and analysis purposes. This paper addresses the spatial variation in the stiffness of RC box culverts with and without edge beams, using linear-elastic finite-element analysis. Stiffness was derived from the load-deflection responses at various locations along the culvert length. The results show that the stiffness depends on the load location, indicating that the culvert system does not behave as a uniform structural element. The presence of the edge beam leads to local stiffness amplification near the opening, which gradually diminishes towards midspan. The reaction distributions also indicate that the edge beam acts primarily as a boundary stiffener and that the global load-transfer mechanism remains unchanged. The contribution of the edge beam was isolated using a relative stiffness parameter that exhibits a consistent exponential-decay trend across different spans. Based on these observations, a span sensitive formulation was developed to describe this behavior as a function of distance, and it showed good agreement with finite-element results (R2 = 0.979). The proposed framework offers a physically interpretable representation of edge-beam stiffness participation in an indeterminate structure and adds to a better understanding of the load distribution behavior in the culvert with and without edge beams.
Mechanistic understanding of sodium storage from operando stress measurements in hard-carbon thin-films
Hard carbon is a promising anode material for sodium-ion batteries, yet the sodium-storage mechanism in hard carbon remains debated. Here, operando substrate-curvature measurements on hard-carbon thin films were used to probe the volume-expansion-induced stress during sodiation and desodiation. The volume-expansion-induced stress rises steeply in the higher-voltage sloping region during initial sodiation, then it increases at a slower rate in the low-voltage plateau region, followed by a second steep slope below approximately 0.025 V at the end of sodiation. These regimes in stress evolution are consistent with intercalation-dominated storage in the sloping region, pore filling or adsorption in the plateau region, and a plating process at low potentials. The stress relaxation profile evolves asymmetrically during desodiation, indicating that sodium removal from hard carbon is not a simple reversal of sodium insertion into it. The irreversibility in sodiation-desodiation profiles of hard carbon is associated with sodium retention and/or (micro)structural rearrangement.
Finite Element Modeling of the Structural Response of a Reinforced Concrete (RC) Box Culvert with Edge Beam and Skewness
Reinforced concrete (RC) box culverts are buried in structures installed under highways for various purposes, primarily for water flow. Usually, non-skewed culverts are preferred, but in areas with topography that require skewed culverts, cast-in-place RC culverts may be considered. Researchers have extensively investigated the structural performance of the non-skewed culverts. Limited research studies are available to understand the structural behavior of RC-skewed culverts. Therefore, this study examined the impact of a skew angle in the top slab on the structural response of an RC culvert provided with an edge beam. Finite element modeling (FEM) was employed to simulate RC culverts using a shell element model with varying skew angles of 0, 15, 30, 45, and 60 degrees in Abaqus. A solid model was introduced to confirm the shell model’s limitation of capturing localized failure in the edge beam. It is observed that the culvert’s edge beam with adequate shear reinforcement is essential to maintain its ultimate capacity. The study establishes a finite-element-based approach for evaluating load-deflection response in skewed culvert systems, supported by solid-element modeling to examine localized effects. The results provide a consistent basis for comparison across configurations, with emphasis on relative response trends rather than absolute prediction of ultimate capacity.
The discrete origin of configurational forces
We develop a discrete formulation of configurational forces for open subsystems of a finite particle system. Membership in an open subsystem may change by particle admission or deletion. We first use zero-one membership functions to formulate standard balances for mass, standard momentum, angular momentum, and kinetic energy: continuous terms are evaluated on fixed-membership subintervals, but admission and deletion enter through jump-transfer sums. We then introduce a configurational momentum balance for open subsystems and configurational contact-force resultants associated with the ordered separation between a subsystem and its complement. To describe membership changes geometrically, we introduce an auxiliary smooth description based on a scalar membership field on the Euclidean space of particle placements. For each particle, the level set through the current particle position is used as a local membership cut, and the gradient at that position defines a normal to the cut. We assign an observed velocity to these level sets; its tangential component can be changed without altering the smooth membership value or its rate. We require the working associated with membership transfer to be invariant under such tangential changes, and we refer to this invariance as intrinsicity. If this invariance is imposed on a working involving only standard contact-force assignments and standard momentum transfer, then an artificial normality condition is imposed on the standard contact-force assignment. We therefore add configurational contact-force assignments. For a particle with assigned mass, standard momentum, standard velocity, and specific configurational momentum, we impose the intrinsicity requirement and obtain that the specific configurational momentum is the negative of the standard velocity. For nondissipative membership transfer, we use a mechanical energy imbalance to identify the particlewise membership tension: the combined standard-plus-configurational cut-force assignment equals the difference between the membership interaction-energy increment and the kinetic energy, multiplied by the cut normal. After imposing localization hypotheses for contact-force assignments, current representative volumes, and energy increments, we obtain the continuum relation $\bu=-\bv$ for the specific configurational momentum and the spatial inertial Eshelby relation $\C=\rho(\psi-\tfrac12|\bv|^2)\sidem-\T$, where $\C$ is the spatial configurational stress, $\T$ is the Cauchy stress, $\rho$ is the mass density, $\psi$ is the specific free energy, $\bv$ is the standard velocity, and $\sidem$ is the identity tensor.
A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials
A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.
Driven Odd Elasticity in Passive Mechanical Metamaterials
We present a mechanical mechanism leveraging passive mechanical components, i.e. chiral gears and a square lattice metamaterial, to demonstrate driven odd elasticity in a mechanical metamaterial. The mechanism couples tension and shear in a non-reciprocal way, resulting in an odd shear modulus. The emergence of this odd shear modulus enables non-conservative work in a standard quasistatic strain cycle, and further enables the non-Hermitian skin effect in dynamics. Our results demonstrate that odd elasticity can be achieved in mechanical structures using passive elements without electronic components coupled with feedback or robotic control systems.
Odd Elasticity Metamaterial non-Hermitian
Conformal Mechanics of Serpentine Meshes for Millimeter-Scale Neural Probes
The mechanical reliability of implantable neural probes depends on their ability to accommodate large deformations during implantation and chronic operation while limiting stress concentrations within conductive interconnects. Despite extensive studies of serpentine interconnects in stretchable electronics, their mechanics under loading conditions relevant to cylindrical neural probes remain poorly understood. This work investigates the mechanics of two stretchable neural interface architectures, Single Serpentine Traces and Interconnected Mesh networks, designed with gold (Au) interconnects encapsulated in polyimide (PI) and embedded within a soft elastomeric substrate. Finite element analysis and experiments are used to characterize their response under stretching, conformal wrapping onto cylindrical neural probes, and bending of the wrapped structure. Deformation in both architectures is accommodated primarily through bending and rotation of the serpentine segments, with localized metal yielding initiating at strains of approximately 5.5–8.25% depending on loading direction and topology. During conformal wrapping onto probes with radii as small as 0.4 mm, the Single Serpentine Traces architecture remains below the Au yield stress, reaching a maximum stress of 145 MPa, whereas the Interconnected Mesh develops localized yielding at interconnection junctions with peak stresses exceeding 215 MPa. Subsequent bending produces only modest stress amplification, although the Interconnected Mesh exhibits approximately twofold greater stress sensitivity than the Single Serpentine Traces. The results demonstrate that rotational compliance governs stress redistribution, while geometric constraints at interconnection junctions control failure initiation. These findings reveal a fundamental tradeoff between electrical connectivity and stress concentrations and provide mechanics guidelines for conformal neural probes and related stretchable bioelectronic systems.
Thermo-elastic properties of hydrated epoxy-graphene nanocomposites from ensemble-based molecular dynamics simulations
Epoxy-based materials are inherently hygroscopic, absorbing moisture from the environment, which can significantly alter their short and long-term performance. The presence of graphene is often considered as a potential candidate to act as a microscopic barrier, mitigating the adverse effects of hydration on the matrix. This study investigates the impact of hydration on the glass transition and elastic mechanical properties of epoxy resins and their graphene nanocomposites, focusing on water content up to 5 wt%. Using large-ensemble molecular dynamics simulations, we analyze the temperature-driven glass transition and mechanical response of both neat epoxy and epoxy-graphene systems under varying hydration levels. Our results reveal a distinct threshold at 3 wt% water content: below this, hydration primarily reduces the glass transition temperature, while mechanical properties remain unaffected. Beyond 3 wt%, however, the mechanical properties deteriorate, highlighting a non-linear sensitivity to water uptake. Furthermore, we emphasize the critical role of ensemble size in ensuring the reliability of molecular dynamics predictions for such heterogeneous systems. Our simulations demonstrate that ensembles substantially larger than current state-of-the-art standards are necessary to achieve converged distributions of the predicted mechanical properties, particularly in highly heterogeneous hydrated epoxy-graphene nanocomposites. These findings provide novel insights into the hydration behavior of epoxy-based materials and underscore the potential of graphene to enhance their environmental resistance. This work also advances the understanding of structure-property relationships in polymer nanocomposites, offering guidance for the design of more robust materials in humid environments.
First-Order Compatible-Strain Mixed Quadrilateral Finite Elements for $2$D Nonlinear Elasticity
Compatible-strain mixed finite elements (CSMFEs) use the differential complex of nonlinear elasticity to construct discretizations that preserve the underlying topological structure. Existing developments of CSMFEs have focused on simplicial meshes, for which efficient formulations have been developed for first- and second-order elements and successfully applied to compressible and incompressible nonlinear elasticity problems. In this paper, we develop two compatible-strain mixed formulations for quadrilateral elements applicable to compressible and incompressible nonlinear elasticity. For quadrilateral elements, the Piola transformation preserves vector fields tangent and normal to element edges only for special classes of elements, such as rectangles, parallelograms, and trapezoids. Consequently, it cannot be used to construct compatible shape functions for general quadrilateral elements. To overcome this limitation, the shape functions are computed directly in the physical space using numerical integration. N\'ed\'elec shape functions of the first kind are used to construct the interpolation of the displacement gradient. We also introduce a new class of shape functions for the stress tensor that is compatible with the displacement and displacement-gradient discretizations. The formulation for compressible elasticity follows the framework previously developed for first- and second-order simplicial CSMFEs, whereas a new formulation is proposed for incompressible elasticity. The incompressible formulation employs element-level condensation of the pressure field and therefore does not increase the number of global degrees of freedom relative to the corresponding compressible formulation. These developments extend the compatible-strain mixed finite element framework from simplicial to general quadrilateral meshes for both compressible and incompressible nonlinear elasticity. Numerical examples demonstrate that the proposed quadrilateral elements can successfully solve problems that require second-order simplicial CSMFEs while using fewer degrees of freedom.
Interpenetrating Gyroid Lattice - Foam Composites with Synergistically Enhanced Stiffness and Energy Absorption for Impact Mitigation
Advanced lightweight structural materials require both high stiffness and energy-absorption capacity for demanding protective applications. Low-density polymer foams offer excellent specific energy absorption but have inadequate stiffness and structural stability for load-bearing applications. Stiff structural materials, on the other hand, provide load-bearing capacity at the expense of deformability and energy absorption capacity. Here, we overcome this trade-off by creating lattice–foam interpenetrating phase composites (IPCs) via in-situ foaming that integrate stochastic polymeric foam with elastomeric gyroid lattices featuring robust interfacial integration and precisely controlled architecture and density profile. This hybrid design couples the high specific energy absorption of foam with the tunable stiffness and structural integrity of architected lattices, leading to synergistically improved mechanical performance that neither standalone constituent achieves. Introducing a density gradient to IPC enables spatially programmed deformation and gradient-governed load transfer. Under impact loading, the IPCs exhibit dynamic synergy beyond the response of each individual component, markedly reducing transmitted peak stress and acceleration while simultaneously increasing energy absorption at low strain levels. The gyroid lattice–foam IPCs offer a versatile strategy for designing lightweight structural materials that integrate load-bearing capacity with impact-mitigation capability.
Why is the strength of an elastomeric polymer network so low?
Experiments have long shown that a polymer network of covalent bonds commonly ruptures at a stress that is orders of magnitude lower than the strength of the covalent bonds. Here we investigate this large reduction in strength by coarse-grained molecular dynamics simulations. We show that the network ruptures by sequentially breaking only a small fraction of bonds, and that each broken bond lies on a path belonging to the left-tail of the “shortest paths” distribution. A shortest path is the path of the fewest bonds that connect two monomers at the opposite ends of the network. As the network is stretched, the strands along these left-tail shortest paths straighten and bear high tension set by covalent bonds, while most strands off these paths deform via entropic elasticity. After a bond on one of the left-tail shortest paths breaks, the load shifts to other left-tail shortest paths and the process repeats. As the network is stretched and bonds are broken, the scatter in lengths of the shortest paths first narrows, causing stress to rise, and then broadens, causing stress to decline. This sequential breaking of a small fraction of bonds causes the network to rupture at a stress that is orders of magnitude below the strength of the covalent bonds.
Inward buckling of spiral layered structures subject to volumetric expansion and external constraint
Spiral layered structures subjected to thermal or diffusion-induced expansion often develop inward collapse, yet predictive models that connect geometry, confinement, and contact remain limited. Here we formulate a planar beam-based theory for an Archimedean spiral confined by a rigid circular ring, in which eigenstrain is converted into compressive circumferential resultants through kinematic constraint and unilateral contact. Using a variational framework, we derive spiral-path Föppl–von Kármán–type governing equations including a one-sided Winkler penalty representation of wall contact. A Rayleigh–Ritz energy estimate is then used to obtain closed-form scaling relations for the onset of instability. As an analytical benchmark, we reduce the spiral to the zero-pitch limit and recover a circular ring model, yielding mode-dependent critical compressive resultants for detached and fully contacting pre-buckling states. Complementary Dynamic/Explicit finite-element simulations under prescribed thermal expansion validate the theory and provide robust onset identification via internal-energy release, kinetic-energy bursts, and Fourier-mode growth. Finally, we study physically realistic multi-turn spirals, where turn-to-turn self-contact produces intrinsic kinematic locking without artificial end constraints, and we nondimensionalize the parameter space using the inner radius as the reference length to characterize the response in terms of thickness and turn number. The results establish a unified eigenstrain-to-compression mechanism for inward buckling, quantify the roles of confinement and contact state, and provide dimensionless design trends for layered spiral structures.
Crack-Parallel Tension Effects on Fracture of Soft Knitted Polymer Composites deduced from Gap Tests via Microplane Triads
Soft composites are increasingly used in wearable and soft robotic systems as advances in material architecture enable greater damage tolerance under large deformation. In these mesoscale architectures, the crack-parallel stresses bias geometric rearrangements of reinforcement fibers, modifying the crack initiation and growth beyond the opening-mode fracture. Here, we introduce a tensile gap test to quantify how the crack-parallel stress affects the onset and trajectory of damage localization, as well as the load- and energy-based fracture responses. We also develop and experimentally validate a continuum model that captures nonlinear behavior and progressive damage of knitted composites, using an ensemble of oriented microplane triads aligned with the yarn direction, capturing the axial load-transfer mechanisms while incorporating the transverse and shear effects. Together, the experiments and the computational model provide a tool to predict fracture under realistic stress states and to guide the rational design of soft composites in engineering applications.
A closed-form correction for three-point bend testing of functionally graded beams, with application to endovascular devices
Three-point bend testing offers simple, non-destructive quantification of the flexural rigidity of a slender structure, but the single apparent stiffness that it returns misrepresents the true local properties if flexural rigidity varies along the span. The error can be severe in structures with deliberately engineered stiffness gradients, such as endovascular catheters and guidewires whose graded transition zones govern clinical performance, and which are thus the regions most in need of accurate characterization. We solve the Euler-Bernoulli bending of a linearly graded beam in closed form and show that the true midspan rigidity exceeds the apparent value by a correction factor with the compact expansion W = 1 + m2/10 + O(m4), where m is the dimensionless change in stiffness across the support span. The leading measurement error term therefore grows quadratically with the local gradient. To recover m from discrete, noisy data we estimate the local gradient by windowed linear regression with optional Gaussian pre-smoothing, and identify the sampling and smoothing needed for stable inversion. On synthetic profiles spanning the gradient range of real devices, the correction reduces transition-zone error from as much as 10% to a fraction of a percent; applied to a commercial graded long sheath it removes a systematic transition-zone bias of order 1%. We further distinguish where the correction helps and where standard three-point testing already suffices, yielding a simple decision rule for the recovery of local properties from bending of any functionally graded beam.
Nonlinear Anisotropic Visco-Anelasticity
We formulate a nonlinear geometric theory of visco-anelasticity that unifies viscoelastic and anelastic responses within a single thermodynamic framework. At each material point, the total deformation gradient is multiplicatively decomposed into elastic, viscous, and anelastic distortions, thereby generalizing the Bilby-Kr\"oner-Lee decomposition to visco-anelasticity. The theory explicitly incorporates the material metric, which encodes the evolving natural configuration of the solid, the transformed structural tensors, and provides a consistent formulation of the constitutive equations, the balance laws, the thermodynamic potentials, and the kinetic equations. The first and second laws of thermodynamics are systematically applied to derive the constitutive and evolution equations without invoking observer invariance. Anisotropy is treated in full generality through structural tensors. As illustrative examples, we specialize the general framework to isotropic and transversely isotropic visco-anelastic solids. Two examples within the class of universal deformations, which admit closed or partially closed form solutions, show how the proposed framework can be used to model the coupled viscous and anelastic response of incompressible anisotropic solids with distributed eigenstrains and the associated residual stresses. This geometric framework unifies nonlinear viscoelasticity and anelasticity by coupling time-dependent and eigenstrain-driven effects within a single, fully consistent geometric formulation. In particular, the proposed framework clarifies the geometric structure of the elastic, viscous, and anelastic distortions and resolves ambiguities associated with intermediate configurations in existing formulations of nonlinear viscoelasticity and viscoplasticity.
Harnessing Functional Gradients for Enhanced Shock Absorption in Foam Materials
Shock generating high-velocity impacts produce intense, stress waves and rapid accelerations—unlike low-velocity impacts that deform materials under dynamic equilibrium—posing severe risks to human organs, structures, and sensitive equipment. Functionally graded protective foams are promising candidates for shock mitigation due to their spatially tunable density and constitutive profile. However, limited mechanistic understanding of energy absorption and stress attenuation during compaction shock formation in graded foams may hinder their application-specific design. Here, in an integrated experimental and theoretical study, we investigate the compaction shock characteristics of graded foams using intrinsically graded vertically aligned carbon nanotube (VACNT) foams as a model system. Our analysis shows that while energy absorption is governed by compaction shock evolution from impact to the protected boundary, transmitted dynamic stress is primarily dictated by local material impedance. Using our generalizable shock modeling framework applicable to diverse functionally graded foam types, we demonstrate how density and density-dependent constitutive gradation dictate compaction shock characteristics. By selecting appropriate foam types and tailoring functional gradients, simultaneous optimization of energy absorption and transmitted stress attenuation can be achieved, facilitating designs for application-specific shock-mitigation.
Analysis of Stress Wave Interaction with a 180° Bend Junction Between Two Square Bars
An analytical model for wave propagation through an unrestrained 180° bend junction connecting two long bars of rectangular cross-section is developed and the results are validated using experimental and numerical analyses. Upon arrival of a longitudinal stress wave, the bend junction is assumed to undergo rigid translation followed by rotation. By analyzing the normal and shear forces as well as the bending moments acting at the intersection of the bend junction, a set of 15 equations consisting of fifteen variables has been derived. Solving the system of equations in Laplace domain leads to transfer functions that relate the incident pulse to reflected and transmitted wave characteristics, as well as to the translation and rotation of the bend junction. These results in Laplace domain are converted back to time domain using the convolution integral. Concurrently, finite element analysis and experimental validation of the bend junction behavior were carried out to verify the results obtained from the analytical model. In addition to revealing the influence of individual parameters explicitly, the model revealed that the efficiency of the unrestrained bend junction for transmission of the longitudinal waves is at most ∼70% for a long duration stress pulse. This limitation is a result of the rotation of the bend junction which emanates flexural waves into both the bars. Thus, further increase in transmission efficiency of longitudinal wave is possible if the bend junction is restrained to move only in the axial direction with no rotation.
Universal deformations and universal residual stresses in incompressible isotropic Cauchy elasticity
We study universal deformations in incompressible isotropic Cauchy elastic solids with residual stress, without assuming any specific origin for the residual stress. Starting from the constitutive representation of the Cauchy stress as an isotropic tensor-valued function of strain and residual stress, we derive the universality constraints for residually-stressed incompressible isotropic Cauchy elastic solids. We show that for the six known families of universal deformations the set of universal deformations is identical to that of incompressible isotropic elasticity in the absence of residual stress. We also show that residual stress does not enlarge the space of universal deformations. We then determine the universal residual stress fields corresponding to the six known families of universal deformations. Assuming that the residual stress field has the same symmetry as the corresponding universal deformation, the universality constraints reduce to systems of ordinary differential equations that can be solved explicitly. The resulting universal residual stress fields are characterized and discussed for each family.
On the stability of Euler’s elastica with natural curvature: Out-of-plane bifurcation with twisting
Elastic rods can exhibit distinct buckling behavior in the presence of natural curvature due to the induced prestress. Recent work has shown that prestressed, clamped rods can undergo a secondary bifurcation from in-plane Euler buckling and subsequently exhibit twisting or snapping under axial compression. In this work, a bifurcation analysis for the secondary out-of-plane bifurcation of Euler’s elastica is performed based on Kirchhoff’s three-dimensional theory of inextensional rods. The critical end-shortening, critical load, and associated eigenmode at the onset of bifurcation are determined, and the role of natural curvature in the out-of-plane bifurcation from the Euler solution is systematically examined. It is found that the effect of natural curvature depends on the bending direction of Euler buckling. When the Euler buckling direction is consistent with the rod’s naturally curved direction, the critical end-shortening decreases as the natural curvature increases, and vice versa. The imperfection sensitivity of the out-of-plane bifurcation is further investigated. The results reveal that the primary role of in-plane imperfections is to select the in-plane Euler buckling direction, which in turn has a major effect in the presence of substantial natural curvature. By contrast, the primary role of out-of-plane imperfections is to trigger the out-of-plane bifurcation and induce three-dimensional twisting or snapping.
The elastica; Euler buckling; Out-of-plane bifurcation; Natural curvature; Imperfection
Sequential prediction of transverse crack paths in CFRP composites via a deep learning approach
Transverse cracking is one of the earliest damage modes in carbon fiber-reinforced polymer (CFRP) composites under transverse or complex loading, leading to stiffness degradation and reduced fatigue life. Its initiation and early propagation occur at the microscale and are strongly influenced by random fiber distributions and local streconcentrations. However, transverse crack propagation cannot be fully characterized within a single microstructural window, owing to the combined effects of the local fiber arrangement and crack state inheritance from the preceding region. To address this challenge, a physics guided deep learning framework is developed for sequential prediction of transverse crack paths in CFRP composites. Specifically, the framework directly predicts crack paths from microstructural images and incorporates the predicted crack segment as the initial crack information for the subsequent prediction window, thereby enabling sequential prediction across neighboring regions. An attention enhanced encoder decoder network is employed to capture multiscale features of crack evolution, while physical guidance derived from phase-field fracture analysis is incorporated to improve the consistency of the predicted paths. Compared with phase-field model results, the proposed framework accurately reconstructs transverse crack paths in extended microstructural regions with a prediction accuracy of 93.8%. This study provides an efficient surrogate model for sequential transverse crack path prediction and multiscale damage analysis of CFRP composites.
deeplearning, composites, crack propogation
In-Plane Wave Homogenization and the Emergent Electromomentum Tensor
The electromomentum coupling is a macroscopic interaction between momentum density and electric field in piezoelectric composites, absent from the response of their constituents. Existing works have focused mainly on its analysis scalar mechanical settings. Here, we develop and apply homogenization scheme for the vectorial settings of in-plane motions of periodic composites, where two wave polarizations coexist. The method defines macroscopic fields by ensemble averaging and uses driving sources to obtain a unique effective model for arbitrary frequency and wavevector excitations. Numerical examples for composites with circular and circular-sector fibers show that the homogenized model recovers the Bloch dispersion of the underlying microstructure while satisfying physical restrictions, whereas equivalent models that suppress electromomentum coupling may violate these restrictions. The structure of the effective properties distinguishes mesoscale effects, present even for axisymmetric cells at finite wavelengths, from symmetry-breaking contributions that persist in the local response of asymmetric cells. Time-domain scattering simulations further demonstrate that the local effective medium reproduces the macroscopic reflected and transmitted response of the underlying composite for the excitations considered. These results advance the modeling and analysis of electromomentum metamaterials, towards their integration in future wave-control applications.
Nonlinear dynamics of miniaturized dielectric elastomer actuators with surface effects
Dielectric elastomer actuators (DEAs) have attracted considerable attention for applications requiring lightweight, compliant, and large-strain electromechanical transduction. However, the reduction of operating voltage through miniaturization introduces pronounced surface and interfacial effects that can significantly alter the dynamic response and stability characteristics of these systems. In this work, a dynamic electromechanical framework is developed to investigate the nonlinear dynamics of miniaturized dielectric elastomer actuators while explicitly incorporating surface elasticity, intrinsic surface energy, and surface tension. The dielectric elastomer is modeled as an incompressible neo-Hookean ideal dielectric, and the governing nonlinear equation of motion is derived using an Euler-Lagrange formulation under finite deformation. An energy-based approach is further employed to predict the onset of dynamic pull-in instability and the associated critical conditions. The dynamic response under both DC and AC voltage excitations is examined through transient time-history analysis, phase portraits, Poincaré maps, and frequency-response characteristics. Particular attention is devoted to dynamic pull-in instability and its dependence on surface parameters. The predictions of critical instability parameters are verified through direct numerical integration of the nonlinear governing equation, showing close agreement. A comprehensive parametric study reveals how surface elasticity, intrinsic surface energy, and surface tension modify the effective stiffness, resonance behavior, and critical instability thresholds of miniaturized DEAs. The results demonstrate that surface effects substantially shift dynamic pull-in voltages and alter nonlinear oscillatory characteristics, highlighting their critical role in the design and development of miniaturized dielectric elastomer actuators operating under transient electromechanical loading.
A Unified Stiffness Evolution Model and Its Application to 3D-Printed Regular and Re-Entrant Honeycombs
The evolution of the elastic modulus in cellular materials involves both post-yield stiffness degradation and densification-induced recovery, yet a unified theoretical framework to describe this non-monotonic behavior remains lacking. This study investigates the stiffness evolution and deformation mechanisms of regular hexagonal (HC) and re-entrant (NHC) honeycombs under quasi-static uniaxial compression. Specimens with varied wall thicknesses were fabricated using fused deposition modeling, and incremental loading–unloading tests were performed along two orthogonal in-plane directions. A stiffness evolution model was developed to describe the complete non-monotonic variation of the global modulus, incorporating a linear elastic pre-yield response within a modified rigid–plastic hardening framework. The model captures both stiffness degradation induced by localized collapse and subsequent recovery driven by structural compaction, outperforming conventional approaches that neglect modulus rebound. Pronounced anisotropy in modulus evolution is observed, governed by direction-dependent collapse mechanisms. Bending-dominated deformation in the 1-direction leads to progressive compaction and earlier stiffness recovery as wall thickness increases. In contrast, fracture-dominated crushing in the 2-direction delays the modulus rebound in thicker specimens due to enhanced structural strength and toughness. These results reveal that wall thickness not only scales the stiffness magnitude but also modulates its evolution path: thicker walls accelerate compaction in bending-dominated modes while delaying it in fracture-dominated modes. The proposed framework provides a robust theoretical foundation for the optimized design of honeycombs and offers predictive insights into the interplay between geometry, thickness, and performance evolution in architected materials.