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 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.
Universal Displacements in Linear Strain-Gradient Elasticity
We study universal displacement fields in three-dimensional linear strain-gradient elasticity within the Toupin-Mindlin first strain-gradient theory. Building on the approach of Yavari (2020), we derive, for each material symmetry class, the universality PDEs obtained by requiring the equilibrium equations (in the absence of body forces) to hold for any material in that class, and we determine the complete set of universal displacements. Using the full symmetry classification together with compact matrix representations of the elasticity tensors, we provide explicit characterizations for all 48 strain-gradient symmetry classes, including centrosymmetric and chiral classes. For several high-symmetry classes, the strain-gradient universality PDEs impose no additional restrictions beyond the classical ones, so the universal displacement families coincide with those of classical linear elasticity (for example, the isotropic classes SO(3) and O(3)). For lower symmetry classes, the strain-gradient universality PDEs can be stricter than their classical counterparts, so the universal displacements form proper subsets of the classical universal displacement families due to additional higher-order differential conditions.
Finite Element Investigation of Optimal Reinforced Concrete Shear Wall Placement for Vibration Mitigation in Adjacent Buildings with Open-Trench Isolation
Vibration transmission in coupled soil--structure systems remains a fundamental challenge in the serviceability and resilience assessment of reinforced concrete (RC) buildings subjected to external dynamic excitations. Among the various sources of ground-borne vibration, railway-induced excitation constitutes a particularly significant engineering concern due to the continuing expansion of urban rail transportation networks and the increasing proximity of buildings to railway infrastructure. Motivated by this practical problem, the present study investigates the combined effectiveness of open-trench wave barriers and optimized shear wall placement for vibration mitigation in RC buildings subjected to railway-generated ground motion. A two-dimensional plane-strain finite element framework was developed in ABAQUS to simulate the fully coupled soil--track--structure interaction problem. The computational model consists of a six-story RC frame structure founded on layered soil, a railway embankment subjected to dynamic excitation, and a 3~m-deep open trench positioned between the vibration source and the structure. To examine the influence of stiffness redistribution on structural vibration characteristics, four structural configurations were considered, including a reference model without a shear wall and three additional cases incorporating a 0.30~m-thick RC shear wall located in the first, second, and third structural spans, respectively. The numerical framework was verified against established benchmark studies for ground-borne wave propagation and dynamic soil--structure interaction. Structural vibration response was evaluated at multiple roof-level monitoring locations using peak particle velocity (PPV), root mean square velocity (RMS), and vibration decibel level (VdB). The results demonstrate that the open trench effectively attenuates incident wave energy before interaction with the structure, while the incorporation of strategically positioned shear walls further suppresses vibration transmission through enhanced global stiffness and altered dynamic load-transfer mechanisms. Among the investigated configurations, the shear wall located in the third span, corresponding to the span farthest from the excitation source, exhibited the highest mitigation efficiency, yielding reductions of up to 30.7\% in PPV, 13.8\% in RMS response, and 2.05\% in VdB. The observed reductions indicate a substantial decrease in structural vibration demand and highlight the importance of stiffness distribution in controlling dynamic response characteristics. The findings reveal a pronounced synergistic interaction between path-based isolation and receiver-based structural stiffening mechanisms and provide a mechanics-based framework for the vibration-resilient design and optimization of RC buildings subjected to externally induced ground vibrations.
Inverse Design of Metamaterials with Adaptable Force-Displacement Characteristics
Metamaterials with tailored force-displacement characteristics hold significant promise for applications ranging from soft robotics and energy dissipation to biomedical devices such as prosthetic sockets, where distinct regions of a structure must simultaneously satisfy fundamentally different mechanical requirements. Existing inverse design frameworks, however, are restricted to single loading conditions and homogeneous desired behaviors, limiting their utility in real-world scenarios where complex, spatially varying mechanical demands must be met within a single continuous material. We present an inverse design method that closes this gap by combining finite element simulation, surrogate optimization, and machine learning within a unified framework. Starting from a fixed unit cell topology governed by eleven geometric shape parameters, we first construct a surrogate model that replaces each unit cell with a polynomial energy density, reducing the metamaterial-scale inverse problem to a tractable optimization over polynomial coefficients. A multi-output multilayer perceptron trained on finite element simulations then maps any required unit cell force-displacement response back to the corresponding shape parameters. We extend the formulation to multi-surface loading, enabling two qualitatively distinct force-displacement targets to be achieved simultaneously in different regions of the same structure. Fabricated prototypes tested under prescribed displacements confirm that the predicted responses, spanning superelastic, bistable, and constant-force behaviors, are reproduced with high fidelity. These results demonstrate a flexible and computationally efficient route to multifunctional metamaterial design under realistic, multi-condition loading environments.
Phase-field model for mesoscale simulation of crystallization morphology evolution in 3D printing of thermoplastic composite
3D printing has enabled the production of continuous fiber-reinforced thermoplastic composites (CFRTPCs) with exceptional mechanical properties and design flexibility. The crystalline morphological evolution during 3D printing of CFRTPCs, particularly the transcrystalline layer (TCL) that is critical for the mechanical performance, remains poorly modeled and understood. Herein, we develop a non-isothermal phase-field model (PFM) for mesoscale simulating the crystallization process and morphology evolution during the 3D printing of thermoplastic composites.The PFM is derived by constructing a free energy density functional incorporating order parameters to characterize the crystallization process, with the phase-field evolution equations being intrinsically coupled to heat transfer. In particular, the fiber-crystalline melt contact angle-dependent sporadic nucleation processes are integrated into the PFM using an explicit nucleation algorithm. Phase-field simulations of crystallization behavior in isotactic polypropylene (iPP) under conditions emulating 3D printing are demonstrated to verify the PFM capability. The influence of contact angle (θ), convective coefficient (h), and fiber spacing (D) on non-isothermal crystallization is comprehensively examined. It is found that TCL thickness increases with decreasing θ, smaller h, and larger D, until it reaches saturation. Slower cooling during 3D printing could significantly amplify the effects of both contact angle and fiber spacing on the TCL evolution. The proposed PFM could enable mesoscale simulation of 3D-printed thermoplastics and help optimization of crystallization and printing parameters.
Compatibility Conditions for Singular Strain Fields on Linear Shells
Strain compatibility conditions are derived for orientable linear shells with strain fields which are piecewise smooth and develop concentrations along curves and junctions on the shell surface. The concentrations in strain fields appear due to folds, fold dipoles, and tears in the shell. The compatibility equations include local conditions in the bulk of the shell surface, local equations at the singular curves in terms of jump in strain fields (and their gradients) and strain concentrations, local equations at the junction of singular curves, and global conditions for every family of irreducible curves on the shell surface. These equations couple shell kinematics with the geometry and topology of the shell surface. The applicability of the framework is illustrated assuming the bulk strains to be elastic and the strain concentrations to be plastic. The compatibility equations then lead to a boundary value problem for the determination of stresses and moments in an elastic surface in response to the incompatibility induced by the plastic strains.
Competitive Hardening Dynamics in Viscoplastic Materials with Evolving Threshold Stress
Conventional viscoplasticity frameworks treat the threshold stress as either a material constant or a quantity evolving solely with accumulated plastic strain. Since microstructural evolution — whether precipitation, phase transformation, or solute redistribution — may proceed concurrently with deformation, such a treatment is often inadequate. The present work formulates a constitutive framework, derived from the Clausius–Duhem inequality and Perzyna-type overstress viscoplasticity, in which the threshold stress evolves autonomously with physical time through microstructural kinetics, independently of accumulated strain. Modified Armstrong–Frederick kinematic hardening with static recovery is incorporated, so that back stress develops only during active inelastic flow. The interaction between time-driven threshold evolution and strain-driven back-stress development gives rise to three behavioural regimes: (I) a purely elastic response, (II) flow arrest, in which inelastic flow initiates but subsequently ceases as the threshold overtakes the effective stress, and (III) continuous flow. A constructive Lyapunov function is employed to prove that flow arrest is asymptotically stable, a result not previously established at the material-point level in the viscoplastic creep literature. It is further shown that back-stress development reduces the time to arrest through a kinematic hardening acceleration effect. A physics-informed neural network employing smooth Macaulay bracket approximation with curriculum learning reproduces all three regimes within a single trained surrogate. The framework is validated against experimental data using the creep-ageing and back-stress test (CABT), which provides independent measurements of inelastic strain and back-stress evolution.
Thermoviscoelasticity of polydomain liquid crystal elastomers regulated by soft elasticity
Liquid crystal elastomers (LCEs) are elastomeric networks with rod-like mesogens that reorient under load. In polydomain LCEs, this reorientation drives a polydomain-to-monodomain transition that produces a soft-elastic plateau. The intricate coupling between this soft elasticity and the polymer-network viscoelasticity gives rise to a path-dependent thermoviscoelastic response, central to applications of polydomain LCEs in damping, impact protection, and tough adhesives. However, the physics governing this response under complex thermomechanical histories remains insufficiently studied. In this work, we present a combined experimental and theoretical study of polydomain LCEs under three uniaxial loading protocols: single-cycle loading-unloading, stress-free recovery from various pre-stretches, and multi-cycle loading with progressively increasing amplitude. We develop a finite-deformation constitutive model that combines two parallel mechanisms: rate-independent, temperature-dependent soft elasticity from mesogen reorientation, and time- and temperature-dependent viscoelasticity from various sources. Calibrated with a single parameter set, the model quantitatively reproduces all three protocols and resolves the individual contribution of each mechanism. Across the three protocols, a temperature-dependent soft-elastic limit governs the low-rate response and the long-time recovered stretch, while polymer-network viscoelasticity controls the rate-dependent deviation and the cycle-wise accumulation of residual stretch away from this low-rate limit. A thermal recovery test above the nematic-isotropic transition temperature confirms that all hysteresis and residual deformation are reversible, ruling out irreversible internal damage. The combined experimental-theoretical framework provides mechanistic understanding and a predictive basis for the design of polydomain LCE components under complex thermomechanical histories.
Fractional Calculus based Elasticity obtained from Homogenization
Anomalous phenomena, such as diffusion in biological systems, scale-dependent plasticity in thin films, and electromagnetic wave propagation in complex media, often defy explanation by conventional theories rooted in integer-order calculus. Models based on fractional calculus have proven effective in capturing such behaviors, yet the fractional exponents they employ are typically introduced as empirical fitting parameters without grounding in the underlying physics. In this work, we propose that fractional differential equations can emerge naturally through homogenization of materials with complex microstructures, which are themselves the source of the anomalous behavior that necessitates a fractional description. Focusing on linear elasticity, we identify precise microstructural conditions that give rise to emergent fractional behavior. In the static regime, homogenization reveals that the order of the fractional derivative is directly linked to the power-law exponent of the microstructure’s autocovariance function. By connecting microscale structural variation to macroscale material response, our study opens new avenues for designing architectured materials with tailored anomalous properties. The implications of thiswork extend broadly across physics, biology, materials science, and beyond.
Contact loss in all solid-state Li-ion batteries via deposition of impurities
Solid-state batteries promise high energy storage with enhanced safety but suffer from contact loss at the lithium (Li) metal anode-solid electrolyte interface as Li is stripped into the ionically conducting solid electrolyte. Our measurements demonstrate that, in cells with garnet electrolytes, an important but overlooked mechanism for contact loss arises from the deposition of insulating impurities from within the Li electrode onto the interface. These impurities form a porous layer, and an imposed stack pressure is required for Li to creep through this layer. Insufficient stack pressure results in empty pores between the impurity particles and these pores resemble inter-connected nano to micro-scale voids. This proposed mechanism is supported by our direct observations of the interface and by our finding that contact loss persists at stack pressures which are sufficiently high to collapse any voids in the Li that are not mechanically supported by the skeleton of impurity particles. Theoretical models developed using the impurity deposition mechanism are in excellent agreement with measurements. This finding has significant implications for improving the design of all solid-state batteries including the development of anode-free cells for which impurities within the electrode are expected to be substantially reduced.
Finite-width adiabatic shear banding and dislocation patterning in mesoscale polycrystalline aggregates
Dynamic shear banding under adiabatic conditions in a mesoscale polycrystalline aggregate is studied using a model of mesoscale dislocation mechanics and experiments. The model involves a length scale related to hardening induced by excess/polar/geometrically necessary dislocation (GND) density, and utilizes a simple classical crystal plasticity model with isotropic Voce law hardening. Simulations of statistically representative volume elements of a polycrystal determined from experimental samples are conducted. Studies in 2-d (section) and 3-d capture the experimentally observed finite-width shear bands and the formation of low-angle subgrain boundaries even in the absence of heat conduction in the model, as well as size-dependent strengthening for grain sizes from 1 to 20μm. The 2-d and large-scale 3-d simulations, the latter involving 1 million finite elements, provide access to the progressive evolution of material strength, stress state, and temperature in the course of large deformations. GND distributions accumulate at grain boundaries and form patterned structures within grain interiors, offering insight into the microstructural changes that precede failure in adiabatic shear bands. Mesh-converged, delocalized and localized plastic flow to very large deformations without softening is observed for a significant range of parameters, reflecting a competition between GND hardening and thermal softening in setting the non-softening steady state in the absence of other ductile damage mechanisms in the model.
Dynamic micromagnetism a la Ericksen-Leslie, and the constrained polar continuum mechanics of hard magnetic soft materials
A model of dissipative micromagnetics coupled to (visco-)elasticity is explored, following the procedures of the Ericksen-Leslie theory of nematic liquid crystals allowing for angular momentum due to magnetization. An outcome is the Landau-Lifshitz-Gilbert theory coupled to material spin. A further power-less augmentation to the angular momentum of the theory with classical kinetic energy density is also considered, with a preliminary exploration of its potential in representing the Einstein-de Haas and Barnett effects within continuum mechanics. A treatment of the continuum mechanics of hard magnetic soft materials as a constrained polar material is presented. The models of DeSimone and James (2002) and Zhao et al. (2019) are discussed as two different, namely energetically and kinematically, constrained models of magnetoelasticity encompassed within the overall framework.
Dynamic Mechanical Response of Spinodal Architectures Across Length and Time Scales
High-throughput characterization of architected materials across a wide range of length scales enables rapid screening of topologies for engineering applications. Scaled-down specimens manufactured and evaluated in laboratory environments enable this iteration, but application scenarios may involve differing length scales and loading conditions that complicate direct comparisons. Here, we use a spinodal architected morphology to determine the interplay among the constituent material’s strain-rate sensitivity, the topological length scale, and the imposed deformation rates. We report characterization spanning strain rates from $10^{-3}$ s$^{-1}$ to $10^{4}$ s$^{-1}$ on spinodal architected specimens with length scales of 100~\textmu{}m (microscale) and 30~mm (macroscale). The experiments show that while microscale specimens exhibit moderate increase in strength at high strain rates, macroscale specimens exhibit a nearly tenfold increase in strength at equivalent strain rates. Finite element calculations reveal that this increase is linked to a transition from a response governed by constituent material strain-rate sensitivity to inertia-dominated behavior in macroscale specimens---a transition not observed in microscale specimens at the strain rates investigated here. Using extensive finite element calculations, we develop maps to establish the parameters governing the regimes of behavior, illustrating that the transition from behavior governed by constituent material rate sensitivity to inertia-dominated behavior has analogies to fluids in that it depends on a structural length scale. Our findings provide insights into the physical parameters that govern responses across length and time scales, towards the development and design of new laboratory experiments that extract relevant dynamic properties for structural applications.
Rational Mechanics of Material Strength in Brittle Solids
Material strength is a classical concept that has recently found renewed applications in fracture mechanics, especially in models for crack nucleation in brittle solids. In this paper, we formulate material strength in the setting of finite elasticity and examine its geometric, constitutive, and symmetry-theoretic foundations. We show that spatial covariance requires a strength function to depend on both stress and the corresponding strain measure, so that strength is not controlled by stress alone, but by the pair (stress,strain). Only in this case can a strength function written in terms of one stress measure be consistently rewritten in terms of another, while classical stress-based strength criteria are recovered as a special case in which the strain dependence is suppressed. We discuss the covariance of strength functions under arbitrary spatial diffeomorphisms and use this to relate representations in terms of the first Piola-Kirchhoff, second Piola-Kirchhoff, and Cauchy stresses. Restricting attention to the stress-based criteria that appear in the existing literature, we define the associated strength hypersurface as a subset of the constitutively admissible stress manifold, distinguish constitutive admissibility from fracture, and analyze the geometric and topological properties of the corresponding safe domain. We show that, for stress-based strength functions satisfying standard regularity conditions and the requirement that sufficiently large stresses are inadmissible, the strength surface is a smooth compact hypersurface of the constitutively admissible stress manifold. For isotropic solids, we study the symmetry of strength surfaces in principal stress space and show that the safe domain is star-shaped under a natural proportional-reduction hypothesis. We then extend the formulation to anelastic brittle solids and examine the effects of residual stresses and anelastic distortions on material strength. We also discuss the action of material symmetry on strength functions for anisotropic solids. Finally, we discuss material strength in the setting of linear elasticity and show how the general theory reduces to the classical stress-based criteria in this limit.
Deformation-induced domains in silicone rubber
In-situ X-ray computed tomography observations show the development of spatially heterogeneous deformation in cylindrical silicone rubber specimens subjected to a spatially uniform axial strain. Using a doping agent, we demonstrate that this heterogeneity is associated with the motion of a mobile phase within the silicone rubber. The mobile phase is hypothesised to behave like a liquid crystal, with heterogeneity driven by the formation of nematic domains within it. A constitutive model for the deformation of a rubber with such a mobile phase is presented and analysed for axisymmetric uniaxial loading. An important outcome of this analysis is a phase map showing three regimes of behaviour under uniaxial deformation. Spatial heterogeneity develops due to a switch in the orientation of the mobile phase molecules, resulting in the formation of mechanically induced domains within the rubber. Consistent with observations, the model predicts that imposed tensile strains can result in volume loss in the core of the cylindrical specimen and dilation in the outer shell, whereas imposed compressive axial strains reverse this trend.
Cure-induced viscoelastic effects in in-air photopolymerized droplets for microfluidic droplet-based 3D printing
Motivated by droplet-based additive manufacturing processes, this work presents a multiphysics numerical framework for in-air photopolymerization of resin droplets and their subsequent impact, spreading, and recoil on a solid substrate. The model couples two-phase compressible flow with energy and species transport, incorporating radiative transport through the Beer-Lambert law to describe free-radical photopolymerization. This formulation enables prediction of core-shell droplet morphologies, in which a partially or fully cured outer shell encapsulates an uncured liquid core prior to impact. The key novelty of the proposed framework lies in the introduction of a cure-induced viscoelastic shell model, described using an Oldroyd-B-type constitutive formulation. The evolving stress response during photocuring is decomposed into equilibrium (elastic, spring-like) and non-equilibrium (viscous, Maxwell-type) contributions. The viscoelastic properties of the shell – including relaxation time as well as equilibrium and non-equilibrium moduli – are explicitly linked to the local degree of cure, allowing the progressive evolution of material stiffness and elasticity to be captured. Using this approach, we systematically quantify how cure-dependent viscoelasticity governs droplet-substrate interaction for micron-scale droplets across a range of shell thicknesses, degrees of cure, and impact velocities. Particular emphasis is placed on the role of viscoelasticity in post-impact recoil and rebound suppression. The proposed model provides a predictive tool for understanding and controlling droplet dynamics in UV-curable, droplet-based additive manufacturing processes.
Stress-driven sliding of asymmetric grain boundaries
Grain boundary (GB) deformation significantly influences the mechanical response of polycrystalline materials, yet most atomic-scale studies have focused on special coincidence site lattice (CSL) boundaries. In contrast, engineering polycrystals are typically dominated by asymmetric non-CSL GBs. In face-centered cubic (FCC) metals, these boundaries often undergo sliding with minimal migration, a process primarily mediated by step-free GB dislocations. Motivated by recent in situ atomic-resolution experiments, we use atomistic modeling to investigate stress‑driven sliding in asymmetric, non-CSL tilt GBs. Our results reveal that sliding is governed by the glide of extrinsic GB dislocations and their interactions with intrinsic ones. Despite the structural complexity of non-CSL boundaries, we identify the operative slip geometries of these extrinsic dislocations. Furthermore, we uncover a kink-pair mechanism of GB dislocation glide that acts as the primary rate-controlling step for sliding kinetics. These findings provide critical atomic-scale insights into asymmetric tilt GB deformation and establish a mechanistic foundation for understanding GB-mediated plasticity in engineering polycrystals.
Rise and fall of void population governs the porous-to-solid transition in soft granular materials
Soft granular materials are porous packings of highly deformable particles found in systems ranging from blood clots and tissue scaffolds to starchy foods and 3D-printing inks. They start as collections of discrete, loosely packed motifs, but then transition to a coherent solid under load. Understanding when that {\it granular-to-continuum} transition occurs is critical because it controls whether a biomaterial can be injected through a needle, how easily cells and drugs infiltrate a healing wound, and how nutrients are transported through engineered tissue. Classical approaches rely on counting inter-particle contacts, but this becomes rather ambiguous as contact points evolve into contact surfaces when soft grains undergo large, nonlinear changes in size and shape. Here, we present a paradigm shift: instead of tracking the granular material, we track the empty space between them. Through computational simulations, we discover that porosity evolves through a universal sequence: as the material compresses, interstitial voids undergo a stereotyped cascade of fragmentation (proliferation) followed by collapse (elimination). We identify a topological marker that marks the exact onset of solid-like rigidity and stress homogenization. The critical threshold of this topological marker is independent of the particle size distribution or elasticity, offering a robust geometry-based descriptor for the solidification of soft matter.
Deployable 3D architectures from wafer-fabricated precursors
We demonstrate that standard wafer fabrication can produce free-standing, mechanically stable, doubly-curved 3D structures with prescribed Gaussian curvature --- a capability not previously achieved through semiconductor manufacturing. The stability of the deployed structures is realized through the bistable nature of their constituent auxetic unit cells. To impose prescribed Gaussian curvatures through deployment, we conformally flatten the target 3D mesh onto the 2D plane and locally tune the microstructure of each unit cell such that its second stable equilibrium occurs at the required isotropic expansion. The resulting precursor features a spatially heterogeneous tessellation. This generative method is validated on a spherical cap deployed from a flat disk through indentation, with deployment accuracy and structural stability confirmed numerically and experimentally. The method is further applied to a range of complex 3D shapes with both positive and negative curvatures. As a functional demonstration, paraboloidal reflectors with tunable focal lengths are fabricated and deployed, with reflected patterns agreeing with geometric optics predictions. This work paves the way from flexible electronics towards deployable electronics, broadening the spectrum of realizable 3D semiconductor devices.
Entanglement-driven responses through multiscale 3D-printed knits
Filamentous entanglement underlies the resilience and toughness of systems from polymer networks to textiles, yet most architected materials do not capitalize on this principle. While knitting research across mechanics, architecture, and design has demonstrated that stitch structure governs physical behavior, a quantitative framework linking stitch-level geometry to mechanical response has been lacking. Here we show that 3D printing --- as a topology-agnostic fabrication platform --- enables systematic exploration of entangled architectures, revealing a simple scaling law that unifies the mechanics of traditional and printed knits across materials, geometries, and length scales, from centimeters down to the smallest knit ever fabricated. This framework yields programmable stiffness and dissipation tunable by topology and pre-strain, establishing entanglement as a design primitive for next-generation metamaterials.
Vibration-Assisted Fabrication of Thin Shells with Spatially Distributed Imperfections
Thin-shell structures, found in biological systems such as beetle carapaces and widely used in aerospace and civil mechanical engineering, achieve remarkable strength-to-mass ratio given their slenderness and curved geometries. However, their load-bearing capacity is highly sensitive to geometric imperfections, which are often unavoidable during fabrication and can trigger subcritical buckling. Silicone-based hemispherical domes have served as an experimental surrogate to study this phenomenon, yet prior work has largely focused on localized imperfections, failing to capture the spatially distributed nature of real-world imperfection patterns. Here, we introduce a vibration-assisted method for fabricating thin shells with spatially distributed, vibrational mode-shaped imperfections. Silicone is cast onto a thick elastic mold excited by a speaker, and vibration-induced flow during curing creates thickness variations. High-speed imaging and destructive measurements reveal accumulation of material at the antinodes of the mold's vibrational modes. We show that engineered imperfection can be tuned by excitation frequency and the mold’s shape, while their amplitude increases with speaker volume. Buckling experiments demonstrate significant reductions in critical pressure, offering a scalable platform to study and tune imperfection-sensitivity. Beyond shell mechanics, we offer a scalable and tunable fabrication method for patterning soft materials in applications ranging from morphable surfaces to bioinspired design.
Spatial deformation of a ferromagnetic elastic rod
Ferromagnetic elastic slender structures offer the potential for large actuation displacements under modest external magnetic fields, due to the magneto-mechanical coupling. This paper investigates the phase portraits of the Hamiltonian governing the three-dimensional deformation of inextensible ferromagnetic elastic rods subjected to combined terminal tension and twisting moment in the presence of a longitudinal magnetic field. The total energy functional is formulated by combining the Kirchhoff elastic strain energy with micromagnetic energy contributions appropriate to soft and hard ferromagnetic materials: magnetostatic (demagnetization) energy for the former, and exchange and Zeeman energies for the latter. Exploiting the circular cross-sectional symmetry and the integrable structure of the governing equations, conserved Casimir invariants are identified and the Hamiltonian is reduced to a single-degree-of-freedom system in the Euler polar angle. Analysis of the resulting phase portraits reveals that purely elastic and hard ferromagnetic rods undergo a supercritical Hamiltonian Hopf pitchfork bifurcation, whereas soft ferromagnetic rods exhibit this bifurcation only within a restricted range of the magnetoelastic parameter, $0<\tilde{K}_{dM}<1/8$. Both helical and localized post-buckling configurations are analyzed, and the corresponding load-deformation relationships are systematically characterized across a range of loading scenarios. Localized buckling modes, corresponding to homoclinic orbits in the Hamiltonian phase space, are constructed numerically. In contrast to the purely elastic case, the localized configurations of soft ferromagnetic rods exhibit non-collinear extended straight segments, a geometrically distinctive feature arising directly from the magnetoelastic coupling.
Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder
We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments’ axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [Johanns et al., "Strength of surgical knots under cyclic loading conditions," Science Advances (2023)]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from π/4 to 4π yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies.
Energy Barriers for Reversible Chain Scission and Healing under Tension with Displacement Control
Polymer chain scission is a key mechanism for fracture of soft materials such as elastomers and hydrogels. It is well known from single-molecule force spectroscopy experiments that the critical condition for chain scission depends on the loading rate and other environmental effects (e.g., temperature and solvent). Common approaches to describing the kinetics of chain scission usually assume force-controlled conditions, that is, when the polymer chain is stretched by a prescribed force. As a result of this assumption, chain scission is irreversible, excluding the possibility of healing. In many soft materials, however, self-healing has been observed after fracture, suggesting possibly reversible chain scission. Here, we show that reversible chain scission with healing is possible under displacement-controlled conditions, that is, when the chain is stretched with a prescribed end-to-end distance. We present a breakable freely-jointed chain model, assuming that a polymer chain breaks when one of its links breaks while the other links remain nearly rigid. At a prescribed end-to-end distance, the free energy of the chain has two local minima and a local maximum (the transition state), giving rise to energy barriers for chain scission and healing. As the prescribed displacement increases, the energy barrier decreases for scission but increases for healing, depending on the chain length (number of links) and the potential energy of the link. With the energy barriers, we adopt the kinetic approach to predict the statistics and kinetics of a single polymer chain under tension, first by integrating the rate equation for the survival probability of the chain and then by kinetic Monte Carlo simulations. Notably, the present model predicts rate-dependent chain scission, with a lower bound for the critical force that could be several orders of magnitude lower than the upper bound (which is close to the theoretical strength of the covalent bonds in the backbone).
The strain-energy function for combined bending and stretching of incompressible isotropic elastic plates∗
The strain-energy function of a thin plate composed of an incompressible isotropic elastic material is derived. In contrast to conventional models developed for applications involving large plate deformations with small midplane strains, the present model accommodates large deformations accompanied by finite midplane strains. An extended Kirchhoff-Love hypothesis underpinning prior work on the topic is here justified on energetic grounds. The model, specialized to certain generalized neo-Hookean materials, exhibits bending-stretching coupling and reduces to the classical pure-bending energy in the absence of midplane strain.
Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity
The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schr¨odinger equation, with the expected limiting form when the associated classical force system involves conservative forces.
Scalable Thermoset Informatics and On-Demand Discovery through Autonomous Experimentation
As photo-polymer additive manufacturing matures, there is an increasing need for on-demand, application-specific materials. A major bottleneck is the limited exploration of the vast design space for new thermoset polymer formulations, which must satisfy both material property requirements and processing constraints. This challenge stems from the combinatorial complexity of possible formulations and the high cost of experimental evaluation. In this work, we present an end-to-end pipeline that integrates a self-driving laboratory (SDL) with informatics-driven optimization to discover and validate novel thermoset acrylate formulations. The pipeline starts with a database focusing on thermoset acrylates that consolidates multiple data sources (including manual and SDL experiments, molecular dynamics simulations, and literature data). Selected datasets are used to train both single-task and multitask predictive models, which interface directly with our SDL platform to measure mechanical and processing-related properties. Each component of the pipeline is validated independently and then deployed together to optimize a target elastomeric material in significantly less time and with substantially reduced human effort. This work establishes a scalable framework for embedding multi-fidelity machine learning tools within laboratory workflows, paving the way for the next generation of autonomous, data-driven thermoset formulation discovery for additive manufacturing.
Extraordinarily high fractocohesive lengths in polymer-like networks
The failure resistance of polymer networks dictates their utility as material candidates across industries. However, relating the key length scales driving crack growth to molecular mechanisms remains a key bottleneck in predicting and designing against fracture. The fractocohesive length—defined in terms of the ratio of fracture energy to the specific work to rupture—of a material correlates with the length scale of energy dissipation and controls fracture resistance. Although the Lake-Thomas model predicts the fractocohesive length of a perfect polymer network to match the undeformed mesh size, real soft materials exhibit values that far exceed this prediction. Here we report extraordinarily high fractocohesive lengths in polymer-like networks with and without defects. We find that even perfect networks can have fractocohesive lengths orders of magnitude higher than the undeformed mesh size due to highly nonlinear chain behavior giving rise to nonlocal effects during fracture. Introducing defects further increases the fractocohesive length. We identify quantitative relations between nonlinear chain mechanics, defect length, defect density, and fractocohesive length. Overall, strain-stiffening chain behavior, defect density, and defect size independently correlate with larger fractocohesive lengths in polymer-like networks, and their individual effects can be collapsed into a single power law scaling. These outcomes point the way towards improved physics-informed design of soft yet tough polymers and metamaterials.
fractocohesive length, fracture, rupture, polymer-like networks, flaw sensitivity
Programming nonlinear mechanical responses by topology optimization of limit-point instabilities
Limit-point instabilities provide a powerful but underexplored mechanism for programming nonlinear mechanical responses. However, integrating such instabilities into topology optimization under large deformation remains challenging due to path-tracking and geometric regularity issues. Here, we develop an explicit design framework that programs prescribed force–displacement curves by deliberately exploiting limit-point instabilities over large deformation. We extend the Moving Morphable Void (MMV) method with finite-deformation equilibrium tracing and a curvature regularization that suppresses nonphysical sharp features while retaining design freedom. The framework synthesizes architectures that realize strain-hardening-type, yield-plateau-type, and strain-softening-type structural responses under compressive strains up to 20%, with typical curve-matching errors on the order of 1–2%. Mechanistically, the macroscopic response is governed not only by instability onset but by the spatial distribution, sequential activation, and coupling of buckling and snap-through modes embedded in the topology. We demonstrate overload protection, low-frequency vibration isolation, and instability-driven energy dissipation, and extract low-dimensional parametric templates that preserve the deformation mechanisms while enabling efficient retuning. The results establish controlled limit-point instability as a systematic design resource for programming constitutive-like nonlinear behavior at the structural level.
Stress Asymmetry in Hard Magnetic Soft Materials
Hard magnetic soft materials -- soft polymers embedded with hard magnetic particles -- are modeled using continuum magnetomechanical formulations in which the deformation and the magnetization field are the primary kinematic variables. A recent question in such formulations is whether the Cauchy stress is symmetric, which is directly related to frame invariance and angular momentum balance. This note discusses energetically equivalent formulations, related by a change of variables between referential and current descriptions of the magnetization, and shows that they generally yield different Cauchy stresses, including a change in their symmetry. Specifically, the formulation based on a referential magnetization produces a symmetric Cauchy stress, while that based on a current magnetization generally yields an asymmetric Cauchy stress. We highlight that when the internal variable (magnetization field) is at the energy-minimizing equilibrium configuration, the divergences of these stresses are the same, and both stresses are symmetric.