Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental deformations that involve bending, shear, and normal forces. The unit cell of one class is characterized by elements where deformations are lumped within a finite-degrees-of-freedom

A geometrically characteristic kinetic thermodynamic deformation theory is proposed for effective predictions over the full-life mechanical behaviour of crystalline solid. From a theoretic perspective, the proposed theory is distinguished from existing internal state variable theories at least in two aspects. Firstly, it is “geometrically characteristic” because the quantities employed for summarising

Constructing constitutive models for compressible soft materials is essential for accurately describing their highly nonlinear, large deformation mechanical behavior and volumetric deformation. However, most existing constitutive models rely on predefined assumptions about the form of the strain energy function. Constructing compressible hyperelastic constitutive models is particularly challenging

Of the non-classical nonlinear elastic phenomena, slow dynamics (SD) has received particular attention due to recent modeling efforts and experiments in new systems. SD is characterized by a loss of stiffness after a minor conditioning strain, followed by a slow recovery back towards the original stiffness. It is observed in many imperfectly consolidated granular materials (e.g., rocks and concrete)

Elastic metamaterials possess flexible regulatory capabilities of elastodynamic field information and energy through engineering and tailoring wave amplitudes, phase, and polarization vectors. However, due to the lack of general wave quantities and dynamic mode characterization methods, it is difficult to describe and design customized elastic dispersions with prescribed eigenmodes of interest, especially

Multiphase thin films exhibit unique physical functionalities stemming from their dimensions and interactions among phases. In these materials, elasticity plays an important role both in their growth and physical performance. An outstanding problem in this regard is the elastic formulation of representative volume element (RVE) of thin film systems. As thin films RVEs lack translation invariance in

Bio-inspired composite materials with staggered microstructures exhibit superior mechanical properties compared to traditional composites, paving the way for the development of advanced functional materials. The existing analytical models mainly address the macroscale constitutive response along the staggering direction using plane strain or plane stress assumptions. Consequently, a significant gap

Myocardial infarction (MI), characterized by the death of myocytes in the myocardium, leads to high morbidity and mortality rates worldwide. The persistent imbalance of biomechanical stress and strain within the myocardium is a critical factor contributing to adverse growth and remodelling (G&R) following MI, such as wall thinning and chamber dilation. This study investigates the structural and functional

Anti-icing surfaces are vital for transportation and infrastructure. Low adhesion strength enables energy-efficient wind-driven or vibration-based ice-removal techniques beyond heating. A key challenge is to reduce the tangential adhesion strength of ice below 10 kPa, a goal hindered in practice by the high toughness of the ice-substrate interface. Even superhydrophobic materials with low surface energy

The growing demand for biodegradable elastomers necessitates innovative designs achieving controllable degradation rates while maintaining stable mechanical performance. This work presents a novel polyurethane elastomer (PUE) with dual degradation pathways, including selective degradation of soft and hard domain. This design offers enhanced control over mechanical performance, realizing only 15 % reduction

Biological tissues with core–shell structures usually exhibit non-uniform curvatures such as toroidal geometry presenting interesting features containing positive, zero, and negative Gaussian curvatures within one system, which give rise to intriguing instability patterns distinct from those observed on uniformly curved surfaces. Such varying curvatures would dramatically affect the growing morphogenesis

Based on Hamilton’s principle of stationary action, we present a holistic variational formulation for material modeling including dissipative evolution. To this end, we recall the definition of the action as path integral of the momentum vector. Reformulation of the action and inserting the 1st and 2nd Law of Thermodynamics yield an extended Hamilton functional. We show that the stationarity conditions

Three general modes are distinguished in the deformation of a thin shell; these are stretching, drilling, and bending. Of these, the drilling mode is the one more likely to emerge in a soft matter shell (as compared to a hard, structural one), as it is ignited by a swerve of material fibers about the local normal. We propose a hyperelastic theory for soft shells, based on a separation criterion that

During neurodevelopment, neuronal axons navigate through the extracellular environment, guided by various cues to establish connections with distant target cells. Among other factors, axon trajectories are influenced by heterogeneities in environmental stiffness, a process known as durotaxis, the guidance by substrate stiffness gradients. Here, we develop a three-scale model for axonal durotaxis. At

Entangled matter displays unusual and attractive properties and mechanisms: tensile strength, capabilities for assembly and disassembly, damage tolerance. While some of the attributes and mechanisms share some traits with traditional granular materials, fewer studies have focused on entanglement and strength and there are large gaps in our understanding of the mechanics of these materials. In this

Since its introduction more than 60 years ago, the Hashin-Shtrikman upper bound has stood as the theoretical limit for the stiffness of isotropic composites and porous solids, acting as an important reference against which the moduli of heterogeneous structural materials are assessed. Here, we show through first-principles calculations, supported by finite element simulations, that the Hashin-Shtrikman

Elastomers filled with liquid inclusions — as opposed to conventional solid fillers — are a recent trend in the soft matter community because of their unique range of mechanical and physical properties. Such properties stem, in part, from the very large deformations that the underlying liquid inclusions are capable of undergoing. With the objective of advancing the understanding of the mechanics of

Aluminum (Al) alloys are widely used in aerospace and automotive industries as a result of their high strength-to-density ratio and cost-effectiveness, with their use at room temperature in housings and brackets. Although additive manufacturing (AM) facilitates the manufacturing of high-temperature aluminum alloys (200-400°C) to enable their potential use in intake fans and engine pistons, few alloying

The fracture of polymeric gels has been of growing interest in the last two decades. Well established continuum theories that couple large deformations and fluid diffusion have been applied to gels to determine crack tip fields and the energy release rate. Some studies have combined experiment and calculations to determine the fracture toughness of gels and have shown that fluid effects make a substantial

Odd elastic behavior is investigated in 2d structures with only the odd elastic parameter K0 under classic continuum theory. For the Kirchhoff–Love plate with a constant K0, the displacement formulation is independent of the odd parameter, whereas the moment formulation shows dependence. A simply-supported plate under a uniformly distributed load and center point load is investigated using the displacement

Current constitutive theories and fracture models face difficulties in capturing the extremely large deformation and fracture behaviors of hydrogels, because the structural and mechanical properties of the effective polymer network dominated in hydrogels are still unknown. In this study, we propose a periodic random network (PRN) method to construct the effective polymer network model of polyacrylamide

The role of grain size in determining fracture toughness in metals is incompletely understood with apparently contradictory experimental observations. We study this grain-size dependence computationally by building a model that combines the phase-field formulation of fracture mechanics with dislocation density-based crystal plasticity. We apply the model to cleavage fracture of body-centered cubic

In conventional constitutive models for granular materials, calibration involves estimating a few parameters within known mathematical expressions. In contrast, data-driven constitutive models couple the model structure and parameters. Addressing this fundamental difference, the development of constitutive models based on Physics-encoded Neural Networks (PeNN) is guided from the perspective of conventional

The mechanical behavior of van der Waals (vdW) interfaces under shear is important for micro-nano mechanics. However, due to the diverse structures of vdW interfaces, there is still a lack of systematic and quantitative research. Here we focus on the simplest vdW interface formed by flat carbon rings, construct twisted bilayer graphene (tBLG) with different moiré patterns through the twist angle design

Microfibril reinforced polymer composites (MFCs) are polymer-polymer composites with ductile fibrils embedded, usually increasing the tenacity of the polymer matrix. One of the successful applications is the expanded polytetrafluoroethylene (ePTFE) reinforced perfluorinated sulfonic acid (PFSA) membrane, in which the embedded ePTFE fibrils evolve into drawing fibril connecting crack surfaces, significantly

A new continuous model of shearable rod, subject to large elastic deformation, is derived from nonlinear homogenization of a one-dimensional periodic microstructured chain. As particular cases, the governing equations reduce to the Euler elastica and to the shearable elastica known as ‘Engesser’, that has been scarcely analysed so far. The microstructure that is homogenized is made up of elastic hinges

We present a framework for modeling liver regrowth on the organ scale that is based on three components: (1) a multiscale perfusion model that combines synthetic vascular tree generation with a multi-compartment homogenized flow model, including a homogenization procedure to obtain effective parameters; (2) a poroelastic finite growth model that acts on all compartments and the synthetic vascular tree

Bistable mechanical metamaterials have shown promise for mitigating the harmful consequences of impact by converting kinetic energy into stored strain energy, offering an alternative and potentially synergistic approach to conventional methods of attenuating energy transmission. In this work, we numerically study the dynamic response of a one-dimensional bistable metamaterial struck by a high speed

Determining internal stress and strain fields in solid structures under external loads has been a central focus of continuum mechanics, playing a critical role in characterizing the mechanical behaviors and properties of both engineering and biological systems. With advancements in modern optical and electron microscopy techniques, strain fields can now be directly measured using sophisticated methods

We propose Generalized Standard Material Networks, a machine learning framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of these materials postulates the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential, which alone determine the constitutive material response

With more than 90,000 muscle fascicles, the elephant trunk is a complex biological structure and the largest known muscular hydrostat. It achieves unprecedented control through intricately orchestrated contractions of a wide variety of muscle architectures. Fascinated by the elephant trunk’s unique performance, scientists of all disciplines are studying its anatomy, function, and mechanics, and use

High-entropy alloys (HEAs) have garnered increasing attention for their remarkable mechanical properties. However, due to the highly complex deformation mechanisms of HEAs, the current understanding of the underlying strengthening mechanisms is not yet fully developed, thereby limiting further microstructure optimization and processing. In this study, we have focused on the mechanics and theoretical

The design of solid state batteries with lithium anodes is attracting attention for the prospect of high capacity and improved safety over liquid electrolyte systems. The nature of transport with lithium as the current carrier has as a consequence the accretion or stripping away of the anode with every charge–discharge cycle. While this poses challenges from the growth of protrusions (dendrites) to

Due to the inherent microstructural heterogeneity of heterogeneous materials, their macroscopic fracture behavior differs significantly from that of homogeneous materials, exhibiting phenomena such as anisotropic fracture energy and strain gradient effects. To investigate the effect of microstructure on macroscopic fracture behavior, this study proposes a novel multiscale phase field model. Based on

Materials made from fibers, referred to here as Network materials, are ubiquitous in biology and engineering. In most practical situations, fibers have preferential orientation in one spatial direction or in a plane. Here we use discrete network models to derive the relationship between the stiffness and strength of networks with pre-aligned fibers and network parameters, including the degree of alignment

Magneto-mechanical coupling in the growth of soft materials presents challenges due to the complex interactions between magnetic fields, mechanical forces, and growth-induced deformations. While growth modeling has been extensively studied, integrating magnetic stimuli into growth processes remains underexplored. In this work, we develop a 3D governing system for capturing the coupled magneto-mechanical

This paper presents a thermodynamically consistent model for thermo-chemo-mechanical processes in frontal polymerization (FP). The model consists of cure kinetics, heat transfer, and finite strain kinematics of nonlinear inelastic solid undergoing finite deformation. The constitutive relations are derived by enforcing non-negative entropy production which implies the existence of cure induced inelastic

This paper explores the mechanical behaviour of the composite materials used in modern lithium-ion battery electrodes. These contain relatively high modulus active particle inclusions within a two-component matrix of liquid electrolyte which penetrates the pore space within a viscoelastic polymer binder. Deformations are driven by a combination of (i) swelling/contraction of the electrode particles

Residual stresses play a critical mechanical role in both industrial and biomechanical applications. In biological tissues, residual stresses arise from growth and remodeling processes under physiological or pathological conditions and have been extensively modeled within the framework of nonlinear elasticity. These modeling efforts have enabled direct computation of residual stress patterns based

Experimental determination of the Taylor-Quinney coefficient (TQC), β, from tensile tests at nominal strain rates of 1.0 s-1 and 500 s-1 is presented. Simultaneous full-field measurements of the deformation (strain) and temperature on the surface of the specimens are made throughout the tests, including in the localized region during necking. These measurements provide means to determine the value

Shape memory alloys that can deform and then spring back to their original shape, have found a wide range of applications in the medical field, from heart valves to stents. As we push the boundaries of technology creating smaller, more precise tools for delicate surgery treatments, the behavior of these alloys at tiny scales becomes increasingly crucial. In this study, we discover that the size effect

CO2-induced dynamic covalent polymer networks (DCPNs) have received significant attention due to their capability of sequestering CO2 to remodel material properties. Despite the promising success of carbon sequestration in the polymer, the mechanistic understanding of the CO2-induced polymer network is still at the very beginning. A theoretical framework to understand the CO2-induced formation of bulk

The analogy between frictional cracks, propagating along interfaces in frictional contact, and ordinary cracks in bulk materials is important in various fields. We consider a stress-controlled frictional crack propagating at a velocity cr along an interface separating two strips, each of height H, the frictional counterpart of the classical problem of a displacement-controlled crack in a strip, which

This paper investigates the mechanics of peeling-based microtransfer printing, focusing on the competing delamination at the stamp/ink and the ink/substrate interfaces under both high-degree and zero-degree peeling configurations. We found that the thickness and modulus contrast between the stamp and the ink significantly affect the ratio of the energy release rates at these two interfaces. Our findings

Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand nonlinear phenomena such as failure and morphological instabilities in these systems, accurate numerical models are required to study the interaction between mass

A systematic numerical study using discrete dislocation dynamics has been conducted to investigate the formation of geometrically necessary dislocation boundaries (GNBs), a fundamental component of dislocation patterning and work-hardening. The simulations presented in this paper focus on GNBs forming along the (010) plane, which are observed in the 121111 copper orientation on the β-fibre of the FCC

Highly filled thermosets are widely used to encapsulate chips in the semiconductor packaging industry. A complete set of viscoelastic properties are required for package designs with optimum mechanical reliability. A novel test method, based on inert gas pressure, is proposed and implemented to measure the temperature-dependent viscoelastic hydrostatic creep compliance (or compressibility) of filled

The directors are randomly distributed in polydomain liquid crystal elastomers (LCEs), which can be rearranged upon external loading. This can further lead to a polydomain-monodomain transition, accompanied by a change from an opaque state to a fully transparent state. Currently, the mechanical response and the related phase transition in polydomain LCEs are typically characterized in uniaxial loading

Digital image correlation (DIC) is a prominent technique for full-field, non-contact deformation characterization. Despite its sub-pixel sensitivity for displacement measurement, conventional DIC often suffers from inadequate signal-to-noise ratios (SNRs) when measuring small deformations in stiff and/or brittle materials. This work presents phase-augmented DIC (PA-DIC), a novel method that integrates

Nematic elastomers exhibit transversely isotropic semisoft elasticity due to the coupling of the liquid crystal mesogen and polymer network. Existing constitutive models are unable to simultaneously capture both the elastic anisotropy at small deformations and the semisoft stress plateau under large orthogonal loadings. Based on the decompositions of the strain energy and the deformation gradient,

Liquid crystal elastomers (LCEs), as a unique class of smart soft materials combining the properties of liquid crystals and hyperelasticity, are capable of rapid, anisotropic, and reversible deformations in response to mechanical, thermal or optical stimuli. Here, we report a hitherto unknown stretching-induced twisting behavior of LCE bilayer strips. Under uniaxial stretching, we reveal that due to

To facilitate the understanding of the mechanisms underlying the electric breakdown of dielectric elastomers, we derive a one-dimensional (1d) model for axisymmetric necking in a dielectric membrane subjected to equibiaxial stretching and an electric field, starting from the three-dimensional (3d) nonlinear electroelasticity theory. Our reduction is built on the variational asymptotic method, so that

The mechanical behaviour of composites of liquid crystal inclusions embedded in soft matrices involves a complex interplay between the elasticity of the matrix, the surface elasticity of the interfaces, and the reorientation of the liquid crystal molecules. Directors of the (nematic) liquid crystal tend to be aligned in the bulk, but may ”anchor” along the interface. In addition, the interface deforms

Stretching-dominated lattice materials are renowned for their lightweight nature and exceptional mechanical properties. These materials, however, have historically struggled with scalability towards low relative densities at which they often exhibit unstable oscillation behavior. Here, we propose a viable solution to this issue by integrating hollow truss elements and a grid distribution into the conventional

When a soft elastic layer confined between two rigid substrates is subjected to tensile loads, the stressed layer exhibits various modes of elastic instability that influence its mechanical response. While previous studies have primarily focused on analyzing these instabilities under normal tension, this study systematically investigates the impact of combined tension–torsion loading on the emergence

Fiber-reinforced composite materials have gained considerable traction in various applications due to their exceptional properties, but the multicomponent nature makes their failure modes more complex, so the research of failure mechanism for composites is very important for the safety of the structure in use. In this work, a new unified anisotropic phase field model is proposed. Firstly, a new crack

All-solid-state batteries (ASSBs) are promising candidates for next-generation energy storage. However, realizing their potential requires an understanding of their underlying coupled, multiphysics behaviors. In an effort to understand these complex interactions, the present paper develops and applies a finite-element phase-field model that represents coupled electro-chemo-mechanical behaviors in composite

Through an array of spatially distributed tendril pads, Parthenocissus tricuspidata adheres itself firmly to the surfaces of targets such as trees and walls. The tendril pads, which form unique and intriguing layouts, play a critical role in supporting plant organs. However, the relationship between their geometric forms and mechanical properties remains inadequately understood. In this paper, we combine

Through long-term evolution, biological tissues have optimized their components and structures at multiple length scales to meet the requirements of mechanical properties and biological functions. In this study, we explore how the shell macrostructure of nacre and its brick–mortar microstructure are synergistically designed to adapt to external mechanical conditions. We found that the T-stress effect