Continuum solid mechanics form the foundation of numerous theoretical studies and engineering applications. Distinguished from traditional mesh-based numerical solutions, the rapidly developing field of scientific machine learning, exemplified by methods such as physics-informed neural networks (PINNs), shows great promise for the study of forward and inverse problems in mechanics. However, accurately

Soft-magnetorheological elastomers (s-MREs) are particulate composites made of a non-magnetic elastomeric matrix dispersed with micron-sized particles of a “soft-magnetic” material. The phenomenon of magnetostriction in specimens made from s-MREs is the change in their shape when they are subjected to an external magnetic field. Experiments in the literature show that for circular cylindrical specimens

In this paper, we extend the micromechanics-based phase-field model to simulate fatigue failure. The coupling of a micromechanics-based framework with the phase-field approach helps to differentiate between failure modes, by distinguishing between open and closed microcracks. This integrated framework links continuum field variables, such as plastic strain and damage variable, to micromechanical mechanisms

Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures, and discover the topological edge and corner modes in these structures. We rigorously identify the infinitely many topological edge states within the bandgaps via

This work considers a recently developed finite-deformation elastoplasticity theory that assumes distinct tensorial fields describing macro-plasticity and micro-plasticity, where the latter is determined by a higher-order balance equation with associated boundary conditions. Specifically, micro-plasticity evolves according to a contribution to the Helmholtz free-energy density that depends on a Nye–Kröner-like

A systematic understanding of the toughening and self-healing mechanisms of artificial soft tissues is crucial for advancing their robust application in biomedical engineering. However, current models predominantly possess a phenomenological nature, often devoid of micromechanical intricacies and quantitative correlation between microstructure damage and macroscopic energy dissipation. To bridge this

We propose a novel variational framework to regularize softening plasticity problems. Specifically, we modify the plastic dissipation potential term by adding a contribution depending on the cumulative plastic strain-rate gradient. We formulate the evolution of the so-obtained strain-rate gradient plasticity model with an incremental variational principle. The time-discretized evolution equations are

Finite deformation finite element calculations are carried out to analyze nonuniform plane strain tensile deformation of single crystals using an elastic–viscoplastic crystal plasticity constitutive relation. The planar crystals considered have two potentially active slip systems with the driving force for slip including a non-Schmid stress. The non-Schmid stress on a slip system is taken to be the

We present a formalism for developing cyclic and helical symmetry-informed machine learned force fields (MLFFs). In particular, employing the smooth overlap of atomic positions descriptors with the polynomial kernel method, we derive cyclic and helical symmetry-adapted expressions for the energy, atomic forces, and phonons, i.e., lattice vibration frequencies and modes. We use this formulation to construct

We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an ‘equivalent-rod’ theory from the Kirchhoff rod equations: the helical filament is described as a naturally-straight rod (aligned with the helix axis) for which the extensional and torsional deformations

Conch shells, characterized by a highly mineralized hierarchical crossed-lamellar structure that represents the pinnacle of molluscan evolution, exhibit exceptional crack resistance to protect their soft bodies from predatorial attacks. In this paper, we present a three-dimensional fracture mechanics model to establish a correlation between fracture toughness and the crossed-lamellar structure, elucidating

Double network (DN) gels, composed of two interpenetrating polymer networks with contrasting properties, garnered considerable attention since their invention due to large resistances to crack initiation and propagation. This study systematically investigates the effect of viscous solvent on the fracture behavior of DN gels through pre-notch and post-notch crack tests conducted on both water-swollen

In this work, dislocation density-based recovery and recrystallization models are implemented in an incremental elasto-viscoplastic self-consistent (ΔEVPSC) crystal plasticity model to interpret and predict ex-situ and in-situ thermo-mechanical and neutron diffraction datasets pertaining to deformation, recovery, and recrystallization behavior of pure Ta. A dislocation density-based hardening law available

We regret to say that in our recent publication (Madani and Tarakanova, 2024), we identified two errors in Figs. 2 and 5. Here in this corrigendum, 1) we have corrected these errors and updated the figures based on our original best-performing models. 2) Additionally, we retrained our model with new hyperparameters, resulting in slightly improved performance across almost all datasets compared to the

Data-driven methods have recently been introduced to address complex mechanics problems. While model-based, data-driven approaches are predominantly used, they often fall short of providing generalizable solutions due to their inherent reliance on pre-selected models. Model-free approaches, such as symbolic regression, hold promise for overcoming this limitation by extracting solutions directly from

Fracture resistance of blood clots plays a crucial role in physiological hemostasis and pathological thromboembolism. Although recent experimental and computational studies uncovered the poro-viscoelastic property of blood clots and its connection to the time-dependent deformation behavior, the effect of these physical processes on clot fracture and the underlying fracture mechanisms are not well understood

Jump-to-contact is a commonly observed phenomenon in atomic force microscopy (AFM) measurements. It occurs when the AFM tip approaches the surface of the substrate, and the attractive forces – such as van der Waals forces – between the tip and the surface become sufficiently strong, causing the tip to jump towards the surface suddenly. Here, we investigate how the surface deformation affects the onset

Discrete mesoscale network models, in which explicitly modeled polymer chains are replaced by implicit pairwise potentials, are capable of predicting the macroscale mechanical response of polymeric materials such as elastomers and gels, while offering greater insight into microstructural phenomena than constitutive theory or macroscale experiments alone. However, whether such mesoscale models accurately

Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently by thermodynamics, to further uncover the thermodynamic structure underlying the evolution equations, i.e., the thermodynamic potentials driving the system and

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder

Shear transformation (ST), as the fundamental event of plastic deformation of amorphous solids, is commonly considered as transient in time and thus assumed to be an equilibrium process without inertia. Such an approximation however poses a major challenge when the deformation becomes non-equilibrium, e.g., under the dynamic and even shock loadings. To overcome the challenge, this paper proposes a

When subjected to repeated dynamic impacts at identical load level, a metallic monolithic beam/plate may reach a stable state wherein measurable deformation ceases (i.e., shakedown in elastic state) after undergoing a sequence of elastoplastic deformations, which has been termed as “pseudo-shakedown” (P-S) (Jones, 1973; Shen and Jones, 1992). While the response of a single beam/plate under repeated

Polymer-based nanocomposites (PNCs) are formed by dispersing nanoparticles (NPs) within a polymer matrix, which creates polymer interphase regions that drive property enhancement. However, data-driven PNC design is challenging due to limited data. To address the challenge, we present ViscoNet, a surrogate model for finite element analysis (FEA) simulations of PNC viscoelastic (VE) response. ViscoNet

Two-dimensional (2D) materials hold great promise for future electronic, optical, thermal devices and beyond, underpinning which the predictability, stability and reliability of their mechanical behaviors are the fundamental prerequisites. Despite this, due to the layered crystal lattice structure, extremely high anisotropy and the independent deformation mechanism of out-of-plane bending, the proper

Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided

Accurately understanding and predicting the progressive failure behavior of rock is crucial in rock engineering. In this study, a new microplane prediction model characterized by the intrinsic properties of the traction vector is proposed to describe the rock's multi-scale behavior, anisotropy, and the microscopic tensile and compressive-shear failure effects based on a physical foundation. Under the

Craze and crack propagation in glassy polymers under cyclic mode I loading are investigated by employing a recently developed continuum-micromechanical model for crazing. This model accounts for the local morphology change from microvoids to fibrils during craze initiation, viscoplastic drawing of bulk material into fibrils, and viscoelastic creep recovery of the fibrillated craze matter during unloading

Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting

Experiments have shown that for quasi-static and moderate strain-rates (of the order of 102–103/s) the mechanical response of additively manufactured (AM) and traditionally processed high-strength steels is similar whereas the impact behavior is markedly different. In this paper, we reveal that the main reason for this difference is the retained porosity in the AM material. Fully-implicit finite element

It has been known for some time that constitutive models for the large-deformation response of porous elastomers can develop ‘macroscopic’ instabilities as a consequence of loss of strong ellipticity. Indeed, constitutive models obtained by homogenization methods for porous elastomers with periodic and random microstructures can lose strong ellipticity under appropriate loading conditions. For periodic

Micro-scale structural polymer membranes with desired mechanical properties, such as modulus and stretchability, have extensive applications in repair scaffolds, stretchable electronic devices, etc., yet how to achieve the simultaneous tunability of high modulus (MPa-level) and excellent resilience in micron-scale polymer membrane remains challenge. In this work, based on the material-structure integrated

Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finite-deformation response of anisotropic elastic–inelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as Rij, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations

A micromechanical model for simulating failure of unidirectional composites under cyclic loading has been developed and tested. To efficiently pass through the loading signal, a two-scale temporal framework with adaptive stepping is proposed, with a varying step size between macro time steps, and a fixed number of equally spaced micro time steps in between. With the focus on matrix dominated failure

Growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly

In recent years, lattice kirigami metamaterials have attracted considerable attention due to their unconventional and often intriguing mechanical properties. However, the absence of a comprehensive analytical framework has hindered advancements in both research and practical applications. Here, we introduce an integrated framework that enables the customization, form-finding, analysis, and manufacturing

The Open-hole compressive (OHC) strength of a fiber reinforced laminate is one of the most critical allowables for design of aerostructures. In this paper, results for predicting the OHC strength using the semi-discrete damage modeling framework are presented. The predictions are seen to capture experimentally observed failure mechanisms and measured failure loads. The constitutive model includes local

The objective of this paper is to shed light on the mechanical response of filled elastomers in sliding contact. Compared to situations encountered by tires in breaking conditions, the study only considers smooth obstacles in order to analyze the contribution of finite deformations and of the complex viscosity of filled elastomers without facing all the complexity of surface roughness. For this purpose

Atomic and molecular layer deposition (ALD/MLD) coatings are promising solutions for preventing dendrite formation in aqueous and non-aqueous Li/Na/Zn metal batteries. Notably, alumina and alucone coatings have emerged as highly effective against dendrite formation in Zn anodes. Despite their demonstrated efficacy, a comprehensive understanding of their chemo-mechanical impact on anodes remains elusive

Fatigue has long been studied for many materials, but many aspects are not well understood. Our recent study of the distinct roles of crosslinks and entanglements in the synthesis-property relation of a polymer network under monotonic load leads to a fundamental question: how do crosslinks and entanglements affect the synthesis-property relation of a polymer network under cyclic load? Here we study

Machine learning (ML) enhanced fast structural analysis and design recently attracted considerable attention. In most related works, however, the generalization ability of the ML model and the massive cost of dataset generation are the two most criticized aspects. This work combines the advantages of the universality of the substructure method and the superior predictive ability of the operator learning

The problem addressed in this study is the full coupling between three different contributions to the strain in thermoviscoelastic composites, elasticity, viscosity and temperature changes. It shows that even in simple situations, the coupling with temperature may lead to counter-intuitive effects which are not accounted for through the sole overall stress–strain relations. The correspondence principle

Strain gradient breaks inversion symmetry and induces flexoelectric polarization as well as electromechanical coupling in all material systems, though the effect is usually only significant at the nanoscale. Two-dimensional (2D) materials and thin membranes thus provide an ideal platform to explore flexoelectricity, which has been widely pursued, yet quantitative theoretical analysis is needed to guide

Natural rubber (NR) exhibits strain-induced crystallization (SIC), enhancing tearing strength and crack resistance. However, the reinforcement mechanism along with nonuniform strain around a crack tip remains unclear. We reveal the nonuniform stress field around a crack tip using the DIC-based deformation field data and a hyperelasticity approach. A hyperelastic strain energy density function (W) is

Assessing the comprehensive strength of structures under multiple loading conditions is crucial for designing microstructures. This paper proposes the use of the least failure energy density (LFED) to measure the comprehensive strength of heterogeneous periodic structures, which corresponds to the minimum energy density required to destroy a structure. To enhance the comprehensive strength of a periodic

We study the fracture behavior of glassy polymers using a multiscale simulation method that integrates a molecular dynamics (MD) system within a continuum domain. By employing a nonlinear viscoelastic constitutive model in the continuum domain, the MD system undergoes non-uniform deformation with flexible boundaries through interaction with the surrounding continuum. Systems with pre-defined double

Applying carbon fiber composite honeycomb in curved sandwich shells faces challenges due to the saddle-shaped bending surface in hexagon configurations and potential damage during the shape-forming process. This study analyzes the bending deformation of honeycombs by developing large deformation theoretical model for their bending surfaces. The study introduces two novel honeycomb configurations—Boomerang-shaped

In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the thermal problem (the classical Stefan’s problem) from the elasticity problem, and often limit themselves to linear elasticity with small strains. Treating solidification

Constitutive modelling of nonlinear isotropic elastic materials requires a general formulation of the strain–energy function in terms of invariants, or equivalently in terms of the principal stretches {λ1,λ2,λ3}. Yet, when choosing a particular form of a model, the representation in terms of either the principal invariants or stretches becomes important, since a judicious choice between one or the

This work reports the amplitude-induced topological phase transition and Hall effect in nonlinear elastic waves metamaterials with local resonators. The multi scale method is employed to analyze nonlinear effects on the Bragg scattering and locally resonant band gaps. The amplitude-induced band inversion and topological edge states are numerically investigated. A spin Hall insulator is generated by

It is common practice to characterize the constitutive law of a material indirectly. This takes place by fitting a specific stress component, which is given as a combination of response functions or derivatives of the energy function of the material. Yet, it is possible to characterize each energy derivative of the material directly. Not only that but, through a few well-designed tests, getting a set

Refractory high-entropy alloys (RHEAs) are considered as potential candidates for high-temperature applications, with the glide resistance of edge dislocations being a crucial factor in determining the high-temperature strength. However, the solid-solution strengthening mechanism of edge dislocations in RHEAs is not fully understood. The existing Labusch-type models mainly focus on the long-range interaction

The mechanical behaviour of isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) at various strain rates is systematically investigated via experiments, theoretical analysis, and numerical modelling. Experiments encompassing SEM (scanning electron microscope), DSC (differential scanning calorimetry), TGA (thermogravimetric analyser), quasi-static and dynamic (SHPB – split Hopkinson pressure

Stretchable pressure sensors are a key enabler of human-mimetic e-skin technology, with promising applications in soft robotics, prosthetics, biomimetics, and biosensors. Stretchable hybrid response pressure sensor (SHRPS) is an emerging type of soft pressure sensor that employs hybrid piezoresistive and piezocapacitive responses. A unique feature of SHRPS based on barely conductive porous nanocomposite

The cohesive zone law represents the constitutive traction versus separation response along the crack-tip process zone of a material, which bridges the microscopic fracture process to the macroscopic failure behavior. Elucidating the exact functional form of the cohesive zone law is a challenging inverse problem since it can only be inferred indirectly from the far-field in experiments. Here, we construct

Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale

Polydomain liquid crystalline (nematic) elastomers exhibit unique mechanical properties such as soft elasticity, where the material largely deforms at nearly constant stress, due to microstructural evolution. In this paper, we numerically study the effect of such remarkable soft behavior on the surface instability of a half-space polydomain nematic elastomer, which is uniformly compressed parallel

Localization, in the form of adiabatic shear, is analyzed in viscoplastic solids that may undergo structural transformation driven by pressure, shear stress, temperature, and magnetic field. As pertinent to polycrystalline metals, transformations may include solid–solid phase transitions, twinning, and dynamic recrystallization. A finite-strain constitutive framework for isotropic metals is used to

Whether or not energy dissipation is localized in the vicinity of the rupture tip, and whether any distal energy dissipation far from the crack tip has a significant influence on rupture dynamics are key questions in the description of frictional ruptures, in particular regarding the application of Linear Elastic Fracture Mechanics (LEFM) to earthquakes. These questions are investigated experimentally

3D-printed continuous carbon fiber reinforced composites (CCFRCs) are promising for various engineering applications due to high strength-to-weight ratios and design flexibility. However, the large variations in their mechanical properties pose a considerable challenge to their widespread applications. Here we develop a multiscale Bayesian method to quantify uncertainties in the constitutive parameters

A micromechanical model is developed that generates analytic expressions for the crack displacement vector u given an arbitrary far-field stress state σa for a crack that is bridged by an array of ligaments oriented at an arbitrary angle with respect to the crack plane. The model is applicable to various materials, e.g., fibrous ceramic composites, or polymer composites reinforced by stitches or z-pins