We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of freedom, but exhibits linear-elastic fracture mechanics scaling and therefore no size effect. To higher order, the overall energetics of the metastructure can be characterized

Peeling of thin films has been widely used in adhesion measurement, film transfer and bio-inspired design. Most previous studies focused on the peeling of thin films from rigid substrates, but soft substrates are common in practical applications. Herein, we propose a two-dimensional model based on the bilinear cohesive law to characterize the 90-degree peeling of elastic thin films from elastic soft

The contact between a rigid Hertzian indenter and an adhesive broad-band viscoelastic substrate is considered. The material behavior is described by a modified power law model, which is characterized by only four parameters, the glassy and rubbery elastic moduli, a characteristic exponent and a timescale . The maximum adherence force that can be reached while unloading the rigid indenter from a relaxed

Predicting stress fluctuations in granular media under steady-state shear loading is crucial for applications ranging from geophysical processes to construction engineering. Stress fluctuations emerge from particle rearrangement, usually enabled by frictional slip and force-chain buckling. Existing models used to predict stress fluctuations are largely phenomenological, often accounting for the force

Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft

We model the constitutive equation for nonlinear electro-viscoelastic transversely isotropic solids with short term memory via a generalized strain method, where the method is a change with respect to the methods that have been done in the last decades regarding mechanics of nonlinear solids. Our generalized strain model uses spectral invariants with a clear physical interpretation and hence they are

The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and

In this work a generalized phase-field cohesive zone model () is proposed within the framework of the unified phase-field theory for brittle and cohesive fracture. With the introduction of an extra dissipation function for the crack driving force, in addition to the geometric function for the phase-field regularization and the degradation function for the constitutive relation, theoretical and application

Shear wave elastography (SWE) is an innovative method that allows for the nondestructive and quantitative characterization of muscular mechanical properties. This method finds extensive utility in fields such as sports medicine, sports rehabilitation, and the diagnosis of muscle-related ailments. Existing studies have demonstrated the promise of SWE in probing intramuscular pressure (IMP), a factor

Modeling of subcutaneous injections in soft adipose tissue – a common way to administer pharmaceutical medication – is a challenging multiphysics problem which has recently attracted the attention of the engineering community, as it could help optimize medical devices and treatments. The underlying continuum mechanics of this process is complex and involves finite strain poro-mechanics – where a viscous

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and the supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation mechanics (FDM) theory. The energy density function in our model encodes accepted and simple physical facts related to rocks and granular materials under compression

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) th

We investigate the role of polycrystalline disorder on the effective ferro-electro-elastic behavior of perovskite ferroelectric ceramics under electro-mechanical loading. Assuming random initial grain orientations, we use high-resolution phase-field simulations and periodic homogenization of two-dimensional model polycrystals to study the evolution of the domain microstructure within and across grains

The advent of additive manufacturing technology empowers precise control of multi-material components or specific defects in lightweight lattice metamaterials, however, fracture mechanics and toughening design strategies in such metamaterials remain enigmatic. By incorporating theoretical analysis, numerical simulation, and experimental investigation, our study reveals that stretch-bend synergistic

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility

Photopolymerization-based 3D printing has emerged as a key technology in hydrogel manufacturing, broadening the attributes of hydrogels and extending their applications into diverse engineering fields. However, the mechanical properties of hydrogels dramatically impact the functionality and quality in practice. It is necessary to develop an appropriate theoretical model to predict the evolution of

Folding paper along curves leads to spatial structures that have curved surfaces meeting at spatial creases, defined as curve-fold origami. In this work, we provide an Eulerian framework focusing on the mechanics of arbitrary curve-fold origami, especially for multi-curve-fold origami with vertices. We start with single-curve-fold origami that has wide panels. Wide panel leads to different domains

In the design of structural materials, there is traditionally a tradeoff between achieving high strength and achieving high toughness. Nature offers creative solutions to this problem in the form of structural biomaterials (SBs), intelligent arrangements of mineral and organic phases which possess greater strength and toughness than the constituents. The micro-architecture of SBs like nacre and sea

We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith’s local energy balance at contact edges to the case of a non-conservative (viscoelastic) material, subjected to a generic contact time–history. We apply the proposed

We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a homogeneous isotropic linear elastic material of prescribed shear modulus. Importantly, we find that the same combination of annuli will cloak any possible mode of imposed

In purely normal elastic rough surface contact problems, Persson’s theory of contact shows that the evolution of the probability density function (PDF) of contact pressure with the magnification is governed by a diffusion equation. However, there is no partial differential equation describing the evolution of the PDF of the interfacial gap. In this study, we derive a convection–diffusion equation in

This article presents the first experimental, numerical, and analytical study of the elastoplastic shakedown response of an auxetic metamaterial structure that elucidates interactions between auxeticity and maximum shakedown loading capacity. The study aims to determine the safe elastoplastic shakedown limit of perforated auxetic aluminum sheet structures (AA5083-TO) with fixed void fraction (16.4%)

Willis materials are composites whose the overall constitutive relations exhibit coupling between momentum and strain. Recently, piezoelectric Willis materials have been studied, allowing the macroscopic momentum to be additionally coupled to the non-mechanical stimulus. Such metamaterials classified as first-order Willis materials generate cross-couplings due to their asymmetric microstructures in

Adhesive interactions between soft materials are prevalent in both biological systems and various engineering applications, including soft robots, flexible electronics, and antifouling coatings. Many studies have demonstrated that cavitation and fingering instabilities emerge at the adhesive interface between rigid objects and soft films, owing to the geometric attributes of the contact region. However

We investigate the conditions for crack nucleation in variational gradient damage models used as phase-field models of brittle and cohesive fracture. Viewing crack nucleation as a structural stability problem, we analyze how solutions with diffuse damage become unstable and bifurcate towards localized states, representing the smeared version of cracks. We consider gradient damage models with a linear

We present an analytical framework to study the impact of electromechanical properties on the growth of a ferroelectric nucleus. Ferroelectric domain evolution is typically simulated by phase-field models, which have shown that nuclei evolve from needle-like structures into complex domain patterns. However, there has been limited in-depth analysis of the interplay between electrostatics, mechanics

A discrete numerical analysis of the yield and damage properties associated with a cohesive granular system composed of ductile particles is hereby presented. Such a modelling approach aims at better understanding damage mechanisms which are often encountered during the powder compaction process, widely used in the metallurgical and pharmaceutical fields. The analysis was based on the micromechanical

In this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the

This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I

The adhesion of soft materials often fails due to stress concentration at the interface. Structural design offers an effective approach to disperse stress at the interface and enhance adhesion properties. Herein, we introduce the concept of discretized stress dispersion to achieve ultrastrong adhesion of soft materials. This involves incorporating discrete structures at the adhesion interface, with

A criterion is developed for the unhomogeneous yielding of materials containing arbitrarily oriented ellipsoidal voids. The criterion is built upon classical estimates for pure pressure and pure shear. A data-driven approach is then followed to incorporate the effects of void shape and orientation. A large number of micromechanical unit cell results are used to calibrate the yield criterion. A key

Previous experiments have revealed that the controllable introduction of structural gradients in metallic glasses (MGs) can endow the materials with extra plasticity due to the gradient-induced deflection of shear bands. However, the relation between the spatial structural gradient and the initiation of shear band deflection remains unclear. The current study has been focused on investigating the relationship

Active solids are a large class of materials, including both living soft tissues and artificial matter, that share the ability to undergo strain even in absence of external loads. While in engineered materials the actuation is typically designed , in natural materials it is an unknown of the problem. In such a framework, the identification of inactive regions in active materials is of particular interest

Multicellular tubes are fundamental tissues for transporting and distributing liquids and gases in living organisms. Although the molecular, cellular and mechanical aspects in tube formation have been addressed experimentally, how these factors are coupled to control tube patterning and dynamics at the tissue level remains incompletely understood. Here, we propose a three-dimensional (3D) vertex model

Mode II fracture toughness of interfaces in laminated structures is usually assessed through standardized tests. Standards are based on samples featuring regular shapes and uniform cross-sections, in which mode II propagation happens to be unstable. We explore here, via a semi-analytical approach, the potential of more complex geometry and shapes for stabilizing the crack propagation. Results demonstrate

The solid-solid contact interface is crucial for the reliability of solid-state energy storage systems. The contact condition becomes more complicated when lithium (Li) metal is used as the anode. The contact between solid electrolyte (SE) and Li metal is inferior compared to the liquid/solid interface in conventional Li-ion batteries. Experimental evidence has shown that improper operating conditions

Ferroelectric materials are widely used in energy applications due to their field-driven multiferroic properties. The stress-induced phase transformation plays an important role in the functionality over repeated and consecutive operation cycles, especially at the micro/nanoscales. Here we report a systematic in-situ uniaxial compression tests on cuboidal Barium titanate (BaTiO) nanopillars with size

Disordered biopolymer gels, such as those synthesized from polysaccharide and gelatin, play an important role in biomedical applications, particularly in tissue engineering. During the gelation process of these gels, polymer chains associate in the presence of gelling agents, forming physical cross-links known as the junction zones. In contrast to rubber-like networks, the resulting network comprises

Pressurized solids are ubiquitous in nature. Mechanical properties of biological tissues arise from cell turgor pressure and membrane elasticity. Flat contact between cells generate nonlinear forces. In this work, cells are idealized as pressurized elastic membranes in frictionless contact with one another. Contact forces are experimentally measured on rubber-like membranes and computed using finite

The interaction of crack fronts with asperities is central to fracture criteria in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order, perturbations. However, large and localized disturbances to crack motion induce dynamic and geometric nonlinear effects beyond the existing linear theories. Because the determination

Tunable and reversible dry adhesion possess great potential in a wide range of applications including transfer printing, climbing robots, wearable devices/electronics, and gripping in pick-and-place operations. Multiferroic composite materials offer new routines and approaches to achieve tunable adhesion due to their multi-field coupling effects. In this paper, the classical Johnson-Kendall-Roberts

The fracture toughness of inelastic materials consists of an intrinsic component associated with the crack tip fracture process and a dissipative component due to bulk dissipation. Experimental characterization of the intrinsic component of fracture toughness is important for understanding the fracture mechanism and predictive modeling of the fracture behavior. Here we present an experimental study

Laboratory description of clay normally distinguishes the scale of atoms from the scale of clay particles and aggregates. Contemporary constitutive models for clay tend to ignore this scale separation, and rather focus on phenomenology. By considering scale separation, this paper introduces a robust physics-based phenomenological constitutive model for clay that qualitatively captures their broad spectrum

The foundation of a new concept, coined here as , is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy , akin to hyperelasticity

Magneto-active hydrogels (MAHs) consist of a polymeric network doped with magnetic particles that enable the material to mechanically respond to magnetic stimuli. This multifunctionality allows for modulation of mechanical properties in a remote and dynamic manner. These characteristics combined with the biocompatibility of hydrogels, make MAHs excellent for drug delivery and biological scaffolds.

Light serves a pivotal function in polymer systems, creating a dynamic interplay with the materials. It initiates various photochemical processes such as polymerization, phase transitions, photo-isomerization, photo-ionization, etc, endowing the polymers with diverse functionalities. Concurrently, as these materials undergo the changes, their shape and optical properties evolve, which also change the

Mechanical metastructures have been prevailing recently owing to their unusual mechanical responses. Despite notable progress in designing periodic metastructures, creating irregular and stochastic metastructures with optimized performance remains challenging because of the enlarged design space. In this study, we introduce a novel approach to realize the unstructured growth of irregular architectures

Ice, a quasi-brittle material with a complex crystal organization and found ubiquitously in nature, undergoes an impact fragmentation process that implies a rich physical mechanism, yet remains not thoroughly elucidated. We develop a highly robust and efficient meshless method for fluid–solid coupling, specifically designed to elucidate the mechanisms of crack propagation in S2 columnar ice subjected

The strength-toughness tradeoff in biological materials such as nacre and bone is essentially due to their stacked microstructures formed by hard and soft phases. In some of these materials, purely soft phase acts as interface layers linking hard phases (platelets), while in some others, hard-phase bridges exist in the soft phase to form a hybrid interface. In order to disclose the selection mechanism

Many classes of flexible and stretchable bio-integrated electronic systems rely on mechanically sensitive electromagnetic components, such as various forms of antennas for wireless communication and for harvesting energy through coupling with external power sources. This efficient wireless functionality can be important for body area network technologies and can enable operation without the weight

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D

Displacement-controlled cyclic compressive responses of polycrystalline superelastic NiTi shape memory alloys (SMAs) are investigated at a maximum strain ε of 4.2 % and over frequencies ranging from 0.0007 Hz to 50 Hz in stagnant air. Our focus was on understanding the interactions among phase transition (PT), heat transfer and plastic flow of austenite phase during cyclic operation. We monitored temperature

Compressed elastic films on soft substrates release part of their strain energy by wrinkling, which represents a loss of symmetry, characterized by a pitchfork bifurcation. Its development is well understood at the onset of supercritical bifurcation, but not beyond, or in the case of subcritical bifurcation. This is mainly due to nonlinearities and the extreme imperfection sensitivity. In both types

Living tissues can remarkably adapt to their mechanical and biochemical environments through growth and remodelling mechanisms. Over the years, extensive research has been dedicated to understanding and modelling the complexities of growth. However, the majority of growth laws are based on phenomenological, , proposed evolution equations. This work aims to describe a general bulk growth model that

Cellulose foams are representative of many porous engineering solids that can absorb a large quantity of fluid such as water. Experiments are reported to give insight into water rise in cellulose foams and the underlying mechanisms. The water rise characteristic of water height versus time displays a distinct knee on a log-log plot; this knee separates an initial regime where scales as from a subsequent

Mechanical insight into the packing of slender objects within confinement is essential for understanding how polymers, filaments, or wires organize and rearrange in limited space. Here we combine theoretical modeling, numerical optimization, and experimental studies to reveal spherical packing behavior of thin elastic rod loops of homogeneous or inhomogeneous stiffness. Across varying loop lengths

Extensive experiments over the decades unequivocally point to a pronounced scale-dependency of plastic deformation in metals. This observation is fairly general, and broadly speaking, strengthening against deformation is observed with the decrease in the size of a relevant geometrical feature of the material, e.g., the thickness of a thin film. The classical theory of plasticity is size-independent