A finite deformation mechanism-based thermodynamically consistent constitutive framework is presented for describing the dynamic behaviors of brittle materials under impact loading. The framework is developed based upon a multiplicative decomposition of the deformation gradient in terms of multiple mechanisms, including recoverable elasticity, crack-induced damage, and other inelastic mechanisms such

A fully coupled poroelastic solution for spherical indentation into a half space with an impermeable surface when the indenter is subjected to step displacement loading is presented. The solution is obtained within the framework of Biot’s theory using the McNamee-Gibson displacement function method. Mathematical difficulties associated with solving poroelastic contact problems are overcome by the use

A numerical and analytical study is made of the macroscopic or homogenized viscoelastic response of suspensions of rigid inclusions in rubber under finite quasistatic deformations. The focus is on the prototypical case of random isotropic suspensions of equiaxed inclusions firmly embedded in an isotropic incompressible Gaussian rubber with constant viscosity. From a numerical point of view, a robust

To noninvasively assess the risk of aneurysm rupture and dissection, an accurate material failure metric of the aortic wall is crucial. Previous studies used deterministic or isotropic failure metrics for the aortic wall. However, experimental studies have shown that aortic wall tensile strengths in circumferential and axial directions are significantly different (i.e., anisotropic) and vary greatly

A method based on Singular Value Decomposition (SVD) and Gaussian process machine learning is proposed to build a metamodel of a material that exhibits time dependent and nonlinear behavior. To test this method, we apply it to determine the material parameters of a nonlinear viscoelastic (poly(vinylalcohol)) hydrogel (PVA). Using the metamodel, we are able to rapidly generate the stress histories for

In molecular dynamics or molecular statics (MD/MS) multi-body potentials empirically capture the energetic interactions in atomistic systems enabling the computation of the corresponding atomistic forces as energetic conjugates to the atomistic positions. We distinguish here between spatial and material atomistic positions and consequently between the corresponding spatial and material atomistic forces

Nanocrystalline (NC) metals often show transition from Hall-Petch (HP) strengthening to inverse HP softening as the average grain size decreases below a critical value. Compared to the HP behavior whose mechanism is well understood as the dislocation pile-up at grain boundaries (GBs), several hypotheses have been proposed to explain the veiled inverse HP behavior and no consensus has been reached yet

The present paper provides a generalized Maugis-Dugdale analytical model of adhesive contact between an axisymmetric rigid punch of arbitrary shape and a graded elastic half-space with Young's modulus varying with depth according to a power-law. Based on the principle of superposition and an equivalent indentation method to solve an axisymmetric external crack problem, a series of closed-form solutions

When a soft bilayer system with curved surface is subject to uniaxial compression, surface wrinkles may appear when the compressive strain is beyond a critical value. Interestingly, diverse wrinkling patterns can occur by modulating the feature of the curved surface though the load is simple. Here we study the effect of the sign of Gauss curvature and curvature anisotropy on the wrinkling pattern selection

Indentation testing is a well-known method to measure the rate dependence of the strength of materials at small scales through a variety of different testing methodologies. In many cases, a power-law creep constitutive relationship relating the indentation strain rate to the hardness, or the mean pressure applied to the material by the indenter, is assumed. However, this method of analysis does not

Due to the high demand for materials with superior mechanical properties and diverse functions, designing composite materials is an integral part in materials development. However, due to the heterogeneity and complexity of composites, measurements of properties and designs of optimal structures are often experimentally or computationally intractable. Here we report complete strain and stress tensors

Using in-situ nanoindentation experiments it is possible to study the dislocation mechanisms which unfold under an indenter.Large-scale atomistic simulations of the same are possible due to similarities in length scale, provided that defects can be included in the simulation. Yet, nanoindentation simulations have so far been mostly undertaken on defect free samples, while studies with pre-existing

We formulate and implement Helical Density Functional Theory (Helical DFT) — a self-consistent first principles simulation method for nanostructures with helical symmetries. Such materials are well represented in all of nanotechnology, chemistry and biology, and prominent examples include nanotubes, nanosprings, nanowires, miscellaneous chiral structures and important proteins. The overwhelming preponderance

Extreme localization of damage in conventional brittle materials is the source of a host of undesirable effects. We show how artificially engineered metamaterials with all brittle constituents can be designed to ensure that every breakable sub-element fails independently. The main role in the proposed design is played by high contrast composite sub-structure with zero-stiffness, furnishing nonlocal

The model of diffusional deformation is revisited by accounting for the dependence of the diffusion potential on grain boundary curvature. The issue is developed through the analysis of two case-studies: the deformation of a lattice of columnar grains in conditions of Coble creep, and the rotation of a grain embedded in a polycrystal in conditions of either Nabarro-Herring creep or Coble creep. The

In this paper we investigate the mechanical problem of piercing a soft solid body with a needle. This phenomenon is controlled by the critical condition of needle insertion. Needle insertion involves physical and geometrical nonlinearities and a complex failure mechanism. To overcome the complexity of the problem, we describe needle insertion as a sharp transition between two needle-specimen configurations

The partial or complete confinement of waves in an open system is omnipresent in nature and in wave-based materials and technology. Here, we theoretically analyze and experimentally observe the formation of a trapped mode with perfect mode conversion (TMPC) between flexural waves and longitudinal waves, by achieving a quasi-bound state in the continuum (BIC) in an open elastic wave system. The latter

Motivated by recent experiments on the bending of porous strips towed through a fluid bath, a combined theoretical and experimental study is made of the bending response of perforated plates. The focus is on the practically relevant class of thin plates (with thickness h) made of a homogeneous isotropic material that is perforated with periodic distributions (with unit-cell size ε) of monodisperse

The behavior of porous materials under shock loading is a multi-scale problem bridging orders of magnitude across the macroscale geometry and the microscale pores. Under static loading, this problem is well understood, relating mechanisms of pore closure and crushing to the equivalent macroscale models. The dynamic response of porous solids under shock loading is related to the effects of viscoplasticity

A versatile constitutive model for load-carrying soft biological tissue should incorporate salient microstructural deformation mechanisms and be able to reliably predict complex non-linear viscoelastic behavior. The advancement of treatment and rehabilitation strategies for soft tissue injuries is inextricably linked to our understanding of the underlying tissue microstructure and how this defines

Aluminium alloys contain various types of intermetallic particles with different sizes, such as constituent particles and dispersoids. The main mechanism of ductile fracture in these materials is assumed to be nucleation of voids around the constituent particles, which grow during plastic deformation and eventually coalesce, resulting in material failure. The role of the dispersoids is less certain

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging

Shear localization is a frequent feature of granular materials. While the discrete element method can properly simulate such a phenomenon as long as the grain representation is accurate, it is computationally intractable when there are a large number of grains. The continuum-based finite element method is computationally tractable, yet struggles to capture many grain-scale effects, e.g., shear band

The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational

This paper presents a peridynamics-based computational approach for modelling blasting induced rock fractures. A new non-ordinary state-based peridynamics approach is proposed in conjunction with a Johnson-Holmquist (JH2) constitutive model to consider the pressure dependency, strain rate effect, and viscoplasticity of rocks under blasting loads. The fracturing process in a rock is assessed based on

Imaging studies have shown, and more recently quantified, the collagen fiber dispersions within the aortic wall. Simultaneously, experimental and numerical studies highlight a significant influence of the dispersion on the aortic mechanical response. On the other hand, none of the numerical studies describing the adaptation of healthy and diseased aortas in response to different stimuli take fiber

Nucleic acid is indispensable to most viruses, and its mechanical property is an important factor for virus infectivity. Recent experiments found a temperature dependence of viral apparent stiffness, which stirred up controversy if apparent stiffness variation was ascribed to temperature-dependent structure variation of viral DNA. This paper is aimed to clarify this controversy by exploring the mechanism

Boundary modes localized at the edge or on the interface of topological mechanical lattices are analogous to their electronic counterparts in topological insulators and are robust and immune to structural imperfections. Most studies on the boundary modes in mechanical lattices are based on band theories, focusing on amplitude-independent behaviors at different frequency ranges. However, highly distorted

The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies

Crack-like objects that propagate along frictional interfaces, i.e. frictional shear cracks, play a major role in a broad range of frictional phenomena. Such frictional cracks are commonly assumed to feature the universal square root near-edge singularity of ideal shear cracks, as predicted by Linear Elastic Fracture Mechanics. Here we show that this is not the generic case due to the intrinsic dependence

We present an approach to solving problems in computational micromechanics that is amenable to massively parallel calculations through the use of graphical processing units (GPUs) and other accelerators. We apply it to study microstructure evolution in polydomain liquid crystal elastomers (LCEs). LCEs are rubber-like solids where rod-like nematic molecules are incorporated into the main or a side polymer

The present contribution aims to revisit higher-order homogenization schemes towards micromorphic media based on variational principles and an extension of Hill macrohomogeneity condition. Starting from the microscopic Cauchy balance equations, the local balance equations of the micromorphic continuum are formulated, highlighting the micromorphic stress measures. Relying on both energy and complementary

Precise understanding on the temperature and time-dependent deformation in lithium-metal anode is of compelling need for durable service of Li-based batteries. Due to both temporal and spatial intertwined thermal agitations and the scarcity of experiments, faithful deformation map of Li-metal covering a broad range of service condition is still lacking. Here we design a physics-driven machine learning

Surface instabilities on the top surface of a soft elastomeric dielectric layer bonded on its bottom to a stiff substrate are investigated for two electro-static conditions: (I) a voltage difference imposed across the top and bottom surfaces of the layer which are both conducting, and (II) a voltage difference imposed across a rigid planar electrode above the layer and the conducting top surface of

Rupture of emerging tough hydrogels has received much attention in recent years. It is a fundamental question what length of initial flaws can significantly affect the rupture of a tough hydrogel. Here we study the rupture of a tough hydrogel, using samples with and without initial cuts, under monotonic and cyclic loads. We prepare six samples under the same conditions, either without initial cut,

We probe mechanisms controlling the nonlinear elastodynamic response of intact and fractured rock under both fluid-saturated and dry conditions. We present the results of dynamic acoustoelastic testing (DAET) on Westerly granite in three states: dry-intact, dry-fractured and saturated-fractured to study the influence of in-situ stress, fracture and saturation state on nonlinear elastodynamic behavior

This paper addresses the question of the homogenization of fracture properties for three-dimensional disordered brittle solids. The effective toughness, identified as the minimum elastic energy release rate required to ensure crack growth, is predicted from a semi-analytical framework inspired by both micromechanics and statistical physics, that encompasses the decisive influences of both the material

In this two-part article, we propose elastic models of disordered alloys to study the statistical properties of the random displacement and stress fields emerging from the random distributions of atoms of different sizes. In Part I, we presented real- and Fourier-space approaches enabling to obtain the amplitude of the fluctuations through the mean square displacements and stresses. In the present

Hydrogels are mechanically stabilized through the action of external agents which induce the formation of crosslinks in the polymer network as a consequence of transport and reactive mechanisms. Crosslinking increases the stiffness of the construct, produces inelastic deformations in the polymer network and interacts with the swelling capacity of hydrogels. The control of this process is hence crucial

Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for elastic ribbons with thickness t, width a and length ℓ, assuming t≪a≪ℓ. It takes the form of a rod model with a specific non-linear constitutive law accounting for both the stretching and the bending of the ribbon mid-surface. The model is asymptotically correct and can handle finite rotations. Two popular

In concentrated solid solutions, the random distribution of elements of different sizes induces characteristic displacement and stress fields at the root of solid solution strengthening. The aim of this two-part article is to derive the statistical properties of these elastic fields. The present Part I focuses on the variance of the elastic fields, while Part II addresses their spatial correlations

Mechanical behavior of functionally graded materials (FGMs) with the presence of defects, such as dislocations and cracks, is of great scientific interest and practical importance. Existing methods for dislocation and crack problems are typically for homogenous materials or inhomogeneous materials with special kinds of variations in material properties, for instance variable shear modulus according

We present a novel, fully three-dimensional approach to soft material characterization and constitutive modeling with relevance to soft biological tissue. Our approach leverages recent advances in experimental techniques and data-driven computation. The experimental component of this approach involves in situ mechanical loading in a magnetic field (using MRI), yielding the entire deformation tensor

An isotropic multi-surface model of porous material plasticity is derived and employed to investigate the effects of the third stress invariant in ductile failure. The constitutive relation accounts for both homogeneous and inhomogeneous yielding of a material containing a random distribution of voids. Individual voids are modeled as spheroidal but the aggregate has no net texture. Ensemble averaging

Adherent cells are able to actively generate internal forces, channelled by cytoskeletal protein filaments and transmitted through transmembrane receptors to the surrounding environment by means of focal adhesions. Cells also dynamically interact with extracellular matrix by sensing external chemo-mechanical stimuli and then inducing formation of stress fibres mediated by polymerization/de-polymerization

One of the fundamental but unsolved problems in the phase-field theory is how to obtain the energy density expression based on an arbitrary cohesive law. In this paper, we propose a phase-field model with the energy density determined by the cohesive law with an arbitrary form, which builds a rigorous link between the phase-field theory and the cohesive zone theory. Using the proposed method, the energy

In this study, we explore the mechanics of a bigon and a bigon ring from a combination of experiments and numerical simulations. A bigon is a simple elastic network consisting of two initially straight strips that are deformed to intersect with each other through a fixed intersection angle at each end. A bigon ring is a novel multistable structure composed of a series of bigons arranged to form a loop

Body-Centered Cubic (BCC) metals exhibit anomalous mechanical properties such as twinning/anti-twinning and tension/compression asymmetry, which are attributed to asymmetric behavior of screw dislocations. Unlike Face-Centered Cubic (FCC) metals, the Critical Resolved Shear Stress (CRSS) of BCC metals deviates from the Schmid law. We use a mesoscale modeling approach called Phase Field Dislocation

Bio-inspired network materials composed of regularly aligned repeating filamentary microstructures exhibit promising application prospects in tissue engineering and bio-integrated devices due to the typical J-shaped mechanics curve precisely matched to the biological tissues. During the tensile process, an evident nonlinear mechanical anisotropy is induced by the drastic changes of microstructure geometries

In the present work, two methods, named “continuous” and “discrete”, are proposed to model the fragmentation process in brittle solids. Both methods rely on a preliminary analysis of the existing flaws population in scanned samples with X-ray micro-Computed Tomography (microCT). By converting the size of defects into critical stresses, the density of critical defects versus the applied stress level

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences

Viscoelastic material properties at high strain rates are needed to model many biological and medical systems. Bubble cavitation can induce such strain rates, and the resulting bubble dynamics are sensitive to the material properties. Thus, in principle, these properties can be inferred via measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such bubble-dynamic high-strain-rate

This paper presents a class of 3D single-scale isotropic materials with tunable stiffness and buckling strength obtained via topology optimization and subsequent shape optimization. Compared to stiffness-optimal closed-cell plate material, the material class reduces the Young’s modulus to a range from 79% to 58%, but improves the uniaxial buckling strength to a range from 180% to 767%. Based on small

The bond formation among polymer filaments in the fused deposition modeling (FDM) determines the mechanical behavior of resultant parts and structures. A transient updated Lagrangian finite element formulation is proposed to simulate the bond formation among molten filaments in the FDM process with flexibility in dealing with complex geometry, boundary conditions and gravitational load. Qualitative