Journal of The Mechanics and Physics of Solids最新文献

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 of mechanical responses induced by various generator distributions of the curved surface. The theories are then extended to multi-curve-fold origami, involving additional geometric correlations between creases. As an illustrative example, the deformation and equilibrium configuration of origami with annular creases are studied both theoretically and numerically. Afterward, single-vertex curved origami theory is studied as a special type of multi-curve-fold origami. We find that the extra periodicity at the vertex strongly constrains the configuration space, leading to a region near the vertex that has a striking universal equilibrium configuration regardless of the mechanical properties. Both theories and numerics confirm the existence of the universality in the near-field region. In addition, the far-field deformation is obtained via energy minimization and validated by finite element analysis. Our generalized multi-curve-fold origami theory, including the vertex-contained universality, is anticipated to provide a new understanding and framework for the shape programming of the curve-fold origami system.

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 the mechanical properties of hydrogels during the photopolymerization process. In this work, systematical experiments were performed to investigate mechanical properties of PAAm hydrogel under different photopolymerization condition. The results reveal a noticeable increasement in both elastic and viscous behavior of hydrogel with the advancement of polymerization. To fully capture the experimental observations, we developed a coupled photo-chemo-mechanical theoretical framework that integrates reaction kinetics with a physically-based viscoelastic constitutive model. Within this model, the degree of conversion serves as an internal variable, which related to microscopic structures such as correlation length, and tube diameter. The developed model exhibits remarkable prediction ability for hydrogels with various degree of polymerization. The current work paves a potentially new avenue for understanding the evolution of mechanical properties in photopolymerized hydrogels, providing theoretical guidance for the manufacturing of hydrogels through photopolymerization-based 3D printing.

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 sponge spicules are characterized by weak organic interfaces between brittle mineral phases. To better understand the toughening mechanisms in SBs requires simulation techniques which can resolve arbitrary interface and bulk fracture patterns.

In this work, we present a modified regularization of Variational Fracture Theory (VFT) that allows for simulation of fracture in materials and structures with weak interfaces. The core of our approach is to widen the weak interfaces on a length scale proportional to that of the diffuse damage field, and assign a reduced fracture toughness therein. We show that in 2D the modified regularized functionals $\Gamma$-converge to that for sharp cracks. The resulting thin weak interfaces have fracture toughness which depends on the bulk material fracture toughness, the widened interface fracture toughness, and the ratio of the widened interface length scale to the crack regularization length scale. We next apply our modified regularization within a computer implementation of regularized VFT, which we term RVFTI. We assess the performance of RVFTI in 2D by reproducing the effective interface fracture toughness predicted by the $\Gamma$-convergence theory and simulating crack trapping at a bi-material interface. We then use RVFTI to study toughening in SB-inspired microarchitectures, namely layered materials and materials with wavy interfaces.

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 energy balance criterion to study the approach–retraction motion of a rigid sphere in contact with a viscoelastic half-space. A strong interplay between adhesion and viscoelastic hysteretic losses is reported which can lead to strongly increased adhesion strength, depending on the loading history. Specifically, two different mechanisms are found to govern the increase of pull-off force during either approach–retraction cycles and approach – full relaxation – retraction tests. In the former case, hysteretic losses occurring close to the circular perimeter of the contact play a major role, significantly enhancing the energy release rate. In the latter case, instead, the pull-off enhancement mostly depends on the glassy response of the whole (bulk) material which, triggered by the fast retraction after relaxation, leads to a sort of ‘frozen’ state and results in a flat-punch-like detachment mechanism (i.e., constant contact area). In this case, the JKR theory of adhesive contact cannot be invoked to relate the observed pull-off force to the effective adhesion energy, i.e. the energy release rate $G$, and strongly overestimates it. Therefore, a rigorous mathematical procedure is also proposed to correctly calculate the energy release rate in viscoelastic dissipative contacts.

A generalisation of the hyperinelasticity modelling framework devised in Part I of this sequel is formulated here, by presenting a (principal) stretches-based hyperinelastic deformation energy function $W\left(F\right)$. This generalisation is based on the premise that the (principal) stretches ${\lambda }_j$ may assume any arbitrary real-valued exponents, rather than being restricted to the prescriptive powers 2 and −2, as in principal invariants-based models. The motivation behind this extension is to reduce the overall number of model parameters and thereby increase the versatility of the application of the hyperinelasticity framework, as well as to provide a more universal model. The ensuing hyperinelastic model is then applied to a wide range of extant experimental datasets encompassing foams, glassy and semi-crystalline polymers, hydrogels and liquid crystal elastomers, over both elastic and inelastic deformation ranges including yield, softening and plateau, and hardening behaviours, under tensile and compressive deformations. Upon demonstrating the favourable simulation of the foregoing behaviours by the model, its application is then extended to account for other nuanced aspects of inelasticity such as the effects of rate of deformation, crystallinity volume and angle of printing in 3D printed lattice structures. This augmentation is done via devising a generalised modelling framework which allows for the incorporation of a generic tensorial (including rank zero scalar) field of inelasticity-inducing factors into the core model, resulting in the model parameters to evolve with an appropriate measure of the factor of interest; e.g., deformation rate, crystallinity volume ratio etc. The proposed modelling framework will be shown to capture these effects proficiently. Given the simplicity of this modelling approach, as essentially an extension in the application of hyperelasticity, its versatility of implementation, and the favourable capturing of both elastic and inelastic behaviours, the devised hyperinelasticity framework is presented for application to the large elastic and inelastic deformation of polymers and elastomers.

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 terms of the PDF of the interfacial gap based on stochastic process theory, as well as the initial and boundary conditions. A finite difference method is developed to numerically solve the partial differential equation. The predicted PDF of the interfacial gap agrees well with that by Green’s Function Molecular Dynamics (GFMD) and other variants of Persson’s theory of contact at high load ranges. At low load ranges, the obvious deviation between the present work and GFMD is attributed to the overestimated mean interfacial gap and oversimplified magnification-dependent diffusion coefficient used in the present model. As one of its direct application, we show that the present work can effectively solve the adhesive contact problem under the DMT limit. The current study provides an alternative methodology for determining the PDF of the interfacial gap and a unified framework for solving the complementary problem of random contact pressure and random interfacial gap based on stochastic process theory.

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%) under ambient cyclic asymmetric uniaxial loading conditions. The motivation is that shakedown-based designs can be used to expand the feasible design space under cyclic loading conditions compared to conventional yield-limited designs. Finite element analyses with calibrated hardening models are used to develop Bree load-interaction diagrams that are experimentally validated. It is found that shakedown occurs at stress levels up to almost four times the elastic limit of the structure for a fixed allowable equivalent strain level near three percent. This shakedown multiplier is also sensitive to the extent of auxeticity in the structure and a parametric study and analytical model are used to identify underlying mechanisms and a potential maximum condition.

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 deformation or loading, for any randomly chosen admixture of imposed compression, pure shear and simple shear, without the need to re-design the cloak for different deformation modes. A full range of circular inclusions can be cloaked in this way, from soft to stiff. In consequence, we suggest that an inclusion of any arbitrary shape can also be cloaked, by first enveloping it in a stiff circle, then cloaking the combined structure with three annuli as described. Given that a single inclusion can be fully cloaked in this way, even at near field close to the cloaking perimeter, it also follows that multiple such neutral inclusions arranged with arbitrarily high packing fraction in a surrounding medium can also be cloaked. We confirm this by direct simulation. This indicates a possible route to fabricating composite materials with the same global mechanical response as a counterpart homogeneous material, and with uniform strain and stress fields outwith the cloaked inclusions.

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 order to realize novel phenomena in wave propagation. In this work, we study Willis materials that are flexoelectric and offer an electric field induced by a strain gradient. We show that in the case of flexoelectric Willis materials, the momentum also gets coupled to the strain gradient term under an effective description. Hereby, an ensemble averaging-based dynamic homogenization theory is developed for flexoelectric composites to compute constitutive relations of the macroscopic fields. This second-order Willis metamaterial offers a novel coupling termed gradient elasto-momentum coupling. The presence of non-uniform strain that can break the inversion symmetry of a unit cell is thus significant in generating the imaginary portion of all cross-couplings in the absence of asymmetric microstructures.

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, in the context of peeling configurations, defining the geometric features is challenging, resulting in relatively scant exploration of interfacial instabilities. Hence, the modulation of instability patterns during the peeling process of a flexible plate from a thin elastic film, alongside the consequential effects on mechanical responses, remains poorly understood. To elucidate the mechanisms underlying interfacial instability during peeling process and its impacts on peel-off force, we use finite element methods to simulate the evolution of interface separation. Consistent with previous experimental observations, we find that the interfacial instability will occur when the bending stiffness of the flexible plate is bigger than a critical value. We show that the interfacial instability is mainly induced by the competition between the adhesion energy and the strain energy of the film, and the incompressibility of the thin film is critical for the appearance of the interfacial instability. Combining theory and finite element simulation, we propose the scaling laws for the critical peel-off force for stable and unstable peelings, respectively, and show that the critical peel-off force will decrease when the interfacial instability occurs. Finally, we demonstrate that weakening the tangential adhesion strength and loosening the constraints between the film and the rigid substrate effectively suppress fingering instability. Collectively, our findings elucidate the pivotal factors influencing interfacial instability, offering invaluable insights for the design of structures or systems involving soft materials.