Journal of The Mechanics and Physics of Solids最新文献

{"title":"Thermodynamic potentials for viscoelastic composites","authors":"Martín I. Idiart","doi":"10.1016/j.jmps.2024.105936","DOIUrl":"10.1016/j.jmps.2024.105936","url":null,"abstract":"<div><div>Explicit expressions for the free-energy and dissipation densities of viscoelastic composites at fixed temperature are proposed. The composites are comprised of an arbitrary number of distinct constituents exhibiting linear Maxwellian rheologies and distributed randomly at a length scale that is much smaller than that over which applied loads vary significantly. Central to their derivation is the recognition that any viscous deformation field can be additively decomposed into an irrotational field and a solenoidal field in such a way that variational approximations available for elastic potentials become applicative to viscoelastic potentials. The thermodynamic potentials conform to a generalized standard model with a finite number of effective internal variables with explicit physical meaning. Specific approximations of the Hashin–Shtrikman and the Self-Consistent types are worked out in detail. Under particular circumstances, these approximations may turn out exact. Macroscopic stress–strain relations and intraphase statistics of the stress field up to second order are also provided.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105936"},"PeriodicalIF":5.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parametric extended physics-informed neural networks for solid mechanics with complex mixed boundary conditions","authors":"Geyong Cao,&nbsp;Xiaojun Wang","doi":"10.1016/j.jmps.2024.105944","DOIUrl":"10.1016/j.jmps.2024.105944","url":null,"abstract":"<div><div>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 imposing boundary conditions (BCs) in the training and prediction of neural networks (NNs) has long been a significant challenge in the application and research of PINNs. This paper integrates the concept of isogeometric analysis (IGA) by parameterizing the physical model of the structure with spline basis functions to form analytical distance functions (DFs) for arbitrary structural boundaries. Meanwhile, by means of the energy approach to circumvent the solution of boundary stress components, the accurate imposition of both Dirichlet and Neumann BCs is ultimately achieved in PINNs. Additionally, to accommodate the complex mixed BCs often encountered in engineering applications, where Dirichlet and Neumann BCs simultaneously appear on adjacent irregular boundary segments, structural subdomain decomposition and multi-subdomain stitching strategies are introduced. The effectiveness and accuracy of the proposed method are verified through two numerical experiments with various cases.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105944"},"PeriodicalIF":5.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Time-dependent constitutive behaviors of a dynamically crosslinked glycerogel governed by bond kinetics and chain diffusion","authors":"Ji Lin ,&nbsp;Md. Tariful Islam Mredha ,&nbsp;Rumesh Rangana Manimel Wadu ,&nbsp;Chuanqian Shi ,&nbsp;Rui Xiao ,&nbsp;Insu Jeon ,&nbsp;Jin Qian","doi":"10.1016/j.jmps.2024.105951","DOIUrl":"10.1016/j.jmps.2024.105951","url":null,"abstract":"<div><div>Soft materials featuring dynamic networks represent a burgeoning frontier in materials science, offering multifaceted applications spanning soft robotics, biomaterials, and flexible electronics. Unraveling the time-dependent constitutive behavior of these materials, rooted in dynamic networks, stands as a pivotal pursuit for engineering advancements. Herein, we fabricate a tough and extreme-temperature-tolerant glycerogel with a polymer network crosslinked by metal-coordination crosslinkers and conduct a thorough analysis of its intricate mechanical responses across monotonic loading, relaxation, creep, and cyclic tests. We then develop a physically grounded constitutive model integrating the dynamics of crosslinker association/dissociation and polymer chain diffusion, furnishing a holistic framework to elucidate their interplay. We employ a statistical description, using density functions of chains in terms of end-to-end vectors, to characterize network reconfiguration. The evolution of chain density under external load, mediated by crosslinker kinetics and chain diffusion in a viscous medium, leads to intriguing variations in elastic energy and stress responses. Through meticulous experimental validation and numerical simulations, we demonstrate the efficacy of the model in forecasting the mechanical behavior of dynamic polymer networks under diverse loading scenarios, encompassing strain rate effects, stress relaxation, Mullins effect, and self-recovery phenomena. Our findings provide valuable insights into the design and optimization of dynamic network-based materials for diverse applications in biomedical and engineering fields.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105951"},"PeriodicalIF":5.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Micromechanics-based variational phase-field modeling of fatigue fracture","authors":"Mina Sarem ,&nbsp;Nuhamin Eshetu Deresse ,&nbsp;Els Verstrynge ,&nbsp;Stijn François","doi":"10.1016/j.jmps.2024.105932","DOIUrl":"10.1016/j.jmps.2024.105932","url":null,"abstract":"<div><div>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 like frictional sliding and microcrack opening. We first improve the algorithm’s stability during loading–unloading in the tensile regime through a modification of the plasticity evolution equations. Next, we incorporate fatigue damage accumulation and deterioration due to cyclic loading into the micromechanics-based phase-field model. A fatigue degradation function, driven by free energy accumulation, is introduced to degrade the fracture energy upon reaching a specified threshold during cyclic loading. Various cyclic loads are applied to benchmark tests, both with and without imperfections (e.g. holes, inclusions, voids), under plane strain conditions to capture diverse failure modes. The results demonstrate the model’s capability to accurately describe tensile, shear, and mixed-mode fracture under cyclic loading. Furthermore, the model effectively simulates key features of fatigue behavior, including crack nucleation, growth, and coalescence.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105932"},"PeriodicalIF":5.0,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Magnetostriction of soft-magnetorheological elastomers","authors":"Eric M. Stewart,&nbsp;Lallit Anand","doi":"10.1016/j.jmps.2024.105934","DOIUrl":"10.1016/j.jmps.2024.105934","url":null,"abstract":"<div><div>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 <em>magnetostriction</em> 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 subjected to an axially applied magnetic field the magnetostriction is strongly dependent on their aspect-ratio, with specimens with a low ratio of the length to the diameter exhibiting a larger tensile magnetostrictive strain than specimens with a large aspect-ratio — the “shape-effect.” This response is also hysteretic because of the underlying viscoelasticity of the matrix material. In this paper we report on a large deformation magneto-viscoelasticity theory for s-MREs and its finite element implementation. Using our theory we show that we can model this non-intuitive geometry-dependent magnetostrictive response of cylindrical s-MRE specimens. We show that the effect of the magnetization <span><math><mi>m</mi></math></span> of the cylinder is to <em>decrease</em> the magnetic field <span><math><mi>h</mi></math></span> within the cylinder relative to the applied magnetic field <span><math><msup><mrow><mi>h</mi></mrow><mrow><mi>app</mi></mrow></msup></math></span> outside the cylinder, the well-known <em>demagnetization effect</em>, and that this demagnetization is diminished in more slender cylinders due to magnetic fringing at the boundaries of the cylinder. This is the physical reason behind the macroscopically-observed “shape-effect.”</div><div>Our magneto-viscoelasticity theory is quite broad, and it has many potential applications beyond modeling the magnetostriction of cylindrical specimens. As an example we apply the theory to study the bending actuation response of beams of s-MREs when they are subjected to magnetic fields at different incidence angles to their longitudinal axis.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105934"},"PeriodicalIF":5.0,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The topological dynamics of continuum lattice grid structures","authors":"Yimeng Sun ,&nbsp;Jiacheng Xing ,&nbsp;Li-Hua Shao ,&nbsp;Jianxiang Wang","doi":"10.1016/j.jmps.2024.105935","DOIUrl":"10.1016/j.jmps.2024.105935","url":null,"abstract":"<div><div>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 a theorem, with a clear criterion for the infinite number of topological phase transitions. Then, we obtain analytical expressions for the topological phases of bulk bands, and propose a topological index related to the topological phases that determines the existence of the edge states. The theoretical approach is directly applicable to a broad range of continuum lattice grid structures including bridge-like frames, square frames, kagome frames, continuous beams on elastic springs. The frequencies of the topological modes are precisely obtained, applicable to all the bands from low to high frequencies. Continuum lattice grid structures serve as excellent platforms for exploring various kinds of topological phases and demonstrating the topological modes at multiple frequencies on demand. Their topological dynamics has significant implications in safety assessment, structural health monitoring, and energy harvesting.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105935"},"PeriodicalIF":5.0,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling yield stress scaling and cyclic response using a size-dependent theory with two plasticity rate fields","authors":"Andrea Panteghini ,&nbsp;Lorenzo Bardella ,&nbsp;M.B. Rubin","doi":"10.1016/j.jmps.2024.105930","DOIUrl":"10.1016/j.jmps.2024.105930","url":null,"abstract":"<div><div>This work considers a recently developed finite-deformation elastoplasticity theory that assumes distinct tensorial fields describing <em>macro</em>-plasticity and <em>micro</em>-plasticity, where the latter is determined by a higher-order balance equation with associated boundary conditions. Specifically, <em>micro</em>-plasticity evolves according to a contribution to the Helmholtz free-energy density that depends on a Nye–Kröner-like dislocation density tensor and is referred to as the <em>defect energy</em>. The theory is meant to set the onset of micro-plasticity at a stress level lower than that activating macro-plasticity, such as micro-plasticity aims at explaining and characterizing the increase in yield stress with diminishing size. Additionally, the formulation relies on smooth elastic–plastic transitions for both plasticity fields, even if focusing on rate-independent response. This investigation demonstrates the capability of the proposed theory to predict size-effects of interest in small-scale metal plasticity by focusing on multiple loading cycles and, prominently, on the scaling of the <em>apparent</em> yield stress with sample size, the latter being a crucial open issue in the recent literature on modeling size-dependent plasticity. To this end, this work considers the specialization of the theory to small deformations and proposes a finite element implementation for the constrained simple shear problem. Importantly, it is shown that the simplest treatment of plastic strain gradients, which consists of adopting a quadratic defect energy, can be conveniently used to predict reliable size-effects, although in the literature on strain gradient plasticity quadratic defect energies have always been associated with a relatively poor description of size-effects. In fact, in the present theory the limits of the quadratic defect energy are overcome by leveraging on the complex interplay between micro- and macro-plasticity fields. The capability of the proposed theory is quantitatively demonstrated by predicting results from the literature that are obtained from discrete dislocation dynamics simulations on planar polycrystals of grains with variable size subjected to macroscopic pure shear.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105930"},"PeriodicalIF":5.0,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Damage-induced energy dissipation in artificial soft tissues","authors":"W.K. Sun ,&nbsp;B.B. Yin ,&nbsp;K.M. Liew","doi":"10.1016/j.jmps.2024.105933","DOIUrl":"10.1016/j.jmps.2024.105933","url":null,"abstract":"<div><div>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 gap, we propose a novel energy dissipation mechanism-motivated network model that incorporates three unique physical ingredients with sound theoretical basis for the first time. These innovated features include the bond percolation-mediated network density and stiffness, the damage-induced energy dissipation and stress softening, and the entropic elasticity for the highly stretchable second network. The validity of this model was examined by implementing it within a meshfree peridynamic framework for artificial soft tissues subjected to simple tension and pure shear tests. We quantitatively correlated the dissipation with the network damage to reveal the effects of network density, the breaking stretch dispersion and the stiffness ratio. Our findings highlighted that the inhomogeneity and dispersion of materials properties play significant roles in the controllable progressive damage and dissipation, thereby offering valuable guidance for designing tougher artificial soft tissues. By reactivating the failed network, we further successfully captured the self-healing behaviors of artificial soft tissues. Our work provides an inspiring modeling framework for studying toughening mechanisms of artificial soft tissues.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105933"},"PeriodicalIF":5.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularization of softening plasticity with the cumulative plastic strain-rate gradient","authors":"G. Bacquaert ,&nbsp;J. Bleyer ,&nbsp;C. Maurini","doi":"10.1016/j.jmps.2024.105923","DOIUrl":"10.1016/j.jmps.2024.105923","url":null,"abstract":"<div><div>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 deduced from the corresponding first-order optimality conditions. To investigate the model, the problem of a bar in traction is studied. Analytical solutions are explicitly derived, and characterized by exponential localization profiles. Contrary to other regularization strategies, no spurious spreading of the plastic localization band is observed. A first numerical implementation in 1D and 2D plane strain conditions is proposed based on conic programming solvers and validated against the analytical predictions. Numerical results on plane strain von Mises plasticity show that the proposed framework leads to mesh-independent results and efficient control of plastic localization bands.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105923"},"PeriodicalIF":5.0,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142643206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective extensional–torsional elasticity and dynamics of helical filaments under distributed loads","authors":"Michael Gomez ,&nbsp;Eric Lauga","doi":"10.1016/j.jmps.2024.105921","DOIUrl":"10.1016/j.jmps.2024.105921","url":null,"abstract":"<div><div>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 are coupled. Importantly, our analysis is asymptotically exact in the limit of a ‘highly-coiled’ filament (<em>i.e.</em>, when the helical wavelength is much smaller than the characteristic lengthscale over which the filament bends due to external loading) and is able to account for large, unsteady displacements. In addition, our analysis yields explicit conditions on the external loading that must be satisfied for a straight helix axis. In the small-deformation limit, we exactly recover the coupled wave equations used to describe the free vibrations of helical coil springs, thereby justifying previous equivalent-rod approximations in which linearised stiffness coefficients are assumed to apply locally and dynamically. We then illustrate our theory with two loading scenarios: (I) a heavy helical rod deforming under its own weight; and (II) the dynamics of axial rotation (twirling) in viscous fluid, which may be considered as a simple model for a bacteria flagellar filament. In both scenarios, we demonstrate excellent agreement with solutions of the full Kirchhoff rod equations, even beyond the formal limit of validity of the ‘highly-coiled’ assumption. More broadly, our analysis provides a framework to develop reduced models of helical rods in a wide variety of physical and biological settings, and yields analytical insight into their elastic instabilities. In particular, our analysis indicates that tensile instabilities are a generic phenomenon when helical rods are subject to a combination of distributed forces and moments.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"194 ","pages":"Article 105921"},"PeriodicalIF":5.0,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}