Journal of The Mechanics and Physics of Solids最新文献

{"title":"Unveiling the Evolving Fracture Toughness: The R-curve Phenomenon in Double Network Hydrogels","authors":"Wenjing Lu, Shuai Xu, Chong Wang, Zishun Liu","doi":"10.1016/j.jmps.2026.106531","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106531","url":null,"abstract":"Double network (DN) hydrogels exhibit remarkable mechanical properties, most notably their high fracture toughness, which expands their potential applications across various fields. To guarantee the reliability of DN gels in practical uses, an in-depth comprehension of their fracture characteristics is crucial. Previous studies on the fracture behavior of DN gels mainly concentrated on the crack initiation process, often treating fracture toughness as a constant characteristic of the material. In contrast, our experimental research unveils the evolving fracture toughness as a fracture resistance curve (R-curve) in DN gels, indicating that fracture toughness increases with crack propagation until reaching a plateau of steady-state state, rather than remaining constant. This phenomenon is attributed to mechanisms of crack tip softening and stress de-concentration resulting from the fracture of the brittle PAMPS network in DN gels. We have identified three critical parameters, i.e., the initiation fracture toughness (<mml:math altimg=\"si7.svg\"><mml:msub><mml:mi>G</mml:mi><mml:mtext>init</mml:mtext></mml:msub></mml:math>), steady state toughness (<mml:math altimg=\"si8.svg\"><mml:msub><mml:mi>G</mml:mi><mml:mtext>ss</mml:mtext></mml:msub></mml:math>), steady state crack extension length (<mml:math altimg=\"si9.svg\"><mml:msub><mml:mi>L</mml:mi><mml:mtext>ss</mml:mtext></mml:msub></mml:math>), to quantify this behavior. Additionally, we explore the effect of pre-damage of PAMPS network on the R-curve and develop a theoretical model linking the degree of pre-damage (h) to <mml:math altimg=\"si8.svg\"><mml:msub><mml:mi>G</mml:mi><mml:mtext>ss</mml:mtext></mml:msub></mml:math>. Our model effectively predicts the R-curve of DN gels under various pre-damage conditions. Furthermore, by considering different PAMPS network formulations, we establish a scaling law linking <mml:math altimg=\"si19.svg\"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mtext>ss</mml:mtext></mml:msub><mml:mo linebreak=\"badbreak\">−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mtext>init</mml:mtext></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> with <mml:math altimg=\"si9.svg\"><mml:msub><mml:mi>L</mml:mi><mml:mtext>ss</mml:mtext></mml:msub></mml:math>, thus creating a unified framework for understanding the internal physical properties of diverse DN gels. These insights also differentiate the toughening mechanisms in DN gels: energy dissipation from the PAMPS network affects <mml:math altimg=\"si19.svg\"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mtext>ss</mml:mtext></mml:msub><mml:mo linebreak=\"badbreak\">−</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mtext>init</mml:mtext></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>, while the <mml:math altimg=\"si7.svg\"><mml:msub><mml:mi>G</mml:mi><mml:mtext>init</mml:mtext></mml:msub></mml:math> reflects the intrinsic fracture properties governed by the elastic PAAm network. We antic","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"117 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056278","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":"A generalized higher-order phase-field model for brittle fracture in anisotropic rocks","authors":"Sijia Liu, Yunteng Wang, Xueyu Geng, Wei Wu","doi":"10.1016/j.jmps.2026.106526","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106526","url":null,"abstract":"In this work, we formulate a generalized higher-order phase-field model within the rotated anisotropic framework for simulating brittle phenomena in anisotropic rocks. Our phase-field model accounts for both the anisotropic critical fracture energy release rate and the anisotropic degradation in stiffness. The innovative aspects of this model include (i) a fourth-order structural tensor enabling simulations of strongly anisotropic fractures with arbitrary, non-orthogonal symmetry axes for capturing the complexity of natural geological media; (ii) a volumetric–deviatoric coupling energy density for transitions from anisotropic responses in the undamaged state to isotropic responses in the damaged state; (iii) a patch-based Hessian recovery algorithm ensuring stable solutions of the higher-order PDEs to reduce the computational cost; and (iv) stochastic perturbations integrated into the anisotropic crack surface density function to capture microstructural heterogeneity. Several numerical benchmark examples are provided. The numerical results are compared with some laboratory experiments on brittle fracture in anisotropic rocks.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"13 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056280","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":"Corrigendum to “Combining stretching-dominated and bending-dominated dissipation behavior to optimize energy absorption in liquid crystal elastomer-based lattice structures” [Journal of the Mechanics and Physics of Solids 209 (2026), 106497]","authors":"Beijun Shen, Yuefeng Jiang, Christopher M. Yakacki, Sung Hoon Kang, Thao D. Nguyen","doi":"10.1016/j.jmps.2026.106521","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106521","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"49 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033261","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":"Nonlinear mechanics of arterial growth","authors":"Aditya Kumar ,&nbsp;Arash Yavari","doi":"10.1016/j.jmps.2026.106525","DOIUrl":"10.1016/j.jmps.2026.106525","url":null,"abstract":"<div><div>In this paper, we formulate a geometric theory of the mechanics of arterial growth. An artery is modeled as a finite-length thick shell that is made of an incompressible nonlinear anisotropic solid. An initial radially-symmetric distribution of finite radial and circumferential eigenstrains is also considered. Bulk growth is assumed to be isotropic. A novel framework is proposed to describe the time evolution of growth, governed by a competition between the elastic energy and a <em>growth energy</em>. The governing equations are derived through a two-potential approach and using the Lagrange-d’Alembert principle. An isotropic dissipation potential is considered, which is assumed to be convex in the rate of growth function. Several numerical examples are presented that demonstrate the effectiveness of the proposed model in predicting the evolution of arterial growth and the intricate interplay among eigenstrains, residual stresses, elastic energy, growth energy, and dissipation potential. A distinctive feature of the model is that the growth variable is not constrained by an explicit upper bound; instead, growth naturally approaches a steady-state value as a consequence of the intrinsic energetic competition. Several numerical examples illustrate the efficiency and robustness of the proposed framework in modeling arterial growth.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106525"},"PeriodicalIF":6.0,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033265","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":"Contact in strain gradient elasticity: The rigid flat punch problem","authors":"P.A. Gourgiotis ,&nbsp;Th. Zisis ,&nbsp;A.E. Giannakopoulos ,&nbsp;H.G. Georgiadis","doi":"10.1016/j.jmps.2026.106527","DOIUrl":"10.1016/j.jmps.2026.106527","url":null,"abstract":"<div><div>This work revisits the classical flat-punch indentation problem within the framework of Mindlin’s form-II strain-gradient elasticity, uncovering new phenomena driven by the interplay between contact geometry and material length scale. The analysis is carried out under plane strain conditions, and the corresponding mixed boundary value problem is solved using integral equation techniques. Two distinct contact regimes are examined. In the first, assuming full contact beneath the rigid indenter, the pressure distribution exhibits hypersingular behavior with tensile (adhesive-like) tractions near the contact edges. These arise purely from kinematic constraints, without invoking any cohesive law or surface energy. The second regime emerges by relaxing the flatness assumption, allowing for partial separation beneath the punch. In this case, contact is sustained only within a central region, flanked by separation gaps near the edges and balanced by concentrated edge reactions. The resulting pressure is entirely positive and exhibits a classical square-root singularity. Both the contact width and edge forces are shown to depend sensitively on Poisson’s ratio and the material length scale. Beyond a critical length, the contact region collapses, and the problem reduces to the superposition of two Flamant-type concentrated contact solutions. These findings reveal a rich class of indentation responses naturally captured by strain gradient elasticity-phenomena inaccessible to classical continuum models. They may have important implications for nano/micro-indentation experiments on materials with pronounced internal length scales, such as polymers, ceramics, composites, cellular solids, masonry, and biological tissues.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106527"},"PeriodicalIF":6.0,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033263","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":"Dynamic crushing of metal lattice metamaterials: Shock mode diagrams and transition to topology-independent compaction regime","authors":"Brandon K. Zimmerman,&nbsp;Eric B. Herbold,&nbsp;Mukul Kumar,&nbsp;Jonathan Lind","doi":"10.1016/j.jmps.2026.106515","DOIUrl":"10.1016/j.jmps.2026.106515","url":null,"abstract":"<div><div>Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL’ s ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. To investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a one-dimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities <span><math><mrow><mn>0.1</mn><mo>≤</mo><mover><mi>ρ</mi><mo>¯</mo></mover><mo>≤</mo><mn>0.9</mn></mrow></math></span> and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106515"},"PeriodicalIF":6.0,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033264","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":"3D Phase-Field Modeling of H2→H3 Phase Transition induced Intragranular Cracking in Single-Crystal Ni-Rich Layered Cathodes","authors":"Zhengtao Liao, Xiangbiao Liao, Yuyang Lu, Chengcheng Cao, Linghui He, Yong Ni","doi":"10.1016/j.jmps.2026.106528","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106528","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"258 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033262","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":"High-throughput dynamic experiments: The statistics of spall failure at ultra-high strain rates","authors":"Piyush Wanchoo ,&nbsp;Rohit Berlia ,&nbsp;Timothy P. Weihs ,&nbsp;K.T. Ramesh","doi":"10.1016/j.jmps.2026.106523","DOIUrl":"10.1016/j.jmps.2026.106523","url":null,"abstract":"<div><div>We describe a novel high-throughput experimental framework for dynamic loading based on an automated Laser-driven Microflyer Impact (LMI) platform. The framework is designed to rapidly explore the behavior of materials under dynamic loading, and we demonstrate this capability by performing an unprecedented number (173) of spall experiments to characterize the spall strength of a metal (polycrystalline pure copper). We examine pure polycrystalline copper with two different grain size distributions, one with a mean grain size well below 1.<em>mum</em> (referred to as the nanocrystalline copper) and one with a mean grain size  ∼ 8<em>μm</em> (referred to as the microcrystalline copper). The influence of microstructure and loading kinetics on the spall strength of metals remains poorly determined, largely due to the low throughput of conventional plate-impact experiments, motivating our study. We systematically vary the shock stress and (to a lesser degree) the tensile strain rate in our experiments, and examine the dependence of the spall strength on the prior shock stress, the tensile strain rate, and the grain size. The results provide clear evidence of a strong monotonic increase in spall strength with increasing tensile strain rate, and our microcrystalline copper results are largely consistent with the limited data available in the literature (often on material without a clearly defined grain size distribution). The influence of the prior shock stress on the spall strength is weaker than the strain rate effect, and appears (within our results) to depend also on the grain size distribution. Our results also demonstrate that our nanocrystalline copper has a significantly higher spall strength than its microcrystalline counterpart at these high strain rates. This is a reversal of the established trend that larger grain sizes can provide higher spall strengths when the grain size is sufficiently large, observed in some prior low-rate studies. Our extensive dataset provides validation data for microstructurally-aware spall models that predict an inverse grain-size dependence at high strain rates. This high-throughput LMI approach can also provide the datasets necessary for data-driven design of materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106523"},"PeriodicalIF":6.0,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014553","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":"Machine learning-energized framework for rapid and precise inverse design of programmable structures with multiple design variables","authors":"Qingqing Chen,&nbsp;Chao Yuan,&nbsp;Tiejun Wang","doi":"10.1016/j.jmps.2026.106524","DOIUrl":"10.1016/j.jmps.2026.106524","url":null,"abstract":"<div><div>Programmable structures enable autonomous deformation to achieve target three-dimensional (3D) shapes by triggering stimuli-responsive mismatch strain embedded in precursory configurations. However, the growing complexity of target 3D geometries makes it challenging to efficiently and accurately find optimal precursory design variables in a high-dimensional design space. Here, we propose a machine learning-energized framework for rapid and precise inverse design of programmable 3D structures. Firstly, a finite substructure algorithm is proposed to rapidly generate a large-scale database that accurately maps multiple design variables to programmable deformations. To this end, we decompose the full-scale structure into overlapping substructures and employ machine learning to augment the design variable-substructural deformation data pairs from limited finite element analyses. The deformed substructures are then sequentially stitched to reconstruct global deformation by optimal rotation and translation that minimize the Euclidean distance of overlapping regions. Compared to finite element analysis, the proposed finite substructure algorithm accelerates the forward prediction by four orders of magnitude. Based on the large-scale database, a well-trained neural network is obtained to inversely generate the coarse estimation of target design variables, which equips the gradient-free optimization with prior knowledge to approach the optimal result at an accelerated pace. Also, we establish a 3D printing and vacuum actuation platform to validate the inversely designed pneumatically programmable structures. Finally, we show a bio-inspired robotic arm capable of warping and grasping complex 3D objects to highlight the applicability of the proposed inverse design approach. This work provides a feasible paradigm for the inverse design of programmable structures, paving the way for potential applications in soft robotics and deployable devices.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106524"},"PeriodicalIF":6.0,"publicationDate":"2026-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995460","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 axisymmetric contact problems within strain gradient elasticity","authors":"Lucca Schek ,&nbsp;Aleksandr Morozov ,&nbsp;Sergei Khakalo ,&nbsp;Wolfgang H. Müller","doi":"10.1016/j.jmps.2026.106513","DOIUrl":"10.1016/j.jmps.2026.106513","url":null,"abstract":"<div><div>Experimental testings indicate that the effective hardness of materials, as measured in normal contacts, depends on the size of the indenter. While this effect cannot be described by classical continuum theories, such a size-dependence can be modeled with generalized continuum theories. In this study, the application of simplified strain gradient elasticity in describing frictionless normal contacts is investigated. Axisymmetric contact problems for indenters of different shape are modeled within the framework of simplified strain gradient elasticity using a rigid body penalty-based contact approach in isogeometric analysis. The numerical implementation is verified using an existing semi-analytical solution for strain gradient elasticity. This study reveals significant deviations from classical theory, particularly in the form of the pressure distribution under the indenters. It is shown that the stress singularity present in the classical solution to the indentation test of a flat cylinder vanishes in the case of strain gradient elasticity. Furthermore, the importance of gradient elasticity for describing scale effects of normal contacts with indenters is demonstrated.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106513"},"PeriodicalIF":6.0,"publicationDate":"2026-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995461","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}