Journal of The Mechanics and Physics of Solids最新文献

{"title":"Characterizing dissipated energy density distribution and damage zone in double network hydrogels","authors":"Jiapeng You ,&nbsp;Chong Wang ,&nbsp;Zhixuan Li ,&nbsp;Zishun Liu","doi":"10.1016/j.jmps.2024.106006","DOIUrl":"10.1016/j.jmps.2024.106006","url":null,"abstract":"<div><div>The double network hydrogels (DN gels) process high fracture toughness due to their considerable energy dissipation during fracture. To effectively interpret the energy dissipation, it is imperative to conduct a study on the quantitative characterization of the dissipated energy density distribution and the damage zone around the crack tip. In this study, we propose a series of tearing tests on pre-stretched DN gel specimens to quantitatively characterize the dissipated energy density distribution. According to the dissipated energy density distribution, the damage zone of the DN gel during tearing is divided into three parts: hardening zone, yielding zone and pre-yielding zone. The dissipated energy density distribution determines both the feature size and the contribution of these damage zones to the fracture toughness. We reveal that both the dissipated energy density and the feature size of the damage zones significantly influence the fracture toughness. Additionally, this study delves into the effect of the first network's cross-linking degree on the dissipated energy density distribution and damage zone. The dissipated energy density distribution, determined by tearing test, is validated by available experimental results, which show good agreement. This study proposes a quantitatively experimental method to investigate the dissipated energy density distribution and damage zone. It is anticipated that this approach will provide new insights into the energy dissipation mechanism of soft materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106006"},"PeriodicalIF":5.0,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867401","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 tube-based constitutive model of brain tissue with inner pressure","authors":"Wei Liu ,&nbsp;Zefeng Yu ,&nbsp;Khalil I. Elkhodary ,&nbsp;Hanlin Xiao ,&nbsp;Shan Tang ,&nbsp;Tianfu Guo ,&nbsp;Xu Guo","doi":"10.1016/j.jmps.2024.105993","DOIUrl":"10.1016/j.jmps.2024.105993","url":null,"abstract":"<div><div>Many blood vessels exist in brain tissue. Their internal blood pressure plays a crucial role in physiological disorders, such as brain edema, stroke, or traumatic brain injury (concussion). Homogenized continuum mechanics-based brain tissue models can provide an attractive approach to rapidly simulate blood-pressure related physiological disorders, and traumatic brain injury. These homogenized models are much easier and faster to apply compared to finite element models that detail the microstructure. This paper thus presents a homogenized constitutive model for brain tissue in which the vascular networks and blood pressure are taken into account. The proposed model is microstructurally motivated and derived, in which the matrix of the brain tissue (gray/white matter) is modeled as hyperelastic material, while the blood vessels with their inner pressure define the microstructure. The proposed constitutive model is implemented in finite element software. Despite the simplicity of the model, we show it predicts strains and stresses comparable to finite element models with detailed microstructural representations under different loading conditions, demonstrating the potential usefulness of the model in rapidly estimating brain injury risk, hematoma formation, as well as brain tissue expansion/shrinkage.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 105993"},"PeriodicalIF":5.0,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867402","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":"Topological state switches in hard-magnetic meta-structures","authors":"Quan Zhang,&nbsp;Stephan Rudykh","doi":"10.1016/j.jmps.2024.106001","DOIUrl":"10.1016/j.jmps.2024.106001","url":null,"abstract":"<div><div>We propose a metamaterial design principle that enables the remote switching of topological states. Dynamic breaking of space-inversion symmetry is achieved through the intricate design of magnetic spring structures within the metamaterial building blocks, whose stiffness can be remotely altered using an external magnetic field. We develop a mathematical model to predict the magnetic field-induced deformation and tangential stiffness of the spring structure with hard-magnetic constituent phase. Building on the predictive model, we explore the necessary conditions – including the magnetization distribution and the direction of the actuating magnetic field – that enable magnetically tunable stiffness. To demonstrate the functionality of topological state switching, we apply the proposed magnetic spring to the topological metamaterial design where a tunable stiffness landscape is essential for reversible topological phase transition. Our mathematical modeling indicates that we can remotely modulate both the dispersion properties and the topological invariants (including Zak phase and winding number) of the underlying bands in the proposed metamaterial system. Finally, we show that this tunable capability extends to controlling topologically protected edge and interface states within the finite-sized metamaterial lattice. Our design strategy for the switching of topological state paves the way for the realization of smart and intelligent metamaterials featuring tunable and active wave dynamics. It also highlights the potential of magneto-mechanical coupling in the design of advanced functional materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106001"},"PeriodicalIF":5.0,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142788943","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 continuum model for novel electromechanical-instability-free dielectric elastomers","authors":"Rui Xiao ,&nbsp;Zike Chen ,&nbsp;Ye Shi ,&nbsp;Lin Zhan ,&nbsp;Shaoxing Qu ,&nbsp;Paul Steinmann","doi":"10.1016/j.jmps.2024.105994","DOIUrl":"10.1016/j.jmps.2024.105994","url":null,"abstract":"<div><div>Traditional dielectric elastomers exhibit an unstable response when the electric field reaches a certain threshold, known as electro-mechanical instability, which significantly limits the broad application of these soft active materials. Recently, a bimodal-networked dielectric elastomer has been designed without suffering from the electro-mechanical instability due to a clear strain stiffening effect in the median strain regime (<em>Science, 2022, 377, 228</em>). In this work, we develop a constitutive model to fully describe the mechanical and electro-activated response of this novel dielectric elastomer. The free energy density consists of a time-independent hyperelastic component, time-dependent viscous components and an electrical component. A hyperelastic function dependent on both the first and second strain invariants is proposed to fully capture the stress response. The form of ideal dielectric elastomers is adopted for the electrical free energy. With further incorporation of viscous effects, the model is able to describe both static electro-actuated behavior as well as the frequency-dependent actuation performance upon a square wave voltage loading. The model is also implemented for finite element analysis to design tubular actuators which have been extensively used in the area of soft robotics.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 105994"},"PeriodicalIF":5.0,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821092","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 constitutive model for amorphous solids considering intrinsic entangling of shear and dilatation, with application to studying shear-banding","authors":"W. Rao ,&nbsp;Y. Chen ,&nbsp;L.H. Dai ,&nbsp;M.Q. Jiang","doi":"10.1016/j.jmps.2024.106002","DOIUrl":"10.1016/j.jmps.2024.106002","url":null,"abstract":"<div><div>In amorphous solids, shear transformations, as elementary rearrangement events operating in local regions, are intrinsically entangled with dilatation deformation, which results in the physical process of the shear band being complex. To capture such entanglement, we propose a finite-deformation continuum framework for amorphous solids by incorporating nonequilibrium thermodynamics. Within this framework, we develop a constitutive model where the thermodynamic glass is divided into the kinetic and configurational subsystems. In the model, the dilatation is attributed to an athermal expansion of configuration. As a result, the effect of shear transformation on dilatation can be considered by generating plastic cold work to change the freedom degrees of the configurational subsystem. The effect of dilatation on shear transformation can be realized through the enthalpy change of the configurational subsystem that gives rise to physical aging. Based on the proposed model, we discuss the entangling mechanism of shear and dilatation, and predict the shear-banding behaviors of metallic glasses during tensile and compressive deformations at room temperature. We reveal that due to the shear-dilatation entanglement, the elastic deformations significantly influence the evolution of configurational temperature, which plays a pivotal role in controlling the degree of strain softening and the shear-banding mode.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106002"},"PeriodicalIF":5.0,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821095","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":"Biomimetic Turing machine: A multiscale theoretical framework for the inverse design of target space curves","authors":"JiaHao Li ,&nbsp;Xiaohao Sun ,&nbsp;ZeZhou He ,&nbsp;YuanZhen Hou ,&nbsp;HengAn Wu ,&nbsp;YinBo Zhu","doi":"10.1016/j.jmps.2024.105999","DOIUrl":"10.1016/j.jmps.2024.105999","url":null,"abstract":"<div><div>Morphing ribbons and their inverse design are usually confined to plane curves, since in most cases only the curvature is considered. Given that curvature and torsion are equally important geometric characteristics of space curves, it is urgent to propose a systematic theoretical framework for the inverse design. Toward this end, we here present a multiscale theoretical framework named biomimetic Turing machine (BTM) to achieve desired target space curves, which is inspired from two microstructural regulation mechanisms behind the hydration-driven morphing of plant tissues: the graded curvature regulated by matrix volume fraction (<em>c_m</em>) and the helix-like morphology regulated by fibril orientation angle (FOA). By analogizing to Turing machine encoded by binary mapping, the proposed BTM can inversely encode a morphing ribbon with preset microstructural parameters (FOA and <em>c_m</em>) to achieve desired target space curves. The proposed theoretical framework can first bridge the microstructural fiber-matrix swelling and the macroscopic ribbon morphing as a forward problem, in which a twist field is subsequently introduced to create the kinematic map between the target space curve and the ribbon, innovatively posing the inverse design as an initial value problem. To facilitate the experimental implementation of BTM, we further propose an optimization strategy for selecting the twist field and provide design criteria as guidelines for experiments. As a conceptual display, we present a phase diagram in the <em>c_m</em> versus FOA plane to illustrate the complex target morphologies (e.g., hemisphere, hyperboloid, and tendril) characterized by various parameters of curvature and torsion designed rationally by the BTM theory, while in previous studies the morphing morphologies (e.g., helices, arcs, and helicoid ribbons) exhibit only constant curvature or torsion. This work presents a novel inverse design strategy for space curves with both curvature and torsion, broadening the potential for the design and fabrication of morphing materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 105999"},"PeriodicalIF":5.0,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821094","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 constitutive model of monodomain liquid crystal elastomers with the thermal-mechanical-nematic order coupling","authors":"Weida Kang ,&nbsp;Qian Cheng ,&nbsp;Changyue Liu ,&nbsp;Zhijian Wang ,&nbsp;Dongfeng Li ,&nbsp;Xudong Liang","doi":"10.1016/j.jmps.2024.105995","DOIUrl":"10.1016/j.jmps.2024.105995","url":null,"abstract":"<div><div>Liquid crystal elastomers (LCEs) are a distinctive class of materials that combine the transformative properties of liquid crystals with the flexibility of elastomers, enabling significant reversible deformations in response to various external stimuli. This paper investigates the intricate thermal-mechanical-nematic order coupling behaviors of monodomain nematic LCEs. We propose an enhanced constitutive model that merges the established neo-classical theory with the Landau–de Gennes theory, thereby improving the model's ability to account for temperature influences effectively. Additionally, we use the concept of semi-soft elastic energy and consider the anisotropic behaviors associated with the orientations of the nematic directors, aiming to more accurately capture the nuances of their soft elastic and anisotropic properties under varied loading conditions. The present model has been numerically discretized and implemented in the commercial finite element software, facilitating precise simulations of the stress-stretch relationships and the anisotropic mechanical behaviors associated with specific director orientations. Constitutive simulations have shown a high degree of accuracy, aligning well with experimental data, especially in predicting the complex mechanical behaviors of LCEs under different thermal-mechanical conditions. Our results elucidate the necking observed during uniaxial loading and the unique director evolution during biaxial loading. Additionally, we identify a unique hole-size insensitivity in perforated LCE sheets, attributed to the compensation between anisotropic reinforcement and director orientations. These findings underscore the potential of advanced modeling techniques in exploring the dynamic properties of LCEs, paving the way for applications in artificial muscles, soft robotics, and responsive biomedical devices.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 105995"},"PeriodicalIF":5.0,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163413","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":"Phase field fracture in elastoplastic solids: a stress-state, strain-rate, and orientation dependent model in explicit dynamics and its applications to additively manufactured metals","authors":"Cunyi Li ,&nbsp;Jian Liu ,&nbsp;Le Dong ,&nbsp;Chi Wu ,&nbsp;Grant Steven ,&nbsp;Qing Li ,&nbsp;Jianguang Fang","doi":"10.1016/j.jmps.2024.105978","DOIUrl":"10.1016/j.jmps.2024.105978","url":null,"abstract":"<div><div>Phase field models have gained increasing popularity in analysing fracture behaviour of materials. However, few studies have been explored to simulate dynamic ductile fracture to date. This study aims to develop a phase field framework that considers strain rate, stress state, and orientation dependent ductile fracture under dynamic loading. Firstly, the governing equations of displacement and phase fields are formulated within an explicit finite element framework. Secondly, constitutive relations are established using a hypoelastic-plasticity framework, encompassing the influence of material orientation and strain rate on both plasticity and fracture initiation. Stress state dependent fracture initiation is also considered. Thirdly, the finite element implementation and corotational formulation of constitutive equations are derived. Finally, to validate the proposed model, additively manufactured samples, including material-level and crack propagation specimens, are tested under dynamic loading conditions. Overall, the proposed phase field model can properly reproduce the experimental force-displacement curves and crack paths. Uniaxial tension tests reveal that a higher strain rate can lead to a higher hardening curve and reduced ductility. Other material specimens further demonstrate the model's capability to predict stress state and orientation dependent dynamic fracture. To simulate dynamic crack paths accurately, it is necessary to consider anisotropic fracture initiation. Lastly, the phase field model was applied for the first time to predict the dynamic response of triply periodic minimal surface (TPMS) structures. Dynamic crack patterns were effectively captured, and the fracture mechanisms were thoroughly analysed. This study provides an explicit phase field framework for dynamic ductile fracture, with applications to additively manufactured materials and structures.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"197 ","pages":"Article 105978"},"PeriodicalIF":5.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143294172","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":"A hyperelastic constitutive model for soft elastomers considering the entanglement-dependent finite extensibility","authors":"Jinglei Yang ,&nbsp;Kaijuan Chen ,&nbsp;Chao Yu ,&nbsp;Kun Zhou ,&nbsp;Guozheng Kang","doi":"10.1016/j.jmps.2024.106000","DOIUrl":"10.1016/j.jmps.2024.106000","url":null,"abstract":"<div><div>In this paper, a novel hyperelastic constitutive model for soft elastomers is developed based on the concept of the tortuous tube. This model incorporates the finite extensibility of the polymer chain, the entanglement contribution to elasticity and the non-affine micro-to-macro scale transition in a unified way. To reflect the entanglement effect and its influence on the deformation of soft elastomers, the tortuous tube concept is introduced. The finite extensibility and conformational statistics of an entangled polymer chain in such a tortuous tube are clarified. By embedding the tortuous tube into the microsphere and employing the principle of minimum averaged free energy, a new non-affine scale transition rule is proposed to establish the relationship between the local deformation of a polymer chain at the microscopic scale and the overall deformation at the macroscopic scale. Based on the probability density function related to the conformational statistics, the Helmholtz free energy is established and further decoupled into a volumetric part and an isochoric part. The spatial Kirchhoff stress tensor and spatial elasticity tensor are derived from the newly established Helmholtz free energy. The proposed model is further implemented into the finite element program ABAQUS by writing a user-defined material subroutine. The prediction capability of the proposed model is verified by simulating the homogeneous and inhomogeneous deformations of soft elastomers under various loading modes, including uniaxial tension, uniaxial compression, pure shear, equi-biaxial tension, general biaxial tensile loadings, inflation and indentation. Moreover, the influence of entanglement concentration on the stretchability and stiffness of soft elastomers is predicted and discussed using the proposed model.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106000"},"PeriodicalIF":5.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142788946","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":"Fracture process zone and fracture energy of heterogeneous soft materials","authors":"Xiang Wu,&nbsp;Xiao Li,&nbsp;Shuo Sun,&nbsp;Yilin Yu,&nbsp;Zhengjin Wang","doi":"10.1016/j.jmps.2024.105997","DOIUrl":"10.1016/j.jmps.2024.105997","url":null,"abstract":"<div><div>Bio-inspired heterogeneous soft materials are under rapid development due to their superior fracture and fatigue resistance. In the last few years, several kinds of fibrous soft composites in different length scales have been fabricated. However, the fracture behavior and toughening mechanism of this class of materials are still elusive. Here we develop a theoretical model for the crack tip field of fiber reinforced soft composites. The distribution of deformation around the crack tip and released elastic energy during crack propagation are obtained. The fracture process zone and fracture energy are quantified. There is a critical sample height, below which the fracture process zone size and fracture energy are size-dependent, above which they approach material-specific constants: steady-state fracture process zone size and steady-state fracture energy. A formula is derived to relate the steady-state fracture process zone size and parameters of the composite. It is found that both the steady-state fracture process zone size and the critical sample height scale with the fractocohesive length of the composite. The steady-state fracture energy of the composite can be enhanced either by enlarging the fracture process zone size through tuning fiber geometry or by increasing the work to rupture of the fiber through chemical treatment. This work reveals the toughening mechanism of heterogeneous soft materials and paves the way to design soft materials of high fracture energy, high fatigue threshold, and low hysteresis. It also provides a practical guideline for determining the sample size to measure the steady-state fracture energy of heterogeneous soft materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 105997"},"PeriodicalIF":5.0,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142788949","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}