Journal of The Mechanics and Physics of Solids最新文献

{"title":"Cracking resistance of nanostructured freestanding tungsten films","authors":"S.E. Naceri ,&nbsp;M. Rusinowicz ,&nbsp;M. Coulombier ,&nbsp;T. Pardoen","doi":"10.1016/j.jmps.2025.106143","DOIUrl":"10.1016/j.jmps.2025.106143","url":null,"abstract":"<div><div>The fracture toughness <em>K_c</em> of freestanding tungsten films is explored using a MEMS-based crack-on-chip method and multiscale finite element modelling, in the context of miniaturised testing of structural materials for nuclear fusion applications. The primary ambition is to determine to what extent testing thin nanostructured tungsten films can provide relevant data with respect to bulk tungsten fracture behavior, particularly in view of irradiation testing. The second objective is to enhance fundamental knowledge on the cracking behavior of thin metallic films with a quasi-brittle response. Tungsten films with 370 nm thickness are deposited by magnetron sputtering under different pressures and characterized using grazing incidence X-ray diffraction, surface curvature measurements, scanning electron microscopy and nano-indentation. Microstructure evolution, residual stresses, and tensile properties are analyzed to confirm the BCC α-phase. The fracture toughness of the tungsten films is determined on-chip using a crack arrest approach and finite element modelling to extract <em>K_c</em>. The analysis conducted on 90 successful test structures provides an average fracture toughness value of 3.2 ± 0.36 MPa √m. This value is typically, 50 % lower than for bulk tungsten, despite the submicron thickness, while similar intergranular fracture mechanism is observed. The link with crack tip plasticity is further unravelled by XFEM-based simulations relying on a cohesive zone model. Care is taken to properly resolve the mechanical behavior of the nanometer scale fracture process zone. The calibrated peak strength is equal 7.8 GPa, which is less than two times the large yield stress of the nanocrystalline film. With such a ratio, the impact of plasticity outside the fracture process zone is limited, corresponding to negligible R curve effect and extra dissipation upon crack growth in contrast with bulk specimens for which a ratio above four is expected.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106143"},"PeriodicalIF":5.0,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874621","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 finite deformation theory of dislocation thermomechanics","authors":"Gabriel D. Lima-Chaves ,&nbsp;Amit Acharya ,&nbsp;Manas V. Upadhyay","doi":"10.1016/j.jmps.2025.106141","DOIUrl":"10.1016/j.jmps.2025.106141","url":null,"abstract":"<div><div>A geometrically nonlinear theory for field dislocation thermomechanics based entirely on measurable state variables is proposed. Instead of starting from an ordering-dependent multiplicative decomposition of the total deformation gradient tensor, the additive decomposition of the velocity gradient into elastic, plastic and thermal distortion rates is obtained as a natural consequence of the conservation of the Burgers vector. Based on this equation, the theory consistently captures the contribution of transient heterogeneous temperature fields on the evolution of the (polar) dislocation density. The governing equations of the model are obtained from the conservation of Burgers vector, mass, linear and angular momenta, and the First Law. The Second Law is used to deduce the hyperelastic constitutive equation for the Cauchy stress and the thermodynamical driving force for the dislocation velocity. An evolution equation for temperature is obtained from the First Law and the Helmholtz free energy density, which is taken as a function of the following measurable quantities: elastic distortion, temperature and the dislocation density (the theory allows prescribing additional measurable quantities as internal state variables if needed). Furthermore, the theory allows one to compute the Taylor-Quinney factor, which is material and strain rate dependent. Accounting for the polar dislocation density as a state variable in the Helmholtz free energy of the system allows for temperature solutions in the form of dispersive waves with finite propagation speed, i.e. <em>thermal waves</em>, despite using Fourier’s law of heat conduction as the constitutive assumption for the heat flux vector.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106141"},"PeriodicalIF":5.0,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851687","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":"Geometrically characteristic kinetic thermodynamic deformation theory and intrinsic indices of the plasticity and damage of crystalline solid","authors":"Jinqiu Liu ,&nbsp;Chuang Ma ,&nbsp;Yichao Zhu ,&nbsp;Biao Wang","doi":"10.1016/j.jmps.2025.106139","DOIUrl":"10.1016/j.jmps.2025.106139","url":null,"abstract":"<div><div>A geometrically characteristic kinetic thermodynamic deformation theory is proposed for effective predictions over the full-life mechanical behaviour of crystalline solid. From a theoretic perspective, the proposed theory is distinguished from existing internal state variable theories at least in two aspects. Firstly, it is “geometrically characteristic” because the quantities employed for summarising the underlying defect status bear clear geometric meaning. An inelastic deformation status can be considered as the combination of two modes: a deviatoric mode resulting from the motion of distortional defects mainly underlying plasticity, and a volumetric mode resulting from the evolution of dilating defects likely giving rise to damage. Secondly, the proposed theory is said to be “kinetic”, because the mechanisms of underlying microstructural evolution impeded by local energy barriers are taken into account. A pair of material-intrinsic quantities measuring the hosting materials’ capabilities of resisting further inelastic deformation are then identified, which are employed as indices to assess the mechanical performance of crystalline solid. It is shown that conventional uniaxially loading data should suffice for calibrating the present theory, and this is in comparison with most existing ductile-damage models, where multi-triaxiality data seem necessary for calibration. The present theory, upon calibration against monotonic loading data, is also shown to be capable of describing non-monotonically loading situations, such as scenarios with cyclic loading and the phenomena of anisotropic plasticity.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106139"},"PeriodicalIF":5.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829281","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 unified multi-phase-field model for Rayleigh-Damköhler fluid-driven fracturing","authors":"Bo Li,&nbsp;Hao Yu,&nbsp;WenLong Xu,&nbsp;Quan Wang,&nbsp;HanWei Huang,&nbsp;HengAn Wu","doi":"10.1016/j.jmps.2025.106148","DOIUrl":"10.1016/j.jmps.2025.106148","url":null,"abstract":"<div><div>In geological systems where fractures are driven by low-viscosity reactive fluids (e.g., CO₂ fracturing), the leak-off of the reactive fluid from fractures into the rock matrix induces Rayleigh-Taylor instability, leading to the formation of fingering invasion regions that undergo chemical damage, thereby destabilizing fracture propagation. The fracture propagation is strongly coupled with the heterogeneous chemical damage. The significant variability of Rayleigh number (buoyancy-driven convection / diffusion) and Damköhler number (chemical reaction / advection) within a wide range causes various flow and fracture patterns. Based on the principle of virtual work, a unified multi-phase-field model is proposed to model the mechanics enhanced chemical damage and dissolution-assisted fracturing process. The distinct fracture (<span><math><msub><mi>∅</mi><mi>f</mi></msub></math></span>) and chemical damage (<span><math><msub><mi>∅</mi><mi>d</mi></msub></math></span>) phase field order parameters are introduced to characterize fracture energy, chemical free energy and dissolution interfacial energy. The two phase fields are tightly linked through a synergistic degradation of mechanical energy. The governing equations for the Rayleigh-Damköhler fluid-driven fracturing are derived from the variational formulation of the free energy and micro-force balance. Based on the model, dimensional analysis is employed to establish the scaling laws for rock failure modes. When leak-off fluid flow aligns with fracture propagation, critical curves distinguishing different damage morphology are identified in the phase diagram using penetration lengths. In scenarios where gravity induces a misalignment between leak-off fluid flow and fracture direction, the normalized fracture number (<span><math><msub><mstyle><mi>Π</mi></mstyle><mrow><mi>f</mi></mrow></msub></math></span>) and chemical damage number (<span><math><msub><mstyle><mi>Π</mi></mstyle><mrow><mi>d</mi></mrow></msub></math></span>) are summarized to construct a comprehensive phase diagram encompassing various unstable fluid leak-off structures and rock failure modes.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106148"},"PeriodicalIF":5.0,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858974","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":"Construction of Isotropic Compressible Hyperelastic Constitutive Models Based Solely on Uniaxial Tests","authors":"Pengfei Yang ,&nbsp;Peidong Lei ,&nbsp;Bin Liu ,&nbsp;Huajian Gao","doi":"10.1016/j.jmps.2025.106150","DOIUrl":"10.1016/j.jmps.2025.106150","url":null,"abstract":"<div><div>Constructing constitutive models for compressible soft materials is essential for accurately describing their highly nonlinear, large deformation mechanical behavior and volumetric deformation. However, most existing constitutive models rely on predefined assumptions about the form of the strain energy function. Constructing compressible hyperelastic constitutive models is particularly challenging because, beyond the uniaxial test, it typically requires additional more sophisticated and more costly experiments, such as biaxial, pure shear, and hydrostatic tests. In this paper, we propose an approach to constructing an isotropic compressible hyperelastic constitutive model without assuming a predefined form of the strain energy function. Instead, we derive the strain energy function directly from experimental data. Our method requires only uniaxial tests, significantly simplifying the experimental requirements and costs. This approach is achieved by utilizing the deviatoric-volumetric decomposition of the strain energy function coupled with an interpolation scheme. To validate our proposed approach, we compare our model against traditional compressible constitutive models and well-known experimental data on incompressible rubbers. Additionally, we perform experiments on compressible rubbers, including foamed silicone and foamed EPDM (ethylene propylene diene monomer), for further validation. It is found that our model perfectly predicts the uniaxial test data and accurately predicts mechanical behavior under various other loading conditions. Finally, we discuss strategies for enhancing model accuracy and its ability to decouple uniaxial behavior from compressibility. This decoupling feature is crucial for accurately capturing the distinct mechanical responses associated with different deformation modes, thereby improving the predictive capability of the constitutive model.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106150"},"PeriodicalIF":5.0,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843922","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 mechanical response of biomimetic staggered composites: Closed-form estimates via a micromechanical variational formulation","authors":"Pierfrancesco Gaziano ,&nbsp;Lorenzo Zoboli ,&nbsp;Elisabetta Monaldo ,&nbsp;Giuseppe Vairo","doi":"10.1016/j.jmps.2025.106137","DOIUrl":"10.1016/j.jmps.2025.106137","url":null,"abstract":"<div><div>Bio-inspired composite materials with staggered microstructures exhibit superior mechanical properties compared to traditional composites, paving the way for the development of advanced functional materials. The existing analytical models mainly address the macroscale constitutive response along the staggering direction using plane strain or plane stress assumptions. Consequently, a significant gap remains in the characterization of the equivalent material response in triaxial loading scenarios. This study presents a micromechanical variational formulation to derive an analytical and comprehensive characterization of the anisotropic homogenized behavior of biomimetic staggered composites. The microscale equilibrium problem, tailored to a suitable representative volume element, is tackled by applying stationary conditions to the total potential energy functional, evaluated over a class of quasi-compatible strain fields that capture the dominant microscale kinematics. A linearization technique leads to closed-form expressions that fully characterize the macroscale stiffness tensor of the material. Through a parametric case study, the obtained analytical results are compared with finite element simulations and theoretical solutions and bounds. The results confirm the validity of the proposed formulation, demonstrating the consistency and accuracy of the obtained analytical estimates.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106137"},"PeriodicalIF":5.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829238","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":"Probing Fracture Mechanics of Graphene through Heterocrack Propagation in a Moiré Superlattice","authors":"Yuan Hou ,&nbsp;Jingzhuo Zhou ,&nbsp;Zezhou He ,&nbsp;Shuai Zhang ,&nbsp;Qunyang Li ,&nbsp;Huajian Gao ,&nbsp;Yang Lu","doi":"10.1016/j.jmps.2025.106151","DOIUrl":"10.1016/j.jmps.2025.106151","url":null,"abstract":"<div><div>Understanding the fracture properties of two-dimensional (2D) materials is essential for enhancing their mechanical performance and extending the service life of 2D-based devices. A major challenge lies in examining stress singularities near crack tips at the nanoscale. In this study, we show that we can obtain fracture toughness of monolayer graphene by investigating the propagation of heterocrack in twisted graphene layers. We developed an in situ mechanical measurement to monitor the heterocrack propagation under electron microscopy. The cracks propagated and deflected along the twisted graphene-graphene interfaces, accompanied by periodic stress fluctuations and distorted moiré superlattices. By further leveraging molecular dynamics simulations, we developed a moiré strain analysis method to track strain distributions during heterocrack propagation in the moiré superlattice. The fracture toughness can be measured through the strain fields at the crack tip. Moreover, we examined the effect of the moiré potential on the heterocrack propagation behaviors and proposed an equivalent stress intensity factor to evaluate the fracture properties of graphene under varying twist angles. This work provides key insights into the fracture mechanics of 2D materials, and also offers a foundation for assessing the reliability and mechanical stability of 2D-material-based nanodevices.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106151"},"PeriodicalIF":5.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851686","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":"Force-field-induced energy-based design method for arbitrary prescribed modes in elastic metamaterials","authors":"Zhiwen Ren ,&nbsp;Hao-Wen Dong ,&nbsp;Mingji Chen ,&nbsp;Haiou Yang ,&nbsp;Yue-Sheng Wang ,&nbsp;Li Cheng ,&nbsp;Daining Fang","doi":"10.1016/j.jmps.2025.106144","DOIUrl":"10.1016/j.jmps.2025.106144","url":null,"abstract":"<div><div>Elastic metamaterials possess flexible regulatory capabilities of elastodynamic field information and energy through engineering and tailoring wave amplitudes, phase, and polarization vectors. However, due to the lack of general wave quantities and dynamic mode characterization methods, it is difficult to describe and design customized elastic dispersions with prescribed eigenmodes of interest, especially under large wave vectors or high frequencies. To tackle this challenge, we propose a systematic design method based on force-field-induced energy to inversely customize arbitrary prescribed eigenmodes at required frequencies for both small and large wave vectors. We build up a dynamic mode characterization theory based on energy, which contributes to portraying eigenmode response behavior under external excitations. It theoretically reveals the distribution features of the energy, induced by external excitations, in wave vector-frequency (<span><math><mrow><mi>k</mi><mtext>-</mtext><mi>ω</mi></mrow></math></span>) domain for the solid media. A systematic inverse-design method, using responsive energy maximization, is proposed to tailor-make eigenmodes and dispersions under arbitrarily prescribed <span><math><mrow><mi>k</mi><mtext>-</mtext><mi>ω</mi></mrow></math></span> conditions. Then, a series of periodic porous structures are optimized to support orthotropic/anisotropic longitudinal, transversal and rotational modes at different <span><math><mrow><mi>k</mi><mtext>-</mtext><mi>ω</mi></mrow></math></span> points, alongside customized dispersion. Meanwhile, an inverse strategy fusing longitudinal and transversal modes is forged and used to realize broadband fluid-like mode in porous microstructure with an effective refractive index, in which a strongly suppressed transversal mode in the extremely low-frequency region of the dispersion and a single broadband longitudinal mode are supported. In addition, through inversely designing local vibration modes at three <span><math><mrow><mi>k</mi><mtext>-</mtext><mi>ω</mi></mrow></math></span> points simultaneously, a dispersion passband supporting negative group velocity is generated within an expected frequency range. Meanwhile, entire dispersion curves satisfying the prescribed <span><math><mrow><mi>k</mi><mtext>-</mtext><mi>ω</mi></mrow></math></span> relationship and supporting prescribed modes are customized. The wave behaviors of the optimized metamaterials are elucidated by phonon-band-structure experiments as well as numerical simulations. The established approach provides a universal design paradigm of wave modes that promises to pave the route for engineering extreme dispersion and functionalities.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106144"},"PeriodicalIF":5.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843818","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":"On the elastic problem of representative volume element for multiphase thin films","authors":"Ahmad Ahmad ,&nbsp;Kyle Starkey ,&nbsp;Khaled SharafEldin ,&nbsp;Anter El-Azab","doi":"10.1016/j.jmps.2025.106142","DOIUrl":"10.1016/j.jmps.2025.106142","url":null,"abstract":"<div><div>Multiphase thin films exhibit unique physical functionalities stemming from their dimensions and interactions among phases. In these materials, elasticity plays an important role both in their growth and physical performance. An outstanding problem in this regard is the elastic formulation of representative volume element (RVE) of thin film systems. As thin films RVEs lack translation invariance in the direction perpendicular to the film free surface, the boundary value problem of the RVE involves integral kinematic boundary constraints that must be satisfied together with the governing elastic boundary value problem. These constraints were developed here as a part of a homogenization scheme designed to deliver the elastic solution in a heterogeneous thin film, with both eigenstrain and modulus mismatch within the phases. We formulated this problem together with an iterative solution scheme based on Fast Fourier Transform with an augmented Lagrangian fixed-point iteration algorithm. The numerical solution was benchmarked with the analytical solution of the famous Eshelby problem for the case of homogeneous and inhomogeneous cylindrical inclusions. Diffuse interface and discrete Green's operator methods were tested to investigate the attenuation of Gibbs oscillations at interfaces. Examples of thin film morphologies generated using kinetic Monte Carlo simulations at different growth conditions were used as microstructure input to test the current approach. We show that the elastic energy tends to be concentrated near the pillar/matrix interface. This approach is expected to enable the on-the-fly coupling of elasticity solution with thin film growth models to account for the elastic strain effects on diffusion, bonding, and interfacial energies.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106142"},"PeriodicalIF":5.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843819","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":"Slow dynamic nonlinear elasticity during and after conditioning, a unified theory and a lock-in probe","authors":"John Y. Yoritomo ,&nbsp;Richard L. Weaver","doi":"10.1016/j.jmps.2025.106149","DOIUrl":"10.1016/j.jmps.2025.106149","url":null,"abstract":"<div><div>Of the non-classical nonlinear elastic phenomena, slow dynamics (SD) has received particular attention due to recent modeling efforts and experiments in new systems. SD is characterized by a loss of stiffness after a minor conditioning strain, followed by a slow recovery back towards the original stiffness. It is observed in many imperfectly consolidated granular materials (e.g., rocks and concrete) and unconsolidated systems (e.g., bead packs). Here we posit a simple unified phenomenological model capable of seamlessly describing modulus evolution for SD materials during steady-state conditioning, during conditioning ringdown, and during recovery. It envisions a distribution of breaking and healing bonds, with healing rates governed by the usual spectrum of relaxation times. Well after the end of conditioning, the model recovers the characteristic logarithmic-in-time relaxation. For times during conditioning ringdown, when recovery has initiated but conditioning has not fully ceased, the model predicts deviations from log(t) and a dependence on the ringdown rate. We compare these model predictions with SD measurements on four different systems. To perform the measurements, an ultrasonic digital lock-in (DLI) probe is developed. The advantages of DLI over other techniques to measure SD are a sufficiently high time resolution and an insensitivity to noise from conditioning. We find good agreement between theory and experiment. The model in conjunction with DLI also allows for estimates of the minimum relaxation time. Our measurements indicate that the minimum relaxation time is material dependent.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106149"},"PeriodicalIF":5.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843816","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}