Continuum Mechanics and Thermodynamics最新文献

{"title":"A thermodynamically consistent phase-field framework for crack-induced self-heating in linear thermoviscoelastic solids","authors":"Sayahdin Alfat,&nbsp;Mardiana Napirah,&nbsp;Mohammad Suriyaidulman Rianse,&nbsp;Aditya Rachman,&nbsp; Nurgiantoro,&nbsp;Rosliana Eso,&nbsp;La Ode Ahmad Barata","doi":"10.1007/s00161-026-01471-7","DOIUrl":"10.1007/s00161-026-01471-7","url":null,"abstract":"<div><p>Crack formation is often accompanied by a localized temperature rise, which in turn influences deformation and crack evolution. Although this phenomenon has been extensively studied in plastic solids, it remains less understood in thermoviscoelastic materials. This work presents a thermodynamically consistent phase-field framework for modeling crack-induced self-heating in Maxwell-type linear thermoviscoelastic solids. Two phase-field formulations are developed within a unified thermodynamic setting based on the microforce balance principle, while thermodynamic consistency is ensured through an energy dissipation identity derived from energy conservation and the Clausius–Duhem inequality. The formulation couples viscoelastic dissipation, stored viscoelastic energy, fracture surface energy, and thermal energy within a thermodynamically admissible structure. Numerical simulations are performed using an anisotropic adaptive finite element method implemented in FreeFEM. The results indicate that heat generation during crack propagation arises from irreversible viscoelastic dissipation; higher viscosity enhances self-heating and accelerates thermal softening; and self-heating and crack evolution are strongly coupled. The proposed framework provides a physically grounded approach for analyzing thermally induced fracture processes in thermoviscoelastic solids.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural networks-based fatigue life prediction of natural rubber under combined preaging and temperature effects","authors":"Ala Hijazi,&nbsp;Sameer Al-Dahidi,&nbsp;Alexander Lion","doi":"10.1007/s00161-026-01469-1","DOIUrl":"10.1007/s00161-026-01469-1","url":null,"abstract":"<div><p>This study investigates the fatigue behavior of carbon black-filled natural rubber under combined effects of thermal preaging and testing temperature. A comprehensive experimental dataset comprising 410 fatigue tests under 36 distinct conditions is analyzed. Fatigue life is predicted as a function of displacement amplitude, preaging temperature and duration, and test temperature. Several modeling approaches are examined, including an analytical semi-empirical model, a conventional artificial neural network (ANN), an Assisted-ANN, and a Physics-Informed Neural Network (PINN). The ANN models are trained using carefully designed training, validation, and testing datasets to ensure objective performance assessment. Fatigue life is modeled in logarithmic space to improve numerical robustness and reduce sensitivity to data scatter. Model performance is evaluated using quantitative metrics such as mean absolute percentage error (MAPE) and mean absolute error (MAE), as well as qualitative assessment of the predicted S–N relationships. Results show that conventional ANNs significantly outperform the analytical model in terms of prediction accuracy but may produce physically inconsistent S–N curves when trained on sparse and highly scattered data. Incorporating physics-based guidance improves robustness. With the availability of sufficient training data, the Assisted-ANN achieves the lowest overall relative prediction errors with improved physical consistency, and minimal implementation and computational effort. The proposed PINN further enforces physical consistency by constraining the local log–log slope of the S–N relationship, rather than relying on explicit fatigue damage laws or baseline model predictions. As a result, the PINN approach provides the most physically consistent predictions and superior robustness under severe data scarcity conditions. Overall, the results demonstrate that hybrid physics-guided ANN approaches offer substantial advantages for fatigue life prediction of natural rubber under complex preaging and temperature effects.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147751657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat map analysis of wave dynamics in nonlocal Kelvin–Voigt piezo-semiconductors under memory-dependent heat flux","authors":"Vipin Gupta,&nbsp;Syed Modassir Hussain,&nbsp;Murat Yaylacı,&nbsp;Soumik Das","doi":"10.1007/s00161-026-01472-6","DOIUrl":"10.1007/s00161-026-01472-6","url":null,"abstract":"<div><p>This work investigates the coupled thermo–electro–mechanical behavior of a piezo-semiconductor medium by integrating spatial nonlocality, temporal nonlocality, Kelvin–Voigt (KV) viscoelasticity, and memory-dependent derivatives into a unified analytical framework. The governing equations combine a Klein–Gordon (KG) type nonlocal operator with three-phase-lag heat conduction, semiconductor transport, and piezoelectric coupling, and are solved using the normal-mode approach. The analysis reveals that wave-field modifications remain highly concentrated within a thin boundary-interaction zone determined by the KG nonlocal parameters, where the competing effects of spatial nonlocality, temporal relaxation, KV viscosity, and memory-driven kernels jointly influence the penetration and strength of thermo–electro–mechanical responses. Spatial nonlocality suppresses the mechanical deformation and reduces the near-surface thermal amplitude, while simultaneously intensifying the coupled stress, carrier concentration, electric potential, and electric-displacement fields. Temporal relaxation mechanisms moderate these variations by redistributing amplitudes over depth and smoothing sharp spatial gradients. KV-viscosity significantly suppresses the electrical fields. By capturing the coupled roles of nonlocality, viscoelasticity, thermal relaxation, and memory-driven carrier–electromechanical interactions, the model provides a comprehensive basis for analyzing multiphysics wave behavior in piezoelectric semiconductor media relevant to SAW sensors, acousto-electronic components, transducers, and high-frequency signal-processing devices.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inversion symmetry in separable line, area and volume elastic energies","authors":"Gennaro Vitucci,&nbsp;Francesco Trentadue,&nbsp;Domenico De Tommasi","doi":"10.1007/s00161-026-01473-5","DOIUrl":"10.1007/s00161-026-01473-5","url":null,"abstract":"<div><p>This work introduces a constructive framework for formulating isotropic compressible hyperelastic constitutive laws based on a geometrically transparent generalization of the Valanis–Landel (VL) hypothesis. The strain energy is decomposed into independent line, area, and volume contributions, each governed by a scalar function of the corresponding deformation measure. Physical admissibility is ensured by imposing inversion symmetry on these functions, which automatically enforces a stress-free reference state. The resulting formulation provides a systematic procedure for generating physically coherent models without <i>ad hoc</i> assumptions and naturally reduces to classical incompressible VL-type models as a special case. A central result of the theory is the emergence, both in linear and finite elasticity, of three fundamental Poisson’s ratios–0, 1/3, and 1/2–associated with pure line, area, and volume deformation mechanisms, respectively. In the general case, the macroscopic linear elastic moduli are explicitly recovered as weighted combinations of these mechanisms. The Hencky strain energy is identified as the simplest symmetric member of this class. The framework thus offers a unified, symmetry-based toolbox for the design and analysis of compressible materials, with direct applicability to the microstructurally informed engineering of elastomers, polymers, and metamaterials.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01473-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 homogenization method for thermo-mechanical stress analysis in printed circuit heat exchangers","authors":"Hao Wang,&nbsp;Lujun Cai,&nbsp;Fan Bai,&nbsp;Feng Zhang","doi":"10.1007/s00161-026-01464-6","DOIUrl":"10.1007/s00161-026-01464-6","url":null,"abstract":"<div><p>The compactness and high heat transfer efficiency of Printed Circuit Heat Exchangers (PCHEs) benefit from their dense microchannel networks, but they also introduce multiscale complexities to global thermal stress analysis. In this paper, a homogenization method is proposed for predicting the global temperatures of the fluids and solid, as well as the corresponding thermal stress in PCHEs under steady-state conditions. PCHE cores are modeled as homogeneous media, and the volume-averaged temperatures and stress are adopted as macroscopic variables in the coupled governing equations, where all the equivalent parameters are determined by the Representative Volume Element (RVE) model. To validate the proposed homogenization method, a Homogenization Finite Element Model (HFEM) was developed for a counter-flow PCHE core with 150 channels, and was compared with the Classical Finite Element Model (CFEM). Although the macroscopic temperatures predicted by HFEM for both cold and hot fluids cannot reflect microscale temperature variations in channel flows, they generally matched the cross-sectional average temperatures of the flows obtained from CFEM. Because the solid temperature variation between adjacent cold and hot channels was much smaller than the global variation, the macroscopic solid temperature from HFEM was comparable to the microscale solid temperature from CFEM. Both models consistently predicted that the hot fluid inlet region sustained elevated thermal stress, and the membrane and bending stresses in the channel ridges decreased gradually from the hot channel inlet to the cold channel inlet. Despite minor discrepancies between CFEM and HFEM, HFEM reduced the CPU time for temperature and mechanical calculations by factors of 40 to 75 and 10 to 15, respectively.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical study of Williamson nanofluid flow over a stretching sheet with Newtonian heating embedded in a porous medium in the presence of chemical interaction and non-uniform heat source/sink","authors":"Fakhraldeen Gamar,&nbsp;Prashanth Manthramurthy,&nbsp;S. O. Salawu,&nbsp;Srinivasa Rao Vempati,&nbsp;Yaseen Abbaker,&nbsp;Amal Rahamtalla,&nbsp;Eltayeb Awad","doi":"10.1007/s00161-026-01465-5","DOIUrl":"10.1007/s00161-026-01465-5","url":null,"abstract":"<div><p>Williamson nanofluids have been extensively studied due to their ability to model and enhance non-Newtonian fluid behavior in advanced heat- and mass-transfer applications. Motivated by this, the present work investigates the flow of a Williamson nanofluid over a stretching sheet in a porous medium, subject to Newtonian heating, chemical reactions, and a non-uniform heat source/sink. The governing momentum, energy, and species-concentration equations are transformed into a system of nonlinear ordinary differential equations via suitable similarity transformations. The resulting system is solved via the fourth-order Runge–Kutta method combined with the shooting technique. Graphical results illustrate the influence of key dimensionless parameters on the velocity and temperature fields. It is observed that increasing the Williamson fluid parameter from 0.1 to 0.5 and the permeability parameter from 0.2 to 0.6 reduces the maximum velocity by approximately 12% and 9%, respectively, while increasing the thermal boundary layer thickness by 8% and 6%. An increase in the chemical reaction rate from 0.1 to 0.4 decreases the surface temperature by about 7%. Furthermore, stronger non-uniform heat source/sink effects (from 0.2 to 0.8) combined with Newtonian heating raise the fluid temperature by nearly 10%, whereas increasing the Prandtl number from 0.7 to 7.0 enhances cooling by 15%. Quantitatively, the skin-friction coefficient decreases by 11% with the Williamson parameter and 8% with the permeability factor, while the Nusselt number increases by 12% due to stronger heat source/sink effects and Newtonian heating. These results provide detailed quantitative insight into the coupled effects of non-Newtonian behavior, chemical reaction, and thermal conditions in Williamson nanofluid flows.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometrical and Material Nonlinear Effects in Granular Micromechanics: Effects of Grain-Pair Tangential Plasticity and Induced Anisotropy","authors":"Nurettin Yilmaz,&nbsp;Luca Placidi,&nbsp;Anil Misra","doi":"10.1007/s00161-026-01476-2","DOIUrl":"10.1007/s00161-026-01476-2","url":null,"abstract":"<div><p>Granular materials undergoing large deformations exhibit nonlinearity arising from both geometrical and material effects. Here we extend the earlier Granular Micromechanics Approach (GMA)-based continuum models by enriching the grain-pair elastic energy functional and dissipation potential with new tangential terms and a coupling between normal and tangential parameters to better describe these nonlinear effects. These new terms are expected to better represent various deformation mechanisms that grains experience including grain crushing, rearrangement, rotation/rolling, sliding, loss of lateral support, neighborhood densification and strain localization. The elastic energy of a generic grain-pair direction of the GMA is reformulated consisting of a complete quadratic and quartic (duffing) dependencies on normal and tangential relative displacements to capture various nuances of material nonlinearity. Further, the grain-pair dissipation potential formulation is modified by introducing (i) plastic dissipation in the tangential direction and (ii) coupling between the plastic dissipation in tension and compression. It is shown that the coupling of this nonlinear elastic and the damage-plastic behavior yields an apparent molecular-type, such as Lennard-Jones type, potential for the granular system. The GMA framework is exploited to link the grain-scale behavior to the macroscopic response. In this framework, the evolution of grain-scale dissipation parameters is obtained using a hemi-variational principle. To motivate the adoption of GMA framework, we present a brief review of grain-scale deformation mechanisms that lead to the emergent dissipative macroscale behavior and the evolution of induced anisotropy. The enriched model is used to simulate one-dimensional compression of elasto-frictional granular media. Classical behavior of lateral earth pressure coefficient, the ratio of lateral to axial stress, is predicted by the model. The obtained results are expounded with the aid of the evolution of two sets of parameters during the compaction process, one at the grain-scale and the other at the emergent macroscale. At the grain scale, we investigate the directional evolution of elastic energy, damage and plasticity. At the macroscale, we follow the evolution of macroscale induced anisotropy by considering the eigenvalues and harmonic decomposition of equivalent stiffness.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147702337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Velocity and current are defined without recourse to time according to thermodynamics and formal graphs","authors":"Eric Vieil,&nbsp;Eric Martinet,&nbsp;Hélène Van Melckebeke","doi":"10.1007/s00161-025-01442-4","DOIUrl":"10.1007/s00161-025-01442-4","url":null,"abstract":"<div><p>Two definitions of the velocity in translation mechanics or of the current in electromagnetism exist. A first one, often seen as a classical definition, states that these variables result from variations of distance or charge as a function of time. The second one, less classical, is based on the dependency of energy on momentum or induction flux. This paper discusses the properties that a system must have for using each definition. It is shown that the condition for involving time in a physical model is the existence of an energy conversion between two forms. The approach stems from the theory of Formal Graphs, in which the notion of elementary energy entity is introduced, with each entity containing a quantity of energy called energy-per-entity. The latter can be identical between several entities of the same nature, which then form a cohesive whole called a community of entities. There are as many such communities as there are different elementary forms of energy. These communities are the constituents of our macroscopic world, and are quantified by an extensive variable called the quantity of entities. The extensivity of such a state variable is the essential condition for it to fall within the scope of the first principle of thermodynamics, whose algebraic formulation enables all energies-per-entity to be expressed as partial derivatives of energy with respect to the corresponding quantity of entities. Moreover, these general definitions can be consistently extended to other state variables as this theory is transverse to all physics.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147620157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An interface crack between two elastic semi-planes in the presence of surface energy","authors":"Anna Y. Zemlyanova","doi":"10.1007/s00161-026-01468-2","DOIUrl":"10.1007/s00161-026-01468-2","url":null,"abstract":"<div><p>In this paper, a plane strain problem for an interface nano-sized crack located on a boundary between two semi-planes is studied. The boundaries of the crack possess surface energy in the Steigmann-Ogden form. Using the integral transforms of the stresses and the displacements, the problem is reduced to a system of four singular integro-differential equations with additional tip conditions. The system is further regularized by reduction to a system of Fredholm equations of the second kind, and the existence and uniqueness of the solution is discussed. The numerical solution is obtained by utilizing approximations of the unknown functions based on the Chebyshev polynomials. The computational examples are discussed and the comparison with known results is made.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147586719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 effective stress rate in Non-Linear Continuum Mechanics","authors":"Marzia Sara Vaccaro,&nbsp;Daniele Ussorio,&nbsp;Raffaele Barretta","doi":"10.1007/s00161-026-01449-5","DOIUrl":"10.1007/s00161-026-01449-5","url":null,"abstract":"<div><p>Structures undergoing large displacements and deformations are investigated in a differential geometric framework by a <span>(,4)</span>-D <span>Euclid</span> spacetime approach. The developed variational scheme of rate equilibrium leads to the original notion of effective stress rate, which proves useful for addressing applicative problems in Non-Linear Continuum Mechanics. Notably, the rate virtual power principle is exploited according to the presented paradigm and the coordinate-free expression of the effective stress rate for <span>(,3)</span>-D <span>Cauchy</span> continua is contributed. Constitutive relations are formulated as instantaneous incremental responses to a finite set of tensor state variables and to their time convective rates along the motion, namely the (natural) stress state per unit mass, its convective rate and the elastic stretching. Geometrically nonlinear structural problems are addressed by resorting to an integrable and conservative covariant hypo-elasticity model. Specifically, the simplest linear hypo-elastic constitutive law is considered. Particularization to the <span>(,1)</span>-D case of elastic trusses is provided and two variants of the mentioned constitutive relation are examined. A straightforward incremental solution procedure is implemented to solve the nonlinear structural problem of a representative case-study and comparisons with standard finite elasticity strategies are carried out. It is shown that outcomes of conventional methodologies can be recovered for <span>(,1)</span>-D purely elastic structures by implementing the proposed computational strategy. This denouement paves the way for a theoretically and computationally promising formulation of nonlinear elasto-visco-plastic problems, circumventing long-known and debated issues that affect approaches to finite deformations.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01449-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}