Continuum Mechanics and Thermodynamics最新文献

{"title":"Thermal history-dependent thermomechanical response of talc-filled and unfilled polypropylene","authors":"Yiheng Huang,&nbsp;Loredana Kehrer,&nbsp;Valerian Hirschberg,&nbsp;Eike Reinhardt,&nbsp;Frank Burbulla,&nbsp;Thomas Böhlke","doi":"10.1007/s00161-026-01520-1","DOIUrl":"10.1007/s00161-026-01520-1","url":null,"abstract":"<div><p>The thermomechanical response of semicrystalline polypropylene (PP) depends not only on temperature and loading conditions, but also on its prior thermal state. While structural changes, such as post-crystallization and physical aging, induced by annealing treatments are well documented, their combined influence on thermal expansion, thermomechanical viscoelastic response, and crystalline fraction under service-relevant conditions in an automotive context remains inadequately quantified. In this study, unconditioned and thermally preconditioned unfilled and talc-filled PP were investigated by dilatometry, dynamic mechanical analysis, and differential scanning calorimetry over temperature and frequency ranges that are representative of service-relevant conditions. Thermal preconditioning resulted in a modification of the temperature-dependent coefficient of thermal expansion, as well as alterations in stiffness and damping levels. However, the glass transition temperature and the high-temperature <span>(alpha ^*)</span>-relaxation remained predominantly unaltered. These alterations occurred in conjunction with an increase in the crystalline fraction, indicating a modified structural condition subsequent to thermal treatment. The talc-filled grades exhibited a lower overall level of thermal expansion, higher stiffness and crystallinity, and an effect on the high-temperature relaxation associated with the crystalline phase, without influencing the glass transition temperature. The findings demonstrate that thermal history modifies the structural state of polypropylene (PP) and is accompanied by changes in thermal expansion and dynamic viscoelastic response in both filled and unfilled systems. This is essential for constrained automotive exterior assemblies, which require dimensional stability and tolerance retention.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01520-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768964","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":"Rational extended thermodynamics for moderately dense granular gases","authors":"Elvira Barbera,&nbsp;Annamaria Pollino","doi":"10.1007/s00161-026-01521-0","DOIUrl":"10.1007/s00161-026-01521-0","url":null,"abstract":"<div><p>A closed system of 13 field equations for the description of a moderately dense granular gas is provided in the context of rational extended thermodynamic theory (RET). Starting from the basic assumptions of RET, a particular structure appropriate to moderately dense granular gasses is assumed. Closure of field equations is achieved by universal physical principles, such as the Galileian Invariance Principle and the Principle of Entropy. The obtained field equations are in agreement with balance equations determined within the framework of Grad’s 13-moments theory by Jenkins and Richman. Explicit production terms are identified by comparison with the Grad’s 13-moments theory, adapted to moderately dense granular gases. In order to study the validity of the present model, its hyperbolic nature is investigated through the determination of the characteristic velocities. Spatially homogeneous solutions are computed and the dispersion relation is analyzed for several kinds of moderately dense gases in order to study the stability of the homogeneous solutions.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148769050","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":"Multilevel approach for simulating the reorientation of mesogens in nematic liquid crystal elastomers","authors":"Francesca Concas,&nbsp;Michael Groß","doi":"10.1007/s00161-026-01519-8","DOIUrl":"10.1007/s00161-026-01519-8","url":null,"abstract":"<div><p>Nematic liquid crystal elastomers (LCEs) are well-known for their actuation properties and are thus very suitable for the construction of artificial muscles. The distinguishing features of nematic LCEs are possible due to their molecular configuration and the orientation of the mesogens. The simulation of LCEs is very challenging, since a very large amount of elements is usually needed and also several variables might be necessary for mimicking their unusual behavior. Improving the numerical methods for dealing with the simulation of nematic LCEs is essential. For this purpose, we describe and implement a multilevel numerical procedure for modeling the reorientation of the mesogens. The algorithm is implemented in the dynamic numerical framework with distinct drilling degrees of freedom for the rotations of the mesogens and the bulk elastomer. In each time step, the drilling degrees of freedom are obtained from an elementwise system of equations. In this regard a new invariant free energy density is introduced for the sake of preventing the singularity of the tangent. Afterwards, the rotations at the local nodes are included in the global system of equations by static condensation. We compare results obtained by the multilevel approach with the ones from the monolithic procedure for the case of a virtual experiment, in which Dirichlet and Neumann boundary conditions on the orientation mapping are applied.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01519-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148728744","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":"Crack growth in honeycomb structures under thermal shock","authors":"Navid Roshani Zarmehri,&nbsp;Masoud Mahdizadeh Rokhi,&nbsp;Mohammad Bagher Nazari,&nbsp;Seyed Hadi Bayat","doi":"10.1007/s00161-026-01515-y","DOIUrl":"10.1007/s00161-026-01515-y","url":null,"abstract":"<div><p>In this paper, dynamic crack growth in auxetic and non-auxetic cracked honeycomb structures subjected to thermal shock is investigated. The honeycomb core is modeled as an equivalent homogeneous orthotropic medium based on its effective thermoelastic properties. Auxetic and non-auxetic configurations are generated by varying the interior cell angle, and their dynamic fracture responses are examined for different crack and specimen geometries. The coupled thermoelastic governing equations are solved using the extended finite element method and the Newmark time-integration scheme. Mixed-mode stress intensity factors are evaluated by the interaction integral method, and the crack-growth direction and speed are predicted using an anisotropic crack-growth criterion. Two representative cracked honeycomb structures are studied: a rectangular honeycomb plate with an edge crack and a honeycomb annular disc with a curved crack. The results show that the honeycomb cell angle has a significant influence on the transient temperature field, mixed-mode SIFs, crack-tip temperature, crack-growth speed, and final crack trajectory. Non-auxetic honeycombs generally exhibit larger crack-driving forces, higher Mode I SIFs, faster crack propagation, and greater crack-path deviation. In contrast, auxetic honeycombs reduce the local crack-opening tendency through geometry-induced stress redistribution, resulting in lower crack-growth speeds and improved resistance to thermally induced fracture. These findings highlight the importance of auxeticity and cell-level geometry in controlling dynamic thermal-fracture behavior in honeycomb structures.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782303","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":"A tribute to Professor Mark Kachanov","authors":"Gennady Mishuris,&nbsp;Yulia Pronina","doi":"10.1007/s00161-026-01510-3","DOIUrl":"10.1007/s00161-026-01510-3","url":null,"abstract":"<div><p>This tribute is presented in recognition of Professor Mark Kachanov’s 80th birthday. A leading authority in the mechanics of materials, Professor Kachanov has made substantial contributions to the development of micromechanics, the theory of effective properties, contact mechanics, the electromechanics of piezoelectric materials, and cross‑property relations. The article outlines key milestones of his scientific career and highlights the enduring impact of his research.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148728717","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 the role of elastic anisotropy in the strain energy of decahedral metal particles: finite element analysis","authors":"R. E. Shevchuk,&nbsp;S. A. Krasnitckii,&nbsp;A. M. Smirnov,&nbsp;A. E. Romanov","doi":"10.1007/s00161-026-01509-w","DOIUrl":"10.1007/s00161-026-01509-w","url":null,"abstract":"<div><p>This paper presents a finite element model developed to analyze the role of cubic elastic anisotropy in the strain energy of face-centered cubic (FCC) metal decahedral nanoparticles. The particle can be viewed as an assembly of five single-crystalline tetrahedral domains containing a central wedge disclination. Anisotropic elastic properties are explicitly incorporated by aligning the crystal axes of each domain with the 〈100〉-type crystallographic directions of the cubic lattice. Residual stresses are simulated using a disclination approach, which involves the kinematic closure of the angular gap between tetrahedra followed by the activation of bonded contact along the interfaces. Parametric finite element simulations are performed for a range of FCC metals with the anisotropy ratio <i>A</i> varying from 1.21 (Al) to 3.84 (Pb). The results reveal that for a given value of the Poisson’s ratio, the stored strain energy tends to decrease as <i>A</i> increases. For the isotropic case (<i>A</i> = 1), the finite element solution agrees within ∼ 5% with analytical disclination models for spheres and cylinders. In contrast, disclination models fail to provide accurate predictions across the wide spectrum of material anisotropy studied here. Specifically, for a strongly anisotropic material such as Pb (<i>A</i> ≈ 3.84), analytical models based on the isotropic approximation yield a strain energy approximately three times greater than the anisotropic finite element solution. This analysis underscores the necessity of explicitly accounting for material-specific elastic anisotropy when predicting the thermodynamic stability and catalytic durability of nanoparticles.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148715415","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":"Studies on post-weld heat treatment for residual stress relaxation in grade 91–Inconel 82–316ln dissimilar weld joints","authors":"Anoop A. Pillai,&nbsp;Harish Chandra Dey,&nbsp;Ullissery Balan Jayadeep,&nbsp;Kuttiparambil Vineesh,&nbsp;Manas Mohan Mahapatra","doi":"10.1007/s00161-026-01513-0","DOIUrl":"10.1007/s00161-026-01513-0","url":null,"abstract":"<div><p>Dissimilar welds used in high-temperature power plant components develop complex residual stresses, and the usefulness of post-weld heat treatment (PWHT) in relieving these stresses remains insufficiently understood. This study investigates the influence of PWHT on the relaxation of residual stress in a Grade 91–Inconel 82–316LN weldment using a combined experimental and numerical approach. The generalised plane strain (GPS) approach is employed for the numerical modelling. Through-thickness residual stresses are quantified using the deep hole drilling (DHD) and compared with finite element simulations incorporating elastic–plastic–creep behaviour. Results show that PWHT leads to partial stress relaxation, with compressive stresses developing in the Grade 91 region while tensile stresses remain in the Inconel 82 and 316LN regions. A stress reduction of up to 200 MPa is observed in the weld metal, whereas the 316LN side exhibits only marginal change. In the Inconel 82 region, both DHD measurements and GPS predictions indicate a similar stress trend, with an approximate reduction of 100 MPa after PWHT. Overall, the results demonstrate that PWHT leads to only partial stress relaxation in dissimilar metal welds, and that appropriate representation of out-of-plane constraint through the GPS formulation is essential for accurately predicting residual stress evolution. These findings underline the importance of incorporating reliable residual stress assessment in the life evaluation of dissimilar metal welds operating under high-temperature service conditions.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687957","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":"Memory-spectrum photo-thermoelastic diffusion in ultrafast laser-heated semiconductors: a distributed-order dual-phase-lag model with variable thermal conductivity","authors":"Mumtaz Khan,&nbsp;M. S. Anwar,&nbsp;Xiaoting Gan","doi":"10.1007/s00161-026-01514-z","DOIUrl":"10.1007/s00161-026-01514-z","url":null,"abstract":"<div><p>This paper develops a distributed-order fractional photo-thermoelastic diffusion model for semiconductor plates subjected to ultrafast laser heating with variable thermal conductivity. The present formulation introduces continuous weight functions into both phase lags of the dual-phase-lag heat conduction law, so that each fractional derivative is integrated over a distribution of orders rather than evaluated at a single fixed order. This construction encodes the full spectrum of thermal relaxation mechanisms from ultrafast carrier–lattice energy exchange to slow moisture-assisted redistribution within a single unified framework that contains all classical, single-fractional, and dual-fractional thermoelastic theories as recoverable limiting cases. The generalized heat equation is coupled with carrier diffusion–recombination, moisture transport, and linear thermoelasticity, and the variable thermal conductivity is incorporated through the Kirchhoff transformation. Five physically motivated weight functions are investigated: Dirac delta (recovering the dual-fractional model as a special case), Gamma-type, Uniform, Gaussian, and Bi-modal distributions. The resulting system of distributed-order fractional integro-differential equations is discretized using Gauss–Legendre quadrature for the order-domain integrals, the L1/L1-2 formulas for the Caputo fractional derivatives, selected according to whether the quadrature-node order lies below or above unity, and second-order central finite differences in space; a rigorous convergence analysis establishes the overall truncation error as <span>(O(h_alpha ^{2G} + Delta t^{2-alpha _{max }} + h^2))</span>, which is confirmed numerically. Parametric studies on a silicon plate reveal three principal effects of the distributed-order formulation: (i) a memory spectrum smoothing mechanism in which the superposition of multiple relaxation scales attenuates the thermoelastic wave amplitude by 50–<span>(60%)</span> relative to the dual-fractional reference; (ii) a phase modification effect that elongates the oscillation wavelength of the displacement and stress fields due to dispersive spreading across the memory spectrum; and (iii) a non-trivial interaction between variable thermal conductivity and the memory spectrum, whereby the continuous distribution partially masks the VTC-induced spatial redistribution of thermal energy. These findings demonstrate that distributed-order fractional models capture qualitatively different physics from their fixed-order counterparts and provide a more faithful description of multiscale thermal memory in laser-excited semiconductors.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148682237","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 the influence of powder particle size on single-track formation in laser powder bed fusion of AlSi10Mg alloy","authors":"Y. Solyaev,&nbsp;V. Dobryanskiy,&nbsp;Nguyen Long,&nbsp;Stanislav Chernyshikhin","doi":"10.1007/s00161-026-01516-x","DOIUrl":"10.1007/s00161-026-01516-x","url":null,"abstract":"<div><p>In this paper, we present the results of single-track experiments conducted for different fractions of standard AlSi10Mg powder, which were sieved to achieve varying mean size of the particles. Significant differences in the melting behaviour of these fractions were observed at relatively low input energy levels during laser powder bed fusion (LPBF). Namely, a remarkable particle size effect is observed in the position of lack of fusion boundary on the process map of laser power and velocity. We established that this boundary corresponds to an approximately constant linear energy density at low levels of Peclet number (Pe &lt; 2), while the constant enthalpy density defines it at higher levels (Pe &gt; 2). Specifically, for mean particle sizes ranging from 28 to 64 <span>(upmu )</span>m, the required linear energy density for stable track formation ranges from 50 to 167 J/m and the nominal enthalpy density ranges from 4.4 to 15 J/mm<span>(^3)</span>. Based on the scaling law analysis and numerical simulations, we show that the observed phenomena should be attributed to the change in absorptivity of the powder layer, which depends on particle size and packing density. The presented results can be useful for the adjustment of LPBF process parameters and powder particle size selection for AlSi10Mg alloy as well as for other highly reflective materials.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612820","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":"Surface damage due to multiple edge cracks and its dependence on material anisotropy","authors":"A. V. Savikovskii,&nbsp;A. S. Semenov","doi":"10.1007/s00161-026-01504-1","DOIUrl":"10.1007/s00161-026-01504-1","url":null,"abstract":"<div><p>The problem of interaction of multiple (three) edge cracks in an anisotropic half-infinite plane under tension loading is considered. In particular, we focus on the effect of anisotropy axes orientation on the mechanics of edge crack interactions, such as stress shielding. These factors are of the key importance for processes of crack nucleation and growth under various loading conditions, as well as crack kinking. We analyze these effects by stress intensity factors calculations. Calculations were performed for the orthotropic materials and materials with cubic symmetry. The effect of anisotropy was examined by comparison of the results with the ones for the isotropic material. It is demonstrated, that rotation of material anisotropy axes leads to asymmetry of normal stress distribution and controls mixed mode loading on cracks that deflects cracks from straight-line direction. The results indicated that rotation of anisotropy axes can decrease or increase shielding effect by several times comparing to isotropic material and this effect depends on material anisotropy. Decreasing crack length increase shielding effect by several times.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612808","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}