Mathematics and Mechanics of Solids最新文献

{"title":"Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics","authors":"N. S. Taki, Kundan Kumar","doi":"10.1177/10812865231209256","DOIUrl":"https://doi.org/10.1177/10812865231209256","url":null,"abstract":"In this paper, we study the well-posedness of a class of evolutionary variational–hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme showing that the problem has a unique mild solution. In addition, we established the continuity of the flow map with respect to the initial data. Under the general framework, we consider two new applications for modeling of frictional contact for viscoelastic materials. In the first application, we consider Coulomb’s friction with normal compliance, and in the second, normal damped response. The structure of the friction coefficient [Formula: see text] is new with motivation from geophysical applications in earth sciences with dependence on an external state variable [Formula: see text] and the slip rate [Formula: see text].","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"58 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139867958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of time-dependent attractor of wave equation in locally uniform space","authors":"Xudong Luo, Qiaozhen Ma","doi":"10.1177/10812865231219199","DOIUrl":"https://doi.org/10.1177/10812865231219199","url":null,"abstract":"In this article, we study non-autonomous dynamical behavior of weakly damped wave equation in unbounded domain. First of all, we introduce the time-dependent locally uniform space. After that, the pullback asymptotical compactness is proved by applying the contractive function method. Eventually, we obtain the existence of [Formula: see text]-time-dependent attractor of wave equation.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"6 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a dynamic frictional contact problem with normal damped response and long-term memory","authors":"Imane Ouakil, B. Benabderrahmane, Y. Boukhatem, B. Feng","doi":"10.1177/10812865231218458","DOIUrl":"https://doi.org/10.1177/10812865231218458","url":null,"abstract":"A dynamic frictional contact problem between a viscoelastic body and a foundation is studied. The contact is modeled with normal damped response and a friction law. The constitutive law with long memory is assumed to be nonlinear. The existence result is proved using nonlinear monotone operators, fixed point argument, and extension procedure. Moreover, the exponential stability of the energy solution is established using the multiplier method.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"98 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum","authors":"Y. Cong, Zixu X Xia, Shuitao Gu, Yi Hui, Zhi-Qiang Feng","doi":"10.1177/10812865231212867","DOIUrl":"https://doi.org/10.1177/10812865231212867","url":null,"abstract":"We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal [Formula: see text] continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"107 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139605891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chirality effects in panto-cylindrical structures","authors":"Maximilian Stilz, Jonas Breuling, Simon Eugster, Marek Pawlikowski, Roman Grygoruk","doi":"10.1177/10812865231212145","DOIUrl":"https://doi.org/10.1177/10812865231212145","url":null,"abstract":"In this paper, we apply a numerical integration strategy recently developed for determining the deformation shapes of structures constituted by Cosserat rods, to predict the behavior of panto-cylinders. Panto-cylinders have, as microstructure, a set of two families of helicoidal beams interconnected by perfect or elastic joints. The pivot’s free rotation axis is, in the reference configuration, orthogonal to the cylindrical surfaces spanned by the beams. We perform a series of numerical simulations looking for the mechanical parameters which exalt the chirality effects in the structure. For the performed compression, extensions, shear, and torsion tests, we find chiral deformation patterns with a dependence on the type of joint and its length.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"38 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-dimensional quasi-static general solution for isotropic chemoelastic materials and their application","authors":"Longming Fu, Guocheng Li, Sitong Wang, Hui Wang, He Ma, Xianji Shao","doi":"10.1177/10812865231210505","DOIUrl":"https://doi.org/10.1177/10812865231210505","url":null,"abstract":"Based on potential theory, the three-dimensional quasi-static general solution for isotropic chemoelastic materials is presented in this work. Through the three-dimensional general solution, the Green’s function for an isotropic chemoelastic material subjected to dynamic point loads is derived. This can serve as theoretical guidance for future engineering practices. Four functions constitute the expressions of the general solution that satisfy the harmonic functions and the quasi-static transport equation, respectively. The Green’s function for an isotropic chemoelastic material subjected to dynamic point loads is derived by combining the general solution with the chemical balance boundary conditions at infinity. It can be expressed in terms of the error function and elementary functions. Finally, the numerical results are provided, as shown in the contours. These results can be used to analyze the variation law in the coupling fields of isotropic chemoelastic materials. The corresponding analysis can provide a theoretical basis for elucidating the mechanism of the chemoelastic coupling problem in further work.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"17 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139524927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A quasi-static model of a thermoelastic body reinforced by a thin thermoelastic inclusion","authors":"Irina V. Fankina, A. Furtsev, E. Rudoy, S. Sazhenkov","doi":"10.1177/10812865231217043","DOIUrl":"https://doi.org/10.1177/10812865231217043","url":null,"abstract":"The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter [Formula: see text] describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as [Formula: see text] tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"9 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic long-wave model for a high-contrast two-layered elastic plate","authors":"G. Mikhasev","doi":"10.1177/10812865231215294","DOIUrl":"https://doi.org/10.1177/10812865231215294","url":null,"abstract":"The paper is concerned with the derivation of asymptotically consistent equations governing the long-wave flexural response of a two-layered rectangular plate with high-contrast elastic properties. In the general case, the plate is under dynamic and variable surface, volume, and edge forces. Performing the asymptotic integration of the three-dimensional (3D) elasticity equations in the transverse direction and satisfying boundary conditions on the faces and interface, we derived the sequence of two-dimensional (2D) differential equations with respect to required functions in the first two approximations. The eight independent restraints for the generalized displacements and stress resultants are considered to formulate the 16 independent variants of boundary conditions. One of the main results of the paper is the Timoshenko–Reissner type equation capturing the effect of the softer layer and taking into account the in-plane deformation induced by the edge forces. Comparative calculations of natural frequencies were carried out based on our and alternative models.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"116 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139614388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homogenization of a coupled electrical and mechanical bidomain model for the myocardium","authors":"Laura Miller, R. Penta","doi":"10.1177/10812865231207600","DOIUrl":"https://doi.org/10.1177/10812865231207600","url":null,"abstract":"We propose a coupled electrical and mechanical bidomain model for the myocardium tissue. The structure that we investigate possesses an elastic matrix with embedded cardiac myocytes. We are able to apply the asymptotic homogenization technique by exploiting the length scale separation that exists between the microscale where we see the individual myocytes and the overall size of the heart muscle. We derive the macroscale model which describes the electrical conductivity and elastic deformation of the myocardium driven by the existence of a Lorentz body force. The model comprises balance equations for the current densities and for the stresses, with the novel coefficients accounting for the difference in the electric potentials and elastic properties at different points in the microstructure. The novel coefficients of the model are to be computed by solving the periodic cell differential problems arising from application of the asymptotic homogenization technique. By combining both the mechanical and electrical behaviors, we obtain a macroscale model that highlights how the elastic deformation of the heart tissue is influenced and driven by the difference in the electric potentials at various points in the material.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"60 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139526757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Applications of vector bundle to finite elasto-plasticity","authors":"S. Cleja-Ţigoiu","doi":"10.1177/10812865231209976","DOIUrl":"https://doi.org/10.1177/10812865231209976","url":null,"abstract":"A new approach to finite elasto-plasticity of crystalline materials, with a differential geometry point of view toward the material description, is proposed. In order to define the plastic and elastic distortions, traditionally it is accepted the existence of an intermediate configuration, which is endowed with a differential manifold structure. A more restrictive but physically and mathematically well-motivated structure is assigned to the intermediate configuration, namely, a vector bundle structure. Two approaches to multiplicative decomposition of the deformation gradient can be rebuilt if on the same total space (intermediate configuration) the vector bundle structures are considered, but either the reference configuration, [Formula: see text] (i.e., plastic assumption) or the deformed configuration, [Formula: see text] (i.e., elastic assumption) stands for the base space. As the base spaces are homeomorphic, a pullback vector bundle over one base space is provided by the other one through the motion diffeomorphism. Thus, the total space is endowed with different differential manifold structures. The plastic distortion and the inverse elastic distortion, respectively, are defined for any material points as linear, invertible, and non-integrable maps from the tangent vector space at their material points, with the value on the attached vector fiber. The multiplicative decompositions into their non-integrable components are derived, based on the associate inverse elastic distortion and plastic distortion, respectively. When the plastic and elastic assumptions are simultaneously accepted, then a three-term multiplicative decomposition of the deformation gradient is achieved. The transition functions, which characterize the compatibility of the overlapping charts which belong to these different structures, namely of the vector bundle and of the pullback vector bundle over the same configuration, say [Formula: see text] define the non-uniqueness of the two-term multiplicative decomposition. The material symmetry transformation is defined for elastic-type materials. The compatibility of the models and examples of the bundle vector structures are also discussed.","PeriodicalId":502792,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"57 42","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139527517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}