Mathematics and Mechanics of Solids最新文献_第7页

Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective 研究无血管肿瘤生长动态：变阶非局部建模视角

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-28 DOI: 10.1177/10812865241230269

Mariam Mubarak Almudarra, Ariel Ramírez-Torres

{"title":"Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective","authors":"Mariam Mubarak Almudarra, Ariel Ramírez-Torres","doi":"10.1177/10812865241230269","DOIUrl":"https://doi.org/10.1177/10812865241230269","url":null,"abstract":"This study investigates the growth of an avascular tumour described through the interchange of mass among its constituents and the production of inelastic distortions induced by growth itself. A key contribution of this research examines the role of non-local diffusion arising from the complex and heterogeneous tumour micro-environment. In our context, the non-local diffusion is enhanced by a variable-order fractional operator that incorporates crucial information about regions of limited nutrient availability within the tissue. Our research also focuses on the identification of an evolution law for the growth-induced inelastic distortions recast through the identification of non-conventional forces dual to suitable kinematic descriptors associated with the growth tensor. The establishment of such evolution law stems from examining the dissipation inequality and subsequently determining a posteriori connections between the inelastic distortions and the source/sink terms in the mass balance laws. To gain insights into the dynamics of tumour growth and its response to the proposed modelling framework, we first study how the variables governing the tissue evolution are affected by the introduction of the new growth law. Second, we investigate how regions of limited diffusion within the tumour, encoded into a fractional operator of variable-order, influence its growth.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"135 1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006869","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}

引用次数: 0

Large deformation of soft dielectric cylindrical tubes under external radial electric field 软介质圆柱管在外径向电场作用下的大变形

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-26 DOI: 10.1177/10812865241231208

Pietro Liguori, Massimiliano Gei

引用次数: 0

Towards automated image-based cohesive zone modeling of cracking in irregular masonry 基于图像的不规则砌体裂缝内聚区自动建模

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-19 DOI: 10.1177/10812865241228825

Karim Ehab Moustafa Kamel, Thierry J Massart

{"title":"Towards automated image-based cohesive zone modeling of cracking in irregular masonry","authors":"Karim Ehab Moustafa Kamel, Thierry J Massart","doi":"10.1177/10812865241228825","DOIUrl":"https://doi.org/10.1177/10812865241228825","url":null,"abstract":"The models developed for masonry and historical structures in the literature are usually classified into macromodels considering masonry as an equivalent continuum; and micromodels in which brick, blocks, or stones and mortar joints are represented explicitly. In this second category, many contributions dealt with regular bond masonry for which the geometrical description and the discretization are rather straightforward. For irregular masonry structures however, even though both finite element method (FEM) and discrete element method (DEM) approaches have been developed, obtaining a versatile geometry representation and its discretization remains much less straightforward. This becomes an important issue nowadays with the availability of image acquisition techniques, based on which computational models could be derived. The present contribution proposes an automated methodology to produce a line description of the mortar joints of an irregular masonry blocks/stones and mortar assembly, which can subsequently be used in modeling approaches. The starting point of the development is a generation technique based on inclusions packings which uses distance fields to the nearest neighboring inclusions to describe an assembly of blocks or stones geometrically. It is shown that such an assembly and the corresponding distance fields can be used to extract efficiently and in an automated way a line or lumped description of the corresponding mortar joint based on the concept of a medial axis. This line description can subsequently be used to define computational models. This is illustrated by the automated generation of FEM models that represent mortar joints by interface elements equipped with a cohesive law. Simulations on representative volume elements (RVEs) and on a wall are shown to illustrate the methodology that paves the way towards the image-based modeling of irregular masonry structures through the automated generation of cohesive zone-based models.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"115 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948421","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}

引用次数: 0

Damped Normal Compliance (DNC) and the restitution coefficient 阻尼法向顺应性（DNC）和恢复系数

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-19 DOI: 10.1177/10812865241228230

Meir Shillor, Ian Pahuja

引用次数: 0

On the incremental equations in surface elasticity 论表面弹性的增量方程

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-16 DOI: 10.1177/10812865231226183

Xiang Yu, Yibin Fu

引用次数: 0

On self-contact and non-interpenetration of elastic rods 论弹性杆的自接触和非穿透性

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-16 DOI: 10.1177/10812865231226311

Chiara Lonati, Alfredo Marzocchi

引用次数: 0

Solution of planar elastic stress problems using stress basis functions 利用应力基函数求解平面弹性应力问题

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865231221994

Sankalp Tiwari, Anindya Chatterjee

{"title":"Solution of planar elastic stress problems using stress basis functions","authors":"Sankalp Tiwari, Anindya Chatterjee","doi":"10.1177/10812865231221994","DOIUrl":"https://doi.org/10.1177/10812865231221994","url":null,"abstract":"The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress problems in linear elasticity. In both methods, we split the sought stress σ into two parts, where neither part is required to satisfy strain compatibility. The first part, σ p, is any stress in equilibrium with the loading. The second part, σ h is a self-equilibrated stress field on the unloaded body. In both methods, σ h is expanded using tensor-valued global stress basis functions developed elsewhere. In the first method, the coefficients in the expansion are found by minimizing the strain energy based on the well-known complementary energy principle. For the second method, which is restricted to planar homogeneous isotropic bodies, we show that we merely need to minimize the squared L2 norm of the trace of stress. For demonstration, we solve nine stress problems involving sharp corners, multiple-connectedness, non-zero net force and/or moment on an internal hole, body force, discontinuous surface traction, material inhomogeneity, and anisotropy. The first method presents a new application of a known principle. The second method presents a hitherto unreported principle, to the best of our knowledge.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"42 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948423","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}

引用次数: 0

An experimentally informed continuum grain boundary model 基于实验的连续晶界模型

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-02-14 DOI: 10.1177/10812865231223921

S Syed Ansari, Amit Acharya, Alankar Alankar

{"title":"An experimentally informed continuum grain boundary model","authors":"S Syed Ansari, Amit Acharya, Alankar Alankar","doi":"10.1177/10812865231223921","DOIUrl":"https://doi.org/10.1177/10812865231223921","url":null,"abstract":"A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"195 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948522","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}

引用次数: 0

Numerical methods in Poisson geometry and their application to mechanics 泊松几何中的数值方法及其在力学中的应用

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-25 DOI: 10.1177/10812865231217096

Oscar Cosserat, Camille Laurent-Gengoux, Vladimir Salnikov

引用次数: 0

Growth-induced delamination of an elastic film adhered to a cylinder 粘附在圆柱体上的弹性薄膜的生长诱导分层

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-01-08 DOI: 10.1177/10812865231209412

Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi

{"title":"Growth-induced delamination of an elastic film adhered to a cylinder","authors":"Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi","doi":"10.1177/10812865231209412","DOIUrl":"https://doi.org/10.1177/10812865231209412","url":null,"abstract":"We study the delamination induced by the growth of a thin adhesive sheet from a cylindrical, rigid substrate. Neglecting the deformations along the axis of the cylinder, we treat the sheet as a one-dimensional flexible and compressible ring, which adheres to the substrate by capillary adhesion. Using the calculus of variations, we obtain the equilibrium equations and in particular arrive at a transversality condition involving in a non-trivial way the curvature of the substrate, the extensibility of the ring and capillary adhesion. By numerically solving the equilibrium equations, we show that delamination by growth occurs through a discontinuous transition from the fully adherent solution to the partially delaminated one. The shape of the delaminated part can take the form either of a ruck, with a small slope, or a fold, with a large slope. Furthermore, in the weak adhesion regime, complete delamination may occur. We construct the phase diagram between the different solutions in the parameter space. In the quasi-incompressible limit, numerical results are also supported by asymptotic calculations both in the strong and weak adhesion regimes.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"34 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139446521","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}

引用次数: 0