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When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…

Materials Science · Physics 2015-04-23 A. S. Yurkov

We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…

Numerical Analysis · Mathematics 2017-10-06 Pavel Bochev , James Cheung , Max Gunzburger , Mauro Perego

We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…

Numerical Analysis · Mathematics 2021-12-07 Antoine Laurain

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the…

Numerical Analysis · Mathematics 2015-03-11 Leonardo A. Poveda , Sebastian Huepo , Victor M. Calo , Juan Galvis

The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape defects in a 2D and 3D elastic plate. Given surface…

Analysis of PDEs · Mathematics 2022-10-06 Eric Bonnetier , Angele Niclas , Laurent Seppecher

Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…

Analysis of PDEs · Mathematics 2014-09-26 Philippe Laurencot , Christoph Walker

In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal,…

Numerical Analysis · Mathematics 2023-06-16 Fanyi Yang

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

Numerical Analysis · Mathematics 2025-05-20 Haifeng Ji , Zhilin Li

This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…

Numerical Analysis · Mathematics 2022-05-11 Maximilian Bauer , Mario Bebendorf

The two-phase composite approach of Estrin et al. (1998) describes an evolving dislocation cell structure. Mckenzie et al. (2007) enhanced the model to capture the effects of hydrostatic pressure and temperature during severe plastic…

Materials Science · Physics 2013-03-08 C. B. Silbermann , A. V. Shutov , J. Ihlemann

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…

Numerical Analysis · Mathematics 2023-05-01 Stefan Frei , Gozel Judakova , Thomas Richter

This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…

Numerical Analysis · Mathematics 2025-05-20 Paulo Akira F. Enabe , Rodrigo Provasi

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential…

Analysis of PDEs · Mathematics 2024-12-06 Esmaeal Ghavanloo , Patrizio Neff

We consider the perturbation problem of a Mode III interfacial crack. The perturbation is of geometrical type and can be both perturbation of the crack faces and perturbation of the interface, which can deviate from the initial straight…

Mathematical Physics · Physics 2010-04-05 A. Piccolroaz , G. Mishuris , A. B. Movchan

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…

Classical Physics · Physics 2022-01-31 Nadezhda I. Aleksandrova

We study some spring mass models for a structure having a unilateral spring of small rigidity $\epsilon$. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including…

Dynamical Systems · Mathematics 2011-01-20 Stéphane Junca , Bernard Rousselet

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation…

Numerical Analysis · Mathematics 2013-08-13 Heiko Gimperlein , Matthias Maischak , Elmar Schrohe , Ernst P. Stephan

This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…

Numerical Analysis · Mathematics 2022-09-02 Shuhao Cao , Long Chen , Ruchi Guo , Frank Lin

We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of three-dimensional linear…

Analysis of PDEs · Mathematics 2022-05-03 Marin Bužančić , Kirill Cherednichenko , Igor Velčić , Josip Žubrinić

We present a novel theoretical approach to incorporate electronic interactions in the study of two-dimensional topological insulators. By exploiting the correspondence between edge state physics and entanglement spectrum in gapped…

Mesoscale and Nanoscale Physics · Physics 2023-09-06 Marcela Derli , E. Novais