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This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modelling the friction-based motion of a two-body crawling system. Here for each…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Inhomogeneity and anisotropy play a crucial role in attributing articular cartilage its properties. The frictionless contact model constructed here consists in two thin biphasic transversely isotropic transversely homogeneous (TITH)…
Variational inequalities as an effective tool for solving applied problems, including machine learning tasks, have been attracting more and more attention from researchers in recent years. The use of variational inequalities covers a wide…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
Nonlinear systems and interaction forces are pervasive in many scientific fields, such as nanoscale metrology and materials science, but their accurate identification is challenging due to their complex behaviour and inaccessibility of…
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models…
Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering systems (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on…
The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…
This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed third-medium formulation embeds a…
In this paper we propose on continuous level several domain decomposition methods to solve unilateral and ideal multibody contact problems of nonlinear elasticity. We also present theorems about convergence of these methods.
We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…
Computational modeling of contact is fundamental to many engineering applications, yet accurately and efficiently solving complex contact problems remains challenging. In this work, we propose a new contact algorithm that computes contact…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…
In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…