Related papers: Numerical Studies of a Hemivariational Inequality …
In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…
In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our approach is based on a mixed formulation involving a…
In recent years, a number of experimental studies have been conducted to investigate the mechanical behavior and damage mechanisms of articular cartilage under impact loading. Some experimentally observed results have been explained using a…
This paper presents an analytical model of punctual elastic contact between a rigid body of arbitrary geometry and a plane surface. A simple analytical model is developed in order to evaluate the contact force knowing the volume of…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…
We present a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. The numerical calculations mainly focus on the contact area and the interfacial separation…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming…
An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a…
Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…
We introduce a model of friction between two contacting (stationary or co-sliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact…
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution…
We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the…
For some time now, wood has offered itself as an alternative to other modern construction materials, and has become the material of choice for structures, mainly because of its renewable nature, durability and ease of shaping. However, once…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…