Related papers: Quasistatic contact problem with unilateral constr…
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and…
We study a new nonlinear system which contains a partial differential equation, a quasivariational inequality and a parabolic variational inequality in Banach spaces. We obtain the unique solvability of the coupled system under moderate…
In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a…
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…
Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences…
A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a…
The interaction between visco-elasto-plastic and adhesive particles is the subject of this study, where "meso-particles" are introduced, i.e., simplified particles, whose contact mechanics is not taken into account in all details. A few…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors, for visco-elasticity with large deformations and conditional compatibility, where the…
The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear viscoelasticity. We begin by examining the physical foundations of Boltzmann and…
In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator,…
We present a novel convex formulation that models rigid and deformable bodies coupled through frictional contact. The formulation incorporates a new corotational material model with positive semi-definite Hessian, which allows us to extend…
Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward…
We model numerically the partial normal contact of two elastic rough surfaces with highly correlated asperities. Facing surfaces are unmated and described as self-affine with a Hurst exponent H. The numerical algorithm is based on Fourier…
We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith…
In Part I of this two part series, we presented a multi-neighbor dependent contact model for adhesive elastic-plastic particles built upon the method of dimensionality reduction that is valid for the elastic and fully-plastic contact…
We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…
This paper advances an analytical incremental contact model for the purely elastic or elastic-perfectly plastic Gaussian rough surfaces. The contact is modelled by the accumulation of identical circular contacts with radius given by the…
A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…