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We investigate a novel category of Caputo fractional Moreau's sweeping process, formulated in a real Hilbert space, by the inclusion below − D t α 0 c u ( t ) ∈ N Ξ ( t ) ( A ( D t α 0 c u ( t ) ) + B u ( t ) ) . Our primary focus is to develop a ...

• A novel category of Caputo fractional Moreau's sweeping process is considered.
• The unique solvability of Caputo fractional Moreau's sweeping process is obtained.
• A complicated dynamical viscoelastic contact problem with fractional ...

This paper investigates, without any regularization procedure, the sensitivity analysis of a mechanical friction problem involving the (nonsmooth) Tresca friction law in the linear elastic model. To this aim a recent methodology based on advanced ...

In this paper, we are concerned with numerical analysis on optimal control of a dynamic contact model. Our work builds on some existing results of this model. We derive a weak formulation, and present an approximate problem for the weak ...

A new nonlinear mathematical model is proposed that describes an equilibrium of a two-dimensional elastic body with two interacting thin rigid inclusions. Thin rigid inclusions are defined by straight line segments. In the initial state of the ...

This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are ...

This work focuses on the numerical performance of HHT-$\alpha$ and TR-BDF2 schemes for dynamic frictionless unilateral contact problems between an elastic body and a rigid obstacle. Nitsche’s method, the penalty method, and the augmented Lagrangian ...$\stackrel{}{}$$$

In this paper we investigate a class of time-dependent quasi-variational-hemivariational inequalities (TDQVHVIs) of elliptic type in a reflexive separable Banach space, which is characterized by a constraint set depending on a solution. The ...

We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral contact problems are taken into account, as well as both Tresca and Coulomb friction models. We ...

We deal with a class of elliptic quasivariational inequalities with constraints in a reflexive Banach space. We use arguments of monotonicity, convexity and compactness in order to prove a convergence criterion for such inequalities. This ...

In the paper we deal with a new class of systems of differential quasi-hemivariational inequalities. The system consists of a time-dependent constrained elliptic quasi-hemivariational inequality, an evolution quasi-hemivariational inequality and ...

In this work we introduce a Hybridizable Discontinuous Galerkin (HDG) formulation for Computational Contact Mechanics (CCM). In particular we extend the HDG formulation for nonlinear elasticity originally proposed by Soon, Cockburn, ...

• Finite deformations and computational contact mechanics based on HDG formulations.

We study the Nitsche-based finite element method for contact with Coulomb friction considering both static and dynamic situations. We provide existence and/or uniqueness results for the discretized problems under appropriate assumptions on ...

We investigate indentation of a linear viscoelastic half-space with periodically distributed heterogeneities by a smooth, rigid, axisymmetric indenter of an arbitrary profile. For this, we first show how such materials may be homogenized directly ...

• A new unilateral constraint frictional contact model for a version of normal velocity is studied.

A new model that describes a dynamic frictional contact between a viscoelastic body and an obstacle is investigated in this paper. We consider a nonlinear viscoelastic constitutive law which involves a convex subdifferential inclusion ...

We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is ...

We present a mathematical model of the compression of multicellular aggregates, and we specialise it to a compression-release test that is well known in the biological literature. Within the adopted mechanical setting, a multicellular aggregate is ...

The 2D-model of an elastic body with a finite set of rigid inclusions is considered. We assume that the body can come in frictionless contact on a part of its boundary with a rigid obstacle. On the remaining part of the body’s boundary ...

This paper investigates the sensitivity analysis of a scalar mechanical contact problem described by a boundary value problem involving the Tresca’s friction law. The sensitivity analysis is performed with respect to right-hand source and boundary ...

In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities in real Hilbert spaces. This includes the unique solvability and continuous dependence of the solution on the ...

In this paper we study a new abstract evolutionary variational–hemivariational inequality which involves unilateral constraints and history–dependent operators. First, we prove the existence and uniqueness of solution by using a mixed equilibrium ...