A quasistatic contact problem with normal compliance and damage involving viscoelastic materials with long memory

In this work, a model for the quasistatic frictionless contact between a viscoelastic body with long memory and a foundation is studied. The material constitutive relation is assumed to be nonlinear and the contact is modelled with the normal compliance condition, i.e., the obstacle is assumed defor...

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Vydané v:Applied numerical mathematics Ročník 58; číslo 9; s. 1274 - 1290
Hlavní autori: Campo, M., Fernández, J.R., Rodríguez-Arós, Á.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.09.2008
Elsevier
Predmet:
Damage
Error estimates
Exact sciences and technology
Finite elements
Frictionless contact
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical simulations
Ordinary differential equations
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Viscoelastic material with long memory
Weak solutions
65M15
Finite elements
Error estimates
Numerical simulations
Weak solutions
74S05
49J40
Viscoelastic material with long memory
Frictionless contact
74M15
Damage
Solution uniqueness
Error estimation
Differential equation
Existence of solution
Contact problems
Numerical method
Euler scheme
Partial differential equation
Non linear equation
Finite element method
Variational problem
Numerical solution
Approximate method
Initial value problem
Mechanical contact
Discrete scheme
Numerical analysis
Boundary value problem
Weak solution
Applied mathematics
Two-dimensional calculations
ISSN:0168-9274, 1873-5460
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Popis
Shrnutí:In this work, a model for the quasistatic frictionless contact between a viscoelastic body with long memory and a foundation is studied. The material constitutive relation is assumed to be nonlinear and the contact is modelled with the normal compliance condition, i.e., the obstacle is assumed deformable. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive a variational formulation for the problem and prove the existence of its unique weak solution. Then, we introduce a fully discrete scheme for the numerical solutions of the problem, based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, and we obtain error estimates on the approximate solutions. Finally, some numerical results are presented in the simulation of two-dimensional test problems.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2007.07.003