Abstract
The present paper deals with the mathematical and numerical analysis of evolution problems in nonlinear small strains viscoelasticity of Burger's type. After a brief review of the mechanical model, the viscoelastic problem to be solved is written as an abstract evolution problem. The associated operator is proved to be maximal monotone, thus implying existence and uniqueness of solutions. This problem is then solved numerically by a backward Euler discretization in time, a finite element approximation in space and by using a preconditioned conjugate gradient algorithm for solving the resulting nonlinear algebraic systems. Numerical results are finally presented to illustrate the solution procedure.
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