A viscoelastic-plastic model for skeletal structural systems with clearances

Abstract

The paper is concerned with the mathematical modelling and numerical solution of unilateral problems for viscoelastic-plastic structural systems. A new material model is proposed in which the viscoelastic and plastic strains are governed by different constitutive laws. The model is restricted to isothermal quasistatic deformation processes under conditions of geometric linearity. The mechanical problem is posed in the format of piecewise linear plasticity and the unilateral contact conditions are described by means of the clearance function. The linear viscoelastic laws are integrated by a creep approach method, which allows for jump-discontinuities in the history of stress. For the evolution of plastic strains an implicit method is used. The problem is formulated and solved as a sequence of nested (mixed) linear complementarity problems. The question of existence and uniqueness of a solution to the problem is discussed. A numerical algorithm based on the pivotal transformations is devised and its stability is shown numerically. Results of numerical experiments for several illustrative examples of a beam/foundation system subjected to nonproportional loading histories are presented . The results clearly demonstrate the impact of the history of loading and the unilateral constraints upon the current state of the structural system.