An Incremental Constituve Law for Damaging Viscoelastic Materials

Abstract

ABSTRACT. An incremental formulation suitable for modelling of materials with damaging viscoelastic behaviours is proposed in this work. A constitutive law based on linear viscoelasticity coupled with strain dependent damage is developed. The viscoelastic model is represented by a generalized Maxwell's chain. It is governed by a set of internal stress variables attached to the branches of the Maxwell's chain. The damage evolution is governed by values gained by a pseudo strain. The coupled law is turned into an incremental form suitable for the numerical analysis of damaging time dependent structures. Taking advantage of the incremental form, the coupled damaging viscoelastic law is implemented as a step-by-step procedure. The calculation procedure consists of a damaging elastic step followed by a number of damaging viscoelastic steps. The damage variable is adjusted at each step, according to the value gained by the pseudo strain. Exemplary calculations are worked out for two cases of uniaxial and biaxial variable or cyclic loadings. The results show the efficiency of the incremental model. It is worth noticing that the time increment used for the calculations is not necessarily small. As a consequence, precise analysis of damaging time dependent structures can be performed for low calculation cost.