A simple Kelvin and Boltzmann viscoelastic analysis of three-dimensional solids by the boundary element method

This paper presents a three-dimensional Boundary Element formulation for the analysis of simplified viscoelastic bodies without using internal cells. Two different constitutive models are considered. The first and simplest one is the Kelvin model, which does not consider instantaneous responses. The second, Boltzmann model, considers both instantaneous and viscous behaviour of materials. An appropriate kinematical relation together with differential viscoelastic constitutive representations are employed in order to built the proposed Scheme. Spatial approximations are applied for boundary elements before time solution. The proposed technique results in a time marching process that does not use relaxation (or creep) functions to recover viscous behaviour. Some examples are shown in order to demonstrate the accuracy and stability of the technique when compared to analytical solutions.