Calculation of Transient Response of Viscoelastic Unbounded Domains by Direct Boundary Element Method

Abstract

Mixed boundary value problems of solid mechanics with bounded as well as unbounded domains are treated efficiently by numerical solutions of Boundary Integral Equations (BIE) in time domain with the Boundary Element Method (BEM). Thus, the spatial problem dimension is reduced by one. Viscoelastic constitutive behaviour is implemented by means of a Laplace transform technique based on an elastic-viscoelastic correspondence principle. The concept of fractional differintegration generalizes conventional constitutive equations and provides improved curve fitting of measured material response with less parameters. As the implementation of viscoelasticity is provided in each time step in the Laplace domain, efficient algorithms for the inverse transformation in time domain are needed. This is why the performance of adapted algorithms by Talbot, Durbin and Crump are compared. The impact response of a base plate bonded on a viscoelastic soil halfspace is discussed as numerical example. Viscous forces increase the velocities of surface wave propagation and cause attenuation in addition to the so called geometrical damping by radiation.