Boundary element calculation of transient response of viscoelastic solids based on inverse transformation

Mixed boundary value problems of solid mechanics are treated by numerical solutions of Boundary Integral Equations (BIE) in time domain with the Boundary Element Method (BEM) thus reducing the spatial problem dimension 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 fewer 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 Clump are compared. The impact response of a base plate bonded on a viscoelastic soil halfspace is discussed as a numerical example. Viscous forces increase the velocities of surface wave propagation and cause attenuation in addition to the so called geometrical damping by radiation.