Mathematical modeling of the overall time-dependent behavior of non-ageing viscoelastic reinforced composites

Abstract

New mathematical and numerical formulations are developed for effective time-dependent non ageing viscoelastic behavior of linear viscoelastic composites. The modeling is based on the dynamic Green’s functions, integral equations, and Volterra product. The time concentration tensor is derived through numerical solution of the integral equation and the Mori–Tanaka micromechanical model. The developed modeling gives explicit expressions of effective properties through convolution products in the Stieltjes space. A numerical procedure is developed allowing the calculation of the tensoriel convolution product and its inverse. Based on Carson–Laplace transform, the frequency dependent effective properties are also obtained and converted to the time domain. For viscoelastic Prony laws and inclusions with various shapes, numerical results are presented and compared with the approach based on the Laplace transform and the correspondence principle.