Identification of memory kernels for materials with memory

Abstract

In this contribution, materials with ‘thermal memory’ and viscoelastic materials with ‘inelastic’ behaviour due to memory effects, are considered. In both cases the interesting properties are described by mathematical models consisting of boundary value problems of parabolic and hyperbolic partial differential equations, respectively, where the differential equations contain additional integral expressions including ‘memory-functions’ describing the memory property of the material. Therefore two problems arise; (i) to solve the boundary value problems (which means to describe the property of the material considered) for known memory functions (the direct problem); and (ii) identification of the unknown memory-functions, such that fixed additional information with respect to the material is realised (the inverse problem).