Identifiability of material parameters in solid mechanics

Abstract

Material parameter identification using constitutive models of elasticity, viscoelasticity, rate-independent plasticity and viscoplasticity has a long history with regard to homogeneous and inhomogeneous deformations. For example, uniaxial tensile tests, pure shear tests, torsion experiments of thin-walled tubes or biaxial tensile tests are used to obtain the material parameters by solving the inverse problem. Frequently, the parameters are determined by numerical optimization tools. In this paper, we investigate some very basic single- and two-layered examples regarding identifiability, because these tests are the basis for more complex geometrical and physical nonlinear problems. These simple examples are the uniaxial tensile/compression case, biaxial tensile tests of a cruciform specimen, torsion of a thin-walled tube, a thick-walled tube under internal pressure and the indentation test. For the thick-walled tube under internal and external pressure with an axial pre-strain with several layers, an analytical solution is provided directly suitable for programming. The aim is to get an understanding whether some problems lead to non-identifiable parameters.