Dr. Masato Tanaka, Institut für Mechanik, Universität Duisburg-Essen/Toyota Motor Corporation, Toyota, Japan will hold a lecture on „Complex-Step Derivative Approximation Schemes for the Robust Calculation of Numerical Constitutive Tangent Moduli“ next Wednesday, September 4, 2013, at 10 a.m at Nürnberger Ei, room 301.
In this presentation, a simple, robust and efficient numerical approximation of the tangent moduli from stress calculations at large strains is presented that can be easily implemented within standard FEM software and directly applied to the localization analysis to detect material instabilities. This method is based on the complex-step derivative approximation (CSDA) scheme, which uses complex numbers in computation of the derivatives and can provide nearly analytic accuracy when perturbation values are chosen close to machine precision. Implementation details of the approach are given and its performance is illustrated through representative numerical examples where finite deformations are involved. In addition to that, the accuracy of a localization measure which is computed directly from the numerically approximated tangent moduli are also investigated.