The aim of this project is the formulation and implementation of a method analog to the pRBMOR but without the assumption of small deformations. New problems arise by utilization of nonlinear measures deformation and by consideration of finite rotations. These problems are to be solved with physical-mathematical approaches and numerical techniques.
As a first step, a new method is developed for model order reduction in the hyperelastic case by means of a reduced basis. Based on this, dissipative effects will be addressed. One of the problems that come along is that superposition of self-equilibrated stress-fields is not possible as in the geometrically linear description. Ideas to solve these problems efficiently include variational formulations, development of new numerical approximation techniques, and incorporation of large data sets from pre-calculations.
Oliver Kunc, M. Sc.
Dr.-Ing. Dipl.-Math. techn. Felix Fritzen