The Padé–approximation for matrix exponentials applied to an integration algorithm preserving plastic incompressibility

摘要

The exponential update formalism is applied to an integration algorithm for rate–independent single crystal plasticity to fulfill the compelling constraint of plastic incompressibility. The exponential function of a non–symmetric tensor valued argument is expressed in terms of the Padé–approximation, which is capable to approximate the matrix exponential without large computational efforts. Thus, the plastic incompressibility condition is enforced during the solution of a highly nonlinear system of equations. Examples show the applicability of the method.