Analytical tangents for arbitrary material laws derived from rheological models at large deformations

The development of suitable material laws for various material classes is an essential preliminary task for conducting realistic simulations. Within the framework of large deformations, one recognized approach is the utilization of rheological connections allowing the construction of arbitrary models. A common method to calculate the stress response of such a material model is to formulate a set of algebraic and ordinary differential equations and to solve them numerically. However, in this work, only stress relations between different rheological elements are formulated and directly solved by a numeric algorithm without the need to derive the typical system of algebraic/differential equations. The required derivatives for the solution of these equations for this algorithm and the stiffness of the material model are calculated analytically following the same general principle as the algorithm calculating the stress response. This improves stability and computation effort compared to a forward difference scheme.