Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I. Formulation Original Research Article

The formulation of an Adaptive Dynamic Relaxation algorithm with application to non-linear hyperelastic structures is presented. A complete derivation of the Dynamic Relaxation method is given, and the adaptive scheme used to ensure reliability and improve performance is described. Finite element equations are derived for the non-linear analysis of elastic and hyperelastic solids subject to large deformations. The hyperelastic material is assumed to be nearly incompressible, and it is modeled using the Mooney-Rivlin material law using a penalty method to enforce incompressibility. A very simple and efficient contact algorithm based on solver constraints is developed to enforce frictionless contact conditions.