The material force approach is an efficient, elegant, and accepted means to compute the J‐integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate‐dependent (visco‐elastic) materials described for example by the physically based Bergström‐Boyce model can be investigated. For these investigations, the so‐called material volume forces have to be computed in order to separate the driving forces acting on the visco‐elastic zone around the crack tip from the driving forces acting on the crack tip itself, representing the crack driving force. To illustrate the effectiveness of this approach, the so‐called dwell‐effect of elastomeric materials is investigated.
a b s t r a c tThe nature of elastomeric material demands the consideration of finite deformations, nonlinear elasticity including damage as well as rate-dependent and rate-independent dissipative properties. While many models accounting for these effects have been refined over time to do better justice to the real behavior of rubber-like materials, the realistic simulation of the elastoplastic characteristics for filled rubber remains challenging.The classical elastic-ideal-plastic formulation exhibits a distinct yield-surface, whereas the elastoplastic material behavior of filled rubber components shows a yield-surface free plasticity. In order to describe this elastoplastic deformation of a material point adequately, a physically based endochronic plasticity model was developed and implemented into a Finite Element code. The formulation of the ground state elastic characteristics is based on Arruda and Boyce (1993) eight-chain model. The evolution of the constitutive equations for the nonlinear endochronic elastoplastic response are derived in analogy to the Bergström-Boyce finite viscoelasticity model discussed by Dal and Kaliske (2009).
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