Elastomeric materials show a wide range of different elastic and inelastic properties. Additionally, this class of materials is subjected to large deformations. Considering all these effects, fracture mechanical investigations are very challenging tasks and cannot be performed with standard approaches. Effects of inhomogeneities and discontinuities such as cracks can be investigated with the so-called material force approach in an efficient and elegant way. For comprehensive investigations of inelastic materials, the complete balance of the material motion problem has to be formulated. In this case, the material volume forces depend on the internal history variables which are required for the inelastic constitutive model. This paper derives a general formulation for rate-dependent and rate-independent inelastic materials based on a multiplicative split of the deformation gradient to cover viscoelastic and elastoplastic materials at finite deformations.

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.

Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.

A fully three-dimensional fracture mechanical approach is introduced which may serve as a basis for tire durability simulations utilizing the finite element method. The so-called material force approach is employed as an elegant alternative characterization of the energy release rate or the J-integral to describe discrete cracks. As a vector quantity, it even yields directional information. The method is applicable in the context of finite strains and nonlinear elasticity and inelasticity. Using the shown approach, a physical and efficient modeling of fracture sensitivity of tires is obtained.

The material forces represent the thermodynamically driving forces on any kind of inhomogeneity and discontinuity. For comprehensive investigations, the balance of the inverse motion problem has to be formulated and evaluated to separate different portions of the material forces arising from different inhomogeneities and discontinuities. This paper presents a general approach for inelastic material models based on the multiplicative split of the deformation gradient in order to calculate the J ‐integral of an inelastic crack tip. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)