Invariant anisotropic large deformation deterministic and stochastic combined load failure criteria

The deterministic Shanley-Ryder interaction failure criterion is reformulated in terms of generalized stress tensors and cast into two distinct invariant forms, one for applied stresses and the other for failure stresses. This generalization extends its use to deterministic and stochastic problems with large deformations as well as to any arbitrary anisotropic material. Additionally, the original N-dimensional failure surfaces corresponding to N combined loads are reduced to a universal three-dimensional failure surface in terms of three loading, geometric and material parameters. Although a greater number of such parameters could be used, the accuracy of fit to data based on only three parameters negates such a need. Illustrative examples are presented and the influence of parametric variations is discussed.