Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets Under Plane Stress State

A general proposition of an energy-based limit condition for anisotropic materials exhibiting strength-differential effect (SDE) based on spectral decomposition of elasticity tensors and the use of scaling pressure-dependent functions is specified for the case of orthotropic materials. A detailed algorithm (based on classical solutions of cubic equations) for the determination of elastic eigenstates and eigenvalues of the orthotropic stiffness tensor is presented. A yield condition is formulated for both two-dimensional and three-dimensional cases. Explicit formulas based on simple strength tests are derived for parameters of criterion in the plane case. The application of both criteria for the description of yielding and plastic deformation of metal sheets is discussed in detail. The plane case criterion is verified with experimental results from the literature.