A More General Orthotropic Strain-Rate Potential Based on the Linear Transformation Method

A strain-rate potential (SRP) can be used in place of the classical stress potential to describe the response of plastically deforming solids. Orthotropic potentials are typically developed by extending existing isotropic criteria. For mathematical convenience, the construction of orthotropic SRPs using the linear transformation approach often involves a constrain on the fourth-order orthotropic tensor such that the transformed stress (and therefore strain-rate) tensors are deviatoric. This constrain is not however necessary to ensure plastic incompressibility and in fact reduces the number of independent orthotropic coefficients from nine to six, impairing the flexibility of the criterion. In this work, a new definition is proposed for the fourth-order orthotropic strain-rate transformation tensor with no constrains on the original form of the stress transformation tensor counterpart, such that the number of independent orthotropic coefficients is maximum. Based on this idea, as a proof of concept, a more general orthotropic SRP is construct, dual of a quadratic stress potential with a single linear transformation for materials with the same response in tension and compression.