Symbolic derivation of potential based constitutive equations

Structural alloys used in high temperature applications exhibit complex thermomechanical behavior that is inherently time dependent and hereditary, as the current behavior depends not only on current conditions but on the thermomechanical history. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved, and error-prone, thus intelligent application of symbolic systems to facilitate this tedious processes can be of significant benefit. Here a computerized package, running under MACSYMA, capable of efficiently deriving potential based constitutive models, in analytical form (involving tensors, partial differentiation, invariants, and the like) is presented. Special purpose utility algorithms are designed and implemented to perform partial differentiation (chain rule), tensor manipulation, case distinction and simplification. Four constitutive theories reported in the literature are utilized to verify implementation accuracy. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.