A three‐invariant smooth cap model with mixed hardening

A cap model is presented that uses a multiplicative formulation to define a smooth (continuous derivative) failure surface that includes the third stress invariant. This formulation offers several advantages over previous cap model formulations: elimination of ‘corner’ coding, resulting in a numerical algorithm suitable for vectorization; a three stress invariant implementation that is easily specialized to classical failure surfaces or generalized to represent observed material response; and a framework for easily implementing additional model features such as kinematic hardening as demonstrated.