Incrementalization procedure for elasto‐plastic constitutive model with multiple, intersecting yield surfaces

Constitutive models for description of the non‐linear stress‐strain behaviour of engineering materials are often developed and presented in forms which cannot be employed directly in non‐linear matrix computer analysis codes. Presented herein is a procedure for developing the incremental stiffness matrix for an elasto‐plastic material model with multiple, intersecting yield surfaces. Associated or non‐associated flow may occur on the individual yield surfaces. The material stiffness matrix is non‐symmetric if non‐associated flow occurs on any one of the yield surfaces. In order to illustrate the matrix forms which are generated, the case of a recently developed model with two yield surfaces is presented in detail. This model involves associated flow on one and non‐associated flow on the other yield surface.