A simplified canonical form algorithm with application to porous metal plasticity

A canonical form for the representation of material constitutive equations within standard finite element codes has been developed which is deceptive in its simplicity. Substitution of different equation systems is trivial and a consistent material Jacobian may be obtained automatically. The process is essentially numerical and does not involve the difficult algebraic manipulation associated with more traditional approaches. It is nevertheless exact because partial derivatives are derived analytically and simple because calculation of these derivatives is the only algebraic manipulation required. The remainder of the process is generic. In this paper, the algorithm is simplified further. A much more detailed and transparent explanation of the key to the method is given, namely calculation of the consistent Jacobian. A trivial modification also extends the method to plane stress. The original algorithm was validated for a simple material model. The new form is used to implement the significantly more difficult modified Gurson model for porous metal plasticity with hydrostatic yield dependence. It is tested for single element cases involving total collapse and also used to simulate necking of a notched cylindrical bar