An efficient return mapping algorithm for general isotropic elastoplasticity in principal space

This paper develops an efficient return mapping algorithm for implicit integration of general isotropic elastoplastic constitutive equations. A set of three mutually orthogonal unit base tensors in conjunction with a new set of three invariants are employed for the representation of arbitrary isotropic tensor valued and scalar valued functions of the stress tensor involved. The base tensors are constructed from the stress tensor by using the representation theorem and the three invariants are defined by the projection of the stress onto the base tensors. Geometrically, the base tensors are characterized by three mutually orthogonal unit vector and the three invariants are regarded as the components of a vector in principal space. With them, both the elastic constitutive equations and the flow rule of plasticity are represented as simple relationship among vectors in principal space. The return mapping algorithm associated with the representation is formulated in principal space and dimensions of the problem are reduced from six down to three. The explicit computation of the principal directions and the coordinate transformation from the principal reference frame to the global reference frame are omitted. The expressions for the consistent tangent operator for the proposed algorithm are derived in an efficient and closed-form manner. It consists of two parts: one is consistent with the return mapping in the fixed principal stress directions and another reflects the changes in the principal stress directions. Finally, a numerical example demonstrates the performances of the proposed implementation.

► A set of three mutually orthogonal base tensors is constructed in principal space.
► A new set of three invariants corresponding to the base tensors are defined.
► The constitutive equations are represented using the base tensors and invariants.
► The return mapping algorithm is formulated using the base tensors and invariants.
► The proposed method gives a faster execution time than other existing methods.