A robust multisurface return-mapping algorithm and its implementation in Abaqus

The simulation of complex material failure processes requires a precise differentiation of the involved failure mechanisms like fracture or plasticity. This is commonly achieved by using a so-called multisurface failure criterion, where each failure surface is related to a certain failure mechanism. In the case of plasticity, failure surfaces define the elastic domain of the material and any stress state outside of this domain is considered non-admissible and must be returned to the boundary of the elastic domain. So-called return-mapping algorithms are often used and well-studied methods for finding such valid stress states. However, their implementation in numerical simulation tools is often not robust and efficient enough for complex problems that involve sophisticated multisurface definitions. In this work, we present a multisurface return-mapping algorithm and its implementation in the finite element software Abaqus. We found that with additional and enhanced iterative solver methods, the classic Newton-Raphson-based implementation of the algorithm can be improved in order to find solutions to otherwise not returnable stress states. The added computational burden is minimal, as more stress states can be returned without reducing the size of the load increments. The paper focuses on the implementation aspects of such problems and offers the reader a thorough guide and the source code for an Abaqus implementation. We applied the algorithm to simulate the highly orthotropic behavior of wood, allowing us to predict plastic failure of various wooden structures and components. •We show that classic return-mapping methods not always lead to converged states.•A combination of solution strategies gives a robust and efficient implementation.•The source code for an Abaqus user subroutine is provided.•Various materials can be simulated by adapting the Tsai-Wu yield functions.