On the computational treatment of fully coupled crystal plasticity slip and martensitic transformation constitutive models at finite strains

• Published in: International journal for numerical methods in engineering 2022-11, Vol.123 (21), p.5155-5200
• Main Authors: Vieira de Carvalho, Miguel, Cardoso Coelho, Rui Pedro, Pires, Francisco M. Andrade
• Format: Article
• Language: English
• Subjects: Ablation; Algorithms; consistent linearization; Constitutive models; crystal plasticity; Crystallography; Deformation mechanisms; finite element method; Iterative methods; Iterative solution; martensitic transformation; Martensitic transformations; Mathematical models; numerical integration techniques; Parameters; Plastic properties; Polycrystals; Quadratures; Regularization; viscoplastic regularization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7059

In this article, four numerical techniques are formulated to improve the reliability and numerical efficiency of stress update algorithms of crystal‐plasticity‐like phenomena at finite strains. The resulting algorithmic setting is especially relevant for structural analyses of polycrystals and the multiscale evaluation of anisotropic microstructures in metallic materials. These techniques are exemplified with a constitutive model, which couples crystallographic slip and martensitic transformation deformation mechanisms with a viscous regularization. The model is characterized by a set of highly coupled equations expressed in a single system and solved by a monolithic solution procedure. The first technique employs a sub‐stepping procedure to generate a better initial guess for the Newton–Raphson scheme used in the iterative solution of the equilibrium problem at the Gauss quadrature point. Then, a logarithmic discretization of the exponential parameter of the viscoplastic law is proposed to approximate the target value of the exponential parameter incrementally in the return mapping algorithm. A strategy to remove the strain‐rate dependence and reduce the necessary viscoplastic parameters is also presented to help with the stiff equations that arise in the rate‐independent limit. Finally, an efficient strategy is suggested to complete the transformation process when the full martensitic transformation is approached. These techniques can be easily used in any combination and dramatically improve the model's efficiency by enabling more significant incremental steps to be used within the monolithic solution procedure. A thorough assessment of their impact is shown in a series of ablation studies.