A remapping scheme for history‐dependent material state variables. (23rd March 2020)

• Record Type: Journal Article
• Authors: Versino, Daniele; Mourad, Hashem M.; Luscher, Darby J.
• Is Part Of: International journal for numerical methods in engineering. Volume 121:Number 14(2020)
• Page Start: 3132
• Page End: 3158
• Publication Date: 2020-03-23
• Subjects: advection -- arbitrary eulerian lagrangian -- History variables -- interpolation -- remapping -- state‐dependent variable; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6350
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We present an interpolation scheme for use with material models involving history‐dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history variables and produces admissible interpolations of the material's state variables. After introducing a general solution scheme for the problem, a simplified and more computationally efficient method is derived. Finally, as a validation problem for the proposed methods, we consider the advection of internal state variables belonging to material models with highly nonlinear yield surfaces.