Rate-independent dissipation in phase-field modelling of displacive transformations. (May 2018)

• Record Type: Journal Article
• Authors: Tůma, K.; Stupkiewicz, S.; Petryk, H.
• Is Part Of: Journal of the mechanics and physics of solids. Volume 114(2018)
• Page Start: 117
• Page End: 142
• Publication Date: 2018-05
• Subjects: Phase-field method -- Microstructure -- Martensite -- Twinning -- Non-smooth optimization; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2018.02.007
• Languages: English
• ISSNs: 0022-5096

Abstract

Graphical abstract: Abstract: In this paper, rate-independent dissipation is introduced into the phase-field framework for modelling of displacive transformations, such as martensitic phase transformation and twinning. The finite-strain phase-field model developed recently by the present authors is here extended beyond the limitations of purely viscous dissipation. The variational formulation, in which the evolution problem is formulated as a constrained minimization problem for a global rate-potential, is enhanced by including a mixed-type dissipation potential that combines viscous and rate-independent contributions. Effective computational treatment of the resulting incremental problem of non-smooth optimization is developed by employing the augmented Lagrangian method. It is demonstrated that a single Lagrange multiplier field suffices to handle the dissipation potential vertex and simultaneously to enforce physical constraints on the order parameter. In this way, the initially non-smooth problem of evolution is converted into a smooth stationarity problem. The model is implemented in a finite-element code and applied to solve two- and three-dimensional boundary value problems representative for shape memory alloys.