Rate-independent dissipation in phase-field modelling of displacive transformations. (English) Zbl 1441.74147
Summary: 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.
MSC:
| 74N99 | Phase transformations in solids |
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
| 74N05 | Crystals in solids |
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