An implementation of the phase-field model based on coupled thermomechanical finite element solvers for large-strain twinning, explicit dynamic fracture and the classical Stefan problem

摘要

The implementation of a phase-field model in finite elements usually requires significant expertise and involves the development of a user element with additional degrees of freedom. An alternative implementation of the phase-field model within a thermo-mechanical finite element simulation package was presented in (Cho et al 2012 Int. J. Solids Struct. 49 1973-1992), where the phase-field variable is treated as the temperature degree of freedom. However, this approach has only been used for small strain phase-field modelling of martensitic transformations and quasistatic phase-field modelling of fracture. In this work, we present a phase-field finite element implementation via the temperature degree of freedom for several additional cases from the literature: (i) the large-strain phase-field description of deformation twinning presented in (Clayton and Knap 2011 Physica D 240 841-858), (ii) phase-field description of brittle fracture with inertial effects based on the theory from (Molnar and Gravouil 2017, Finite Elem. Anal. Des. 130 27-38) and (Miehe et al 2010 Int. J. Numer. Methods Eng. 83 1273-1311) and (iii) the classical Stefan problem of solidification presented in (Mackenzie and Robertson 2002 J. Comput. Phys. 181 526-544). The last problem involves the temperature and phase-field variables as unknowns.