Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations
arXiv:1709.03896 · doi:10.1016/j.cma.2018.04.036
Abstract
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for regularization. Metastable martensitic microstructures, defined as solutions that are local minimizers of the total free energy, are of interest and are obtained as steady state solutions to the resulting transient formulation of Toupin's gradient elasticity at finite strain. This type of problem poses several numerical challenges including stiffness, the need for fine discretization to resolve microsstructures, and following solution branches. Stable and accurate time-integration schemes are essential to obtain meaningful solutions at reasonable computational cost. In this work we introduce two classes of unconditionally stable second-order time-integration schemes for gradient elasticity, each having relative advantages over the other. Numerical examples are shown highlighting these features.
References in corpus (3)
- Three-dimensional iso-geometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains
- Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition
- A numerical study of branching and stability of solutions to three-dimensional martensitic phase transformations using gradient-regularized, non-convex, finite strain elasticity
Cited by in corpus (4)
- Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
- A graph theoretic framework for representation, exploration and analysis on computed states of physical systems
- Reduced order models from computed states of physical systems using non-local calculus on finite weighted graphs
- Numerical analysis of non-local calculus on finite weighted graphs, with application to reduced-order modelling of dynamical systems