Blog posts
simulations in materials
Interetsed topics include:
- Material Point Method, eXtended Finite Element Method, and other mesh-free methods;
- Combined atomistic and continuum simulations;
- Multiscale homogenization.
Links to other blogs:
lecture note 13: Interpolating Shape Functions
lecture note 13: Interpolating Shape Functions
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lecture note 12: Material Point Method: 2D problems
lecture note 12: Material Point Method: 2D problems
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Simulations note 11: Material Point Method : Solution Procedure
Map from particles to grids
Interpolate from grid to particles
Constitutive models
Boundary conditions
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Simulations note 10: Material Point Method: Grid Equations
Material Point Method:
Grid Equations
Mass matrix
Lumped mass matrix
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Simulations note 9: Material Point Method: introduction
Variational principle
Particle discretization
Grid interpolation
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Elastic stress driven phase inversion
A typical two phase microstructure consists of a topologically continuous `matrix' phase in which islands of `precipitate' phase are embedded. Usually, the matrix phase is also the majority phase in terms of volume fraction. However, sometimes this relationship between the volume fraction and topology is reversed, and this reversal is known as phase inversion. Such a phase inversion can be driven by an elastic moduli mismatch in two-phase solid systems. In this paper (submitted to Philosophical magazine), we show phase inversion, and the effect of the elastic moduli mismatch and elastic anisotropy on such inversion.
Elastic stress driven rafting
During solid-solid phase transformations elastic stresses arise due to a difference in lattice parameters between the constituent phases. These stresses have a strong influence on the resultant microstructure and its evolution; more specifically, if there be externally applied stresses, the interaction between the applied and the transformation stresses can lead to rafting.