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A computational micro‐sphere model applied to the simulation of phase‐transformations
Author(s) -
Ostwald R.,
Bartel T.,
Menzel A.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900390
Subject(s) - basis (linear algebra) , transformation (genetics) , boundary value problem , phase (matter) , homogeneous , finite element method , mathematics , statistical physics , computer science , mathematical analysis , geometry , physics , thermodynamics , biochemistry , chemistry , quantum mechanics , gene
We present an efficient model for the simulation of polycrystalline materials undergoing solid to solid phase transformations. As a basis, we use a one‐dimensional, thermodynamically consistent phase‐transformation model. This model is embedded into a micro‐sphere formulation in order to simulate three‐dimensional boundary value problems. To solve the underlying evolution equations, we use a newly developed explicit integration scheme which could be proved to be unconditionally A‐stable. Besides the investigation of homogeneous deformation states, representative finite element examples are discussed. It is shown that the model nicely reflects the overall behaviour.