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Extending a finite strain hyperelastic micro‐sphere framework towards phase transformations
Author(s) -
Ostwald Richard,
Bartel Thorsten,
Menzel Andreas
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610179
Subject(s) - hyperelastic material , finite strain theory , helmholtz free energy , phase (matter) , transformation (genetics) , elastic energy , misnomer , mathematics , quadratic equation , materials science , physics , geometry , finite element method , thermodynamics , chemistry , quantum mechanics , biochemistry , philosophy , theology , gene
A finite strain micro‐sphere framework for hyperelastic solids elaborated by Carol et al. is extended towards the modelling of phase transformations in order to simulate polycrystalline solids under large deformations such as, e.g., shape memory alloys and shape memory polymers. The implemented phase transformation mechanism is based on statistical physics and is not restricted in terms of the number of solid material phases that can be considered, though we restrict the provided examples to two phases for the sake of conceptual clarity. The specifically chosen non‐quadratic format of the Helmholtz free energy functions considered on the micro‐plane level includes Bain‐type transformation strains for each of the phases considered. Following the Voigt assumption on the micro‐scale, identical total micro‐stretches act in each of the material phases, where a multiplicative decomposition into elastic and transformation‐related contributions is applied. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)