A finite strain elastoplastic model based on Flory’s decomposition and 3D FEM applications

• Published in: Computational mechanics Vol. 69; no. 1; pp. 245 - 266
• Main Author: Coda, Humberto Breves
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2022; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Constitutive models; Decomposition; Elastoplasticity; Engineering; Finite element method; Mathematical analysis; Mathematical models; Original Paper; Plastic flow; Strain; Theoretical and Applied Mechanics; Finite strain plasticity; Flory’s decomposition; Finite elements; Plastic flow
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-021-02092-4

The Flory’s decomposition is an important mathematical tool used to write hyperelastic constitutive models. As far as the author’s knowledge goes, it has not been used to write plastic flow directions in elastoplastic models and this study is an opportunity to introduce this simple strategy in so important subject. Adopting this decomposition it is possible to write an alternative total Lagrangian elastoplastic framework for finite strains with simple implementation and good response. Using Flory’s decomposition, strains are split into one volumetric and two isochoric parts. The volumetric part is considered elastic along all strain range and isochoric parts are treated as elastoplastic, i.e., the isochoric plastic flow direction is directly defined by the Flory’s decomposition. Assuming this plastic flow direction it is not necessary to employ the classical Kröner-Lee multiplicative decomposition to consider elastic and plastic parts of finite strains. The proposed model is implemented in a 3D geometrical nonlinear positional FEM code and results are compared with literature experimental and numerical data for validation purposes and applications.