Significant differences in the mechanical modeling of confined growth predicted by the Lagrangian and Eulerian formulations

This paper presents an Eulerian formulation of growth for general elastic anisotropic response. The constitutive equations model homeostasis, which is the inelastic process causing the elastic deformation measures to tend towards their homeostatic values. The numerical implementation into ABAQUS usi...

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Bibliographic Details
Published in:International journal of engineering science 2018-08, Vol.129, p.63-83
Main Authors: Safadi, M.M., Rubin, M.B.
Format: Article
Language:English
Subjects:
Anisotropy
Computational mechanics
Computational physics
Computer simulation
Constitutive equations
Constitutive relationships
Deformation mechanisms
Elastic anisotropy
Elastic deformation
Eulerian formulation
Evolutionary algorithms
Finite element method
Formulations
Growth
Homeostasis
Lagrangian formulation
Materials elasticity
Mathematical models
Plastic deformation
Robustness (mathematics)
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Summary:This paper presents an Eulerian formulation of growth for general elastic anisotropic response. The constitutive equations model homeostasis, which is the inelastic process causing the elastic deformation measures to tend towards their homeostatic values. The numerical implementation into ABAQUS using robust, strongly objective integration algorithms for the evolution equations is discussed. Differences between the Eulerian and the Lagrangian multiplicative formulations of growth are examined using examples modeling partially unconfined and confined growth.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2018.03.008