Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a for...

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Bibliographic Details
Published in:Applied sciences Vol. 11; no. 10; p. 4637
Main Authors: Amouzou, Gildas Yaovi, Soulaïmani, Azzeddine
Format: Journal Article
Language:English
Published: Basel MDPI AG 01-05-2021
Subjects:
Algorithms
consistent tangent operator
Construction
Elastoplasticity
Exact solutions
Finite difference method
Finite element method
Methods
Mohr-Coulomb theory
Mohr–Coulomb
Nonlinear equations
Plane strain
plasticity
return mapping
Rockfill dams
Software packages
Yield stress
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Summary:Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.
ISSN:2076-3417
2076-3417
DOI:10.3390/app11104637