A Total Lagrangian based method for recovering the un-deformed configuration in finite elasticity

Grand Joldes; Adam Wittek; Karol Miller

doi:10.1016/j.apm.2014.12.013

A Total Lagrangian based method for recovering the un-deformed configuration in finite elasticity

Grand Joldes, Adam Wittek, Karol Miller

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Abstract

© 2014. The problem of finding the un-deformed configuration of an elastic body, when the deformed configuration and the loads are known, occurs in many engineering applications. Standard solution methods for such problems include conservation laws based on Eshelby's energy-momentum tensor and re-parameterization of the standard equilibrium equations. In this paper we present a different method for solving such problems, based on a re-parameterization of the nodal forces using the Total Lagrangian formulation. The obtained nonlinear system of equations describing equilibrium can be solved using either Newton-Raphson or an explicit dynamic relaxation algorithm. The solution method requires only minor modifications to similar algorithms designed for forward motion calculations. Several examples involving large deformations and different boundary conditions and loads are presented.

Original language	English
Pages (from-to)	3913-3923
Journal	Applied Mathematical Modelling
Volume	39
Issue number	14
DOIs	https://doi.org/10.1016/j.apm.2014.12.013
Publication status	Published - 15 Jul 2015

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© 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
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AB - © 2014. The problem of finding the un-deformed configuration of an elastic body, when the deformed configuration and the loads are known, occurs in many engineering applications. Standard solution methods for such problems include conservation laws based on Eshelby's energy-momentum tensor and re-parameterization of the standard equilibrium equations. In this paper we present a different method for solving such problems, based on a re-parameterization of the nodal forces using the Total Lagrangian formulation. The obtained nonlinear system of equations describing equilibrium can be solved using either Newton-Raphson or an explicit dynamic relaxation algorithm. The solution method requires only minor modifications to similar algorithms designed for forward motion calculations. Several examples involving large deformations and different boundary conditions and loads are presented.

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A Total Lagrangian based method for recovering the un-deformed configuration in finite elasticity

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