Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity
Publication: Journal of Engineering Mechanics
Volume 139, Issue 2
Abstract
The behavior of material nonlinearity with nonassociative plastic flow is frequently analyzed for structures made of soil and rock. It is known that for nonassociated plasticity, the elastoplastic tangential stiffness tensor (matrix) is nonsymmetric. In the FEM, this causes inconvenience for solving a system of equations using the Newton-Raphson solution procedure. In this paper, a mathematical transformation was derived for converting the nonsymmetric tangential stiffness tensor (matrix) into a symmetric tensor such that the global system of equations become unconditionally symmetric. A detailed step-by-step procedure of a stress update algorithm using the tangential stiffness method is elaborated in this paper. The paper also compares the results of the tangential stiffness method with those of the initial stiffness method using an illustrative tunnel problem for associative and nonassociative flow conditions and shows the efficacy of the proposed transformation in elastoplastic problems.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 2 • February 2013
Pages: 105 - 113
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 11, 2010
Accepted: Jun 6, 2012
Published online: Jan 15, 2013
Published in print: Feb 1, 2013
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