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Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity
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.
Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity
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.
Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity
Deb, Debasis (author) / Das, Kamal C. (author) / Raja Sekhar, G. P. (author)
Journal of Engineering Mechanics ; 139 ; 105-113
2013-01-15
92013-01-01 pages
Article (Journal)
Electronic Resource
English
Generalized Symmetric Formulation of Tangential Stiffness for Nonassociative Plasticity
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