In finite element analysis of pressure vessels undergoing elastoplastic deformation, low stiffness of the tangent modulus tensor will engender low stiffness in the tangent stiffness matrix, posing a risk of computational difficulties such as poor convergence. The current investigation presents the explicit tangent modulus tensor in an elastoplastic model based on a Von Mises yield surface with isotropic work hardening, and the associated flow rule. The stiffness of the tangent modulus tensor is assessed by deriving explicit expressions for its minimum eigenvalue using both tensor diagonalization and Rayleigh quotient minimization. The derived expressions are validated computationally. Using the minimum eigenvalue, the stiffness is found to depend on the current path in stress space. The results of the current investigation suggest a way of following a stress path, which bypasses low stiffness, while attaining the prescribed load.
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December 2011
Research Papers
On the Stiffness of the Tangent Modulus Tensor in Elastoplasticity
Thomas W. Silvers
Thomas W. Silvers
Mechanical, Materials and Aerospace Engineering,
tsilvers86@yahoo.com
University of Central Florida
, Orlando, FL 32816
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Thomas W. Silvers
Mechanical, Materials and Aerospace Engineering,
University of Central Florida
, Orlando, FL 32816
tsilvers86@yahoo.com
J. Pressure Vessel Technol. Dec 2011, 133(6): 061208 (7 pages)
Published Online: October 20, 2011
Article history
Received:
September 9, 2010
Revised:
May 12, 2011
Online:
October 20, 2011
Published:
October 20, 2011
Citation
Nicholson, D. W., and Silvers, T. W. (October 20, 2011). "On the Stiffness of the Tangent Modulus Tensor in Elastoplasticity." ASME. J. Pressure Vessel Technol. December 2011; 133(6): 061208. https://doi.org/10.1115/1.4004619
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