Research Papers: Design and Analysis

On the Stiffness of the Tangent Modulus Tensor in Elastoplasticity

[+] Author and Article Information
David W. Nicholson

Thomas W. Silvers

Mechanical, Materials and Aerospace Engineering,  University of Central Florida, Orlando, FL 32816tsilvers86@yahoo.com

J. Pressure Vessel Technol 133(6), 061208 (Oct 20, 2011) (7 pages) doi:10.1115/1.4004619 History: Received September 09, 2010; Revised May 12, 2011; Published October 20, 2011; Online October 20, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 2

Low mean stress proportional path versus high mean stress alternate path

Grahic Jump Location
Figure 1

Minimizing angle θmin versus plasticity parameter b




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