Research Papers

On the Importance of Work-Conjugacy and Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis

[+] Author and Article Information
Wooseok Ji

Research Fellow

Anthony M. Waas

Felix Pawlowski Collegiate Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
University of Michigan,
Ann Arbor, MI 48109

Zdenek P. Bazant

Walter Murphy Professor,
Department of Civil Engineering,
Northwestern University,
Evanston, IL 60208

1Corresponding author.

Manuscript received April 1, 2012; final manuscript received July 22, 2012; accepted manuscript posted October 10, 2012; published online May 23, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 041024 (May 23, 2013) (9 pages) Paper No: JAM-12-1128; doi: 10.1115/1.4007828 History: Received April 01, 2012; Revised July 22, 2012; Accepted October 10, 2012

This paper is concerned with two issues that arise in the finite element analysis of 3D solids. The first issue examines the objectivity of various stress rates that are adopted in incremental analysis of solids. In doing so, it is revealed that large errors are incurred by an improper choice of stress rate. An example problem is presented to show the implications of the choice of stress rate. The second issue addresses the need to maintain work-conjugacy in formulating and solving bifurcation buckling problems of 3D elastic solids. Four popular commercial codes are used to obtain buckling loads of an axially compressed thick sandwich panel, and it is shown that large errors in buckling load predictions are incurred as a result of violating the requirement of work-conjugacy. Remedies to fix the errors in the numerical solution strategy are given.

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Fig. 1

Configuration of the simple shear test problem

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Fig. 2

Numerical and theoretical solutions of the simple shear problem from different types of objectivity stress rates with constant tangential moduli

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Fig. 3

Shear stress obtained from a long strip FE model using periodic boundary conditions

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Fig. 4

Orthotropic strip under uniform axial compression

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Fig. 5

Buckling load predictions from various commercial FEA programs as a function of the aspect ratio

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Fig. 6

Errors in predicting buckling loads shown in Fig. 5

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Fig. 7

Buckling load predictions from various commercial FEA programs as a function of the stiffness ratio between the longitudinal and transverse direction

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Fig. 8

Errors in predicting buckling loads for a thick orthotropic strip shown in Fig. 7

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Fig. 9

Configuration of an axially compressed sandwich panel

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Fig. 10

Comparison of the buckling load of a sandwich panel as a function of the stiffness ratio of the core between the transverse and longitudinal direction

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Fig. 11

Comparison of the buckling load of a sandwich panel as a function of the panel aspect ratio




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