A Bilinear Constitutive Model for Isotropic Bimodulus Materials

[+] Author and Article Information
K. Vijayakumar, J. G. Ashoka

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India

J. Eng. Mater. Technol 112(3), 372-379 (Jul 01, 1990) (8 pages) doi:10.1115/1.2903341 History: Received March 07, 1989; Online April 29, 2008


Proper formulation of stress-strain relations, particularly in tension-compression situations for isotropic biomodulus materials, is an unresolved problem. Ambartsumyan’s model [8] and Jones’ weighted compliance matrix model [9] do not satisfy the principle of coordinate invariance. Shapiro’s first stress invariant model [10] is too simple a model to describe the behavior of real materials. In fact, Rigbi [13] has raised a question about the compatibility of bimodularity with isotropy in a solid. Medri [2] has opined that linear principal strain-principal stress relations are fictitious, and warned that the bilinear approximation of uniaxial stress-strain behavior leads to ill-working bimodulus material model under combined loading. In the present work, a general bilinear constitutive model has been presented and described in biaxial principal stress plane with zonewise linear principal strain-principal stress relations. Elastic coefficients in the model are characterized based on the signs of (i) principal stresses, (ii) principal strains, and (iii) on the value of strain energy component ratio ER greater than or less than unity. The last criterion is used in tension-compression and compression-tension situations to account for different shear moduli in pure shear stress and pure shear strain states as well as unequal cross compliances.

Copyright © 1990 by The American Society of Mechanical Engineers
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