Deviatoric Constitutive Relationship for Anisotropic Materials
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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An anisotropic constitutive formulation is presented in which the deviatoric terms have been completely separated from the hydrostatic terms. In this way, a non-linear equation of state is readily employed. For code calculations employing an incremental strain approach, separating the hydrostatic terms from the deviatoric terms provides for a more accurate means of calculating pressure. This results because of the fact that the proposed deviatoric formulation allows evaluation of hydrostatic stress directly from dilatation. Such a scheme is less prone to cumulative integration error than existing formulations, which use stress increments as the basis for modifying hydrostatic pressure. The error is most severe when calculating pressure for materials with variable compressibility. Additionally, an error in the original formulation produces error in the pressure calculation when the material undergoes plastic flow. This flaw is eliminated in the present formulation.