An investigation of the effects of deformation-induced anisotropy on isotropic classical elastic-plastic materials.

摘要

The effects of recoverable deformation induced anisotropy on the inelastic response of elastic materials are described. Starting by quantifying the degree of deformation induced anisotropy in isotropic materials, it is proved that the resultant anisotropy is significant only in materials capable of realizing large elastic deviatoric strains. For common engineering materials, this condition requires that the material strength increase strongly with pressure. For materials whose strength does not vary strongly with pressure, such as metals, recoverable deformation induced anisotropy is shown to be negligible.;In those materials that are capable of realizing large elastic strains, the effects of recoverable deformation induced anisotropy are revealed through the predicted coupling of hydrostatic and deviatoric responses in isotropic materials. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re-evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic-plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected, giving the appearance of a nonassociated plastic model. It is shown that this behavior agrees with what is experimentally observed.;Numerical algorithms for the incorporation of recoverable deformation-induced anisotropy in existing classical elastic-plastic constitutive models are given. Upgrading existing code base to include recoverable deformation-induced anisotropy involves very few lines of extra coding and very little computational cost. Using the provided algorithms, model results for problems of interest to the geomechanics, defense, or any other engineering community where large pressures and deformations are characterized, are expected to be more predictive than if recoverable deformation induced anisotropy is neglected.