Emergence of bimodulus (tension–compression asymmetric) behavior modeled in granular micromechanics framework

Many materials exhibit a bimodulus behavior which manifests as tension–compression asymmetry under uniaxial loading conditions. From the viewpoint of engineering analyses and design, attempts have been made to properly account for this asymmetry by defining bimodulus models under various multiaxial loading conditions. The models available in the literature propose a complex set of cases valid for different combination of tensile/compressive loading characterized in either strain or stress space based on classical continuum mechanics. The key drawback of these propositions is the attempt to reduce an inherently nonlinear problem to a simpler linear one in opposition to the clear evidence of loading dependency. Moreover, the proposed approaches are generally conceived in an orthotropic framework even though the material is initially isotropic. It is only upon the deformation that an apparent anisotropy is induced due to the tension–compression asymmetry, which cannot be considered in the initial, reference, configuration. Indeed, from a fundamental viewpoint, the emergence of the macroscale asymmetry and induced anisotropy has its roots in the microscale mechanics of an otherwise isotropic (or other) microstructure. To further expatiate the fundamental view, we exploit the granular micromechanics paradigm to present a simple continuum model within the isotropic framework in reference configuration. Using this approach, the macroscale tension–compression asymmetry and induced anisotropy is shown to emerge naturally without the inconsistencies observed in the methods proposed in the literature.