A micromechanical-based damage analysis of a cylindrical bar under torsion: Theoretical results, Finite Elements verification and application

•Exact solutions are established for mechanical fields in a cylindrical bar under torsion.•The bar obeys to an isotropic elastic damage models accounting for unilateral effects.•Different formulations of the damage model are considered based on homogenization schemes.•Loading and unloading regimes are fully examined.•Data from Finite Elements computations are compared to the theoretical predictions.

We first present exact closed-form solutions to the problem of a cylindrical bar subjected to a torsion loading. The bar is made of a material whose behavior is modeled by means of a class of micromechanically based isotropic elastic damage models. It is shown that under an increasing torsion, the bar exhibits a global softening regime related to its progressive deterioration. The paper also provides explicit expressions of the mechanical fields as well as of the damage distribution in the bar. A careful attention is given to the response during an unloading step. Finally, after implementing the damage models in a Finite Element software, we simulate the bar response under the same torsion loading. Interestingly a full agreement is noted between the theoretical predictions and the numerical results, also in the softening regime. Finally, the proposed models are applied to a gray cast iron; the predictions compare well to experimental data.