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.