Modeling of the cyclic behavior of elastic–viscoplastic composites by the additive tangent Mori–Tanaka approach and validation by finite element calculations

• Homogenization based on the additive tangent Mori Tanaka scheme is validated for two phase composite.
• Finite element calculations on a 3D RVE are performed for validation.
• Predictions are accurate for different material behaviors.
• The local response of the different phases is well captured during cyclic loading.
• Isotropization of the interaction law does not improve quality of results.

This work deals with the prediction of the macroscopic behavior of two-phase composites, based on the Mori–Tanaka scheme combined with an additive/sequential interaction rule and tangent linearization of viscoplastic response. Cyclic tension compression loadings are considered to further validate the approach. The composite is made of spherical inclusions dispersed in a matrix. Both materials have an elastic–viscoplastic behavior. In a second part, finite element calculations are performed using ABAQUS/STANDARD software in order to validate the proposed homogenization technique. A representative volume element is analyzed with 30 randomly distributed inclusions. Comparisons between the additive tangent Mori–Tanaka scheme and finite element calculations are made for different volume fractions of inclusions, different contrasts in elastic and viscous properties and different strain rates and strain amplitudes. These comparisons demonstrate the efficiency of the proposed homogenization scheme. The effect of isotropization of the viscoplastic tangent stiffness is also investigated. It is concluded that quality of predictions does not benefit from such simplification, contrary to the known result for elastic–plastic case.