Mean-field constitutive modeling of elasto-plastic composites using two (2) incremental formulations

• Incremental Micromechanics Scheme based on the Eshelby inclusion concept.
• Elasto-plastic tangent operators obtained from the J2 flow rule.
• Derivation of the strain concentration tensor AI after S injection steps.
• Computation of the macro-stress versus macro-strain response.

Based on scale transition techniques, we aim to build the elasto-plastic behavior of composite materials under loading using two (2) incremental mean-field formulations. Such analysis is carried out by the derivation of effective properties using the Incremental Micromechanics Scheme (IMS) proposed by Vieville (1992, 1994). This scheme is known for its capability to overcome the well-known accuracy restrictions of the Mori–Tanaka (MT) scheme and the Self-Consistent (SC) scheme when a high volume fractions of heterogeneities or/and a high contrast between phases properties is reached. This micromechanics formalism is based on the Eshelby’s inclusion concept and the kinematic equation of Dederichs and Zeller (1973). A classical J2 plasticity is implemented that leads to the consistent (algorithmic) tangent operator from the continuum elasto-plastic tangent operator. Hill-type incremental formulation is adopted to compute the non-linear behavior. Numerical results are obtained considering a heterogeneous material with different volume fractions. The predicted results are compared to those obtained using the standard MT and SC schemes and an exact finite element solution.