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Size effects have been predicted at the micro- or nano-scale for porousductile materials from Molecular Dynamics, Discrete Dislocation Dynamics andContinuum Mechanics numerical simulations, as a consequence of GeometricallyNecessary Dislocations or due to the presence of a void matrix interface. Asvoids size decreases, higher stresses are needed to deform the material, for agiven porosity. However, the majority of the homogenized models for porousmaterials used in ductile fracture modeling are size-independent, even thoughmicrometric or nanometric voids are commonly observed in structural materials.Based on yield criteria proposed in the literature for nanoporous materials, asize-dependent homogenized model for porous materials is proposed foraxisymmetric loading conditions, including void growth and coalescence as wellas void shape effects. Numerical implementation of the constitutive equationsis detailed. The homogenized model is validated through comparisons to porousunit cells finite element simulations that consider interfacial stresses,consistently with the model used for the derivation of the yield criteria,aiming at modeling an additional hardening at the void matrix interface.Potential improvements of the model are finally discussed with respect to thetheoretical derivation of refined yield criteria and evolution laws.

A size-dependent ductile fracture model: Constitutive equations, Numerical implementation and Validation