A generalized Gurson model for loaded ‘voids’

Abstract

Abstract The Gurson model successfully solves the problem of void damage within a finite homogeneous matrix. Yet, it is inherently incapable of describing scenarios where the matrix contains inclusions that may trigger the void formation. In this work, we generalize the Gurson model by defining a loaded ‘void’, a combined region comprising both the actual void and its associated inclusions in the matrix. The interfacial stress between matrix and inclusion is treated as an equivalent load acting on the internal surface of the ‘void’. We then derive a new yield-surface function that can reduce to the classical Gurson model without inclusions, the void-pressure model and even the mixture rule of strength of composites. Applying the plastic normality rule to this yield-surface function, we further establish the damage constitutive equations, in which the damage develops via both the volumetric growth of the void–inclusion complex and the stress degradation of the inclusion–matrix interface. The proposed model is validated against unit-cell simulations and experimental data across multiple composite systems, demonstrating its capability as a unified theoretical framework for incorporating inclusion effects into the Gurson-type description.

The authors' abstract, as published at the source. Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 2026 · DOI ↗