We treat selected test cases in the third world wide failure exercise by the approach described as synergistic damage mechanics. This approach utilizes micromechanics and continuum damage mechanics to predict the overall mechanical response of composite laminates with ply cracking in multiple orientations. The material constants needed in the continuum damage mechanic formulation are calculated from stiffness property changes incurred in a reference laminate. For other laminate configurations, the stiffness changes are derived using a relative constraint parameter which is calculated from the constraint on the opening displacement of ply cracks within the given cracked laminate evaluated numerically by a finite element analysis of appropriately constructed representative unit cell. The number density of ply cracks (cracks per unit length normal to the crack planes) under quasi-static loading is calculated by an energy-based approach. Finally, the stress–strain response of a laminate is determined by combining stiffness property changes and evolution of crack number density.

Structural integrity of composite materials is governed by failure mechanisms that initiate at the scale of the microstructure. The local stress fields evolve with the progression of the failure mechanisms. Within the full span from initiation to criticality of the failure mechanisms, the governing length scales in a fibre-reinforced composite change from the fibre size to the characteristic fibre-architecture sizes, and eventually to a structural size, depending on the composite configuration and structural geometry as well as the imposed loading environment. Thus, a physical modelling of failure in composites must necessarily be of multi-scale nature, although not always with the same hierarchy for each failure mode. With this background, the paper examines the currently available main composite failure theories to assess their ability to capture the essential features of failure. A case is made for an alternative in the form of physical modelling and its skeleton is constructed based on physical observations and systematic analysis of the basic failure modes and associated stress fields and energy balances. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.