First, the identification of the damage envelope shape coefficients is presented. The most common way for constructing a theory of plastic deformation of composite materials is to use hypotheses adopted for plasticity models of metals Hill plasticity curve fitting for short fiber reinforced composites | 3.3.1
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Hill yield criterion the material is assumed to have three orthogonal planes of symmetry
Assuming the material coordinate system is perpendicular to these planes of symmetry, the hill yield criterion reads [hill, 1983] These criteria help engineers and researchers determine when a composite material will fail, ensuring that designs are both safe and efficient Due to the anisotropic nature of composite materials, their elastic modulus and strength vary significantly in different directions Developed by nasa langley research center, these criteria are designed to predict both fibre and matrix failures in composite materials
This condition has the form of a function of the average coordinate stresses. Over the years, a large number of failure theories, criteria and models have been proposed to predict the failure of composite lamina/laminates. To predict the strength of a composite with arbitrary fiber orientations, we can follow an approach similar to that used for the homogenization of linear elastic properties Let denote the hill strength tensor of a unidirectional composite with inclusions aligned along the direction.
