On the basis of an upper bound yield function, a rigid–plastic mesodamage constitutive theory for through thickness anisotropic and planar isotropic sheet metals with voids is established. This theory provides a solid foundation for the analysis of plastic deformation and damage evolution in sheet metals under forming. In addition, the physical quantities defined in this theory make it possible for engineers to predict precisely and control optimally the influence of microvoids and through thickness anisotropy on the mechanical properties and forming limits of sheet metals.
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