This article presents a review of the sheet metal formability analysis based on the theory of damage mechanics. Specifically, the damage anisotropy is considered. Forming limit analyses based on the anisotropic damage are summarized, including the accumulative critical damage method, the damage-coupled vertex theory and the damage-coupled acoustic tensor method. The accumulative critical damage method postulates that the critical damage at the localized necking is strain-path or loading history independent. It can be applied to predict the forming limit diagrams under either proportional or nonproportional loading. The vertex theory considers that localized necking is associated with the vertex developed on yield surface. The theory is applicable to engineering materials exhibiting the strain-hardening and/or strain-rate dependent behaviors. The acoustic tensor method, on the other hand, can only be applied to the strain-softening materials, which are often observed in warm/hot sheet metal forming or hydroforming.
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