Abstract
This article presents an inverse method for predicting the reference geometry of plastically deformed material body. The reference configuration is found by solving an elastic-plastic boundary value problem to determine an inverse deformation that maps the spatial material points back to their reference positions. Rate-type elastoplastic constitutive laws are employed in the inverse analysis. When the stress exceeds the yield limit, the plastic flow is invoked and plastic variables are predicted. The ensuing stress field satisfies equilibrium and yield condition. However, the loading history is replicated only approximately and therefore the reference configuration is approximately recovered. The method is limited to a certain family of deformations. In this work, we restrict the method to problems involving monotonic loading and moderately large deformations. Numerical examples demonstrate that the method is effective and reasonably accurate for such problems.
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