Paraboloidal plastic yield criterion appropriately conveys the nonlinear elastoplastic behaviour of the polymers. The elastoplastic stress and strain relationship for the paraboloidal yield criteria is devised using the radial return mapping algorithm. For the numerical implementation of the devised relationship, an exact solution method using the classical loading-unloading conditions is presented. It avoids the erstwhile iterative scheme and improves efficiency of the solution technique. The non-iterative mathematical implementation is verified with the polymer experimental results in tension, compression and shear for simple and real-sized geometries under large strain conditions using the Abaqus solver tool to prove its functionality and computational efficiency.
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