Today, a lot of discrete materials are being used by industries. The diversity requires the different yield criterion with the associated formulations for describing the inelastic behavior, fromwhich the integration of the plasticity's constitutive equations is of utmost importance. Here, an exponential-map scheme is proposed for integrating the BigoniePiccolroaz plasticity model. The plasticity presents a single, convex, and smooth yield surface as a generalization of several yield criteria. The Forward Euler integration is also developed for the plasticity to help validate the proposed scheme. Subsequently, a variety of mathematical studies are employed to verify the suggested algorithm, including stress-updating tests as well as two initial boundary value problems. The universality, comprehensiveness, and correctness of the developed technique are extensively confirmed through the numerical investigations.

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