In the present study, two semi-implicit schemes, based on the exponential maps method, are derived for integrating the pressure-sensitive constitutive equations. In spite of the fact that the consistent tangent operator is necessary to preserve the quadratic rate for the asymptotic convergence of the Newton-Raphson solution in the finite element analyses, there exists no derivation of this operator for the exponential-based integrations of the pressure-sensitive plasticity in the literature. To fulfill this need, the algorithmic tangent operators are extracted for the new semi-implicit as well as the former exponential-based integrations. Moreover, for the accurate integration presented by Rezaiee-Pajand et al. (Eur J Mech A Solids 30:345–361, 2011),the consistent tangent operator is obtained. Eventually, all the investigations are assessed by a broad range of numerical tests.

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