In this paper we suggest a thermodynamically consistent approach to the simulation of a rate dependent material response at finite strains. The nonlinear mechanical phenomena which are covered by the proposed material model include distortional, kinematic, and isotropic hardening. Firstly, we present a new two‐dimensional rheological model of distortional hardening, which predicts the yield curve in the stress space to be a limaçon of Pascal. Such effects like the distortion of the yield surface in the stress space and its orientation depending on the loading path are captured by the rheological model in a vivid way. Next, the rheological model serves as a guideline for the construction of the constitutive equations. In particular, the kinematic assumptions, the ansatz for the free energy, and the form of the yield function are motivated by the rheological model. Further, two types of flow rules are considered in this study: a normality rule and a radial rule, both thermodynamically consistent. Moreover, we formulate explicitly the constraints on the material parameters, which guarantee the convexity of the yield surface. Furthermore, implicit time‐stepping methods are considered which exactly preserve the incompressibility of the inelastic flow. Finally, the basic features of the predicted material response are illustrated by a series of numerical simulations. In particular, the simulation results are compared to the real experimental data.

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