In this work, we explore the influence of various elasto-plastic material models within the context of topology optimization. The use of nonlinear material behaviors requires a nonlinear finite element analysis which, in the case of plasticity, leads to path-dependent solutions. Consequently, the associated sensitivity analysis also becomes path-dependent. These inherent challenges impose significant constraints on the integration of diverse plasticity models into topology optimization algorithms. For this reason, a limited number of studies address material nonlinearities, and the majority of them focus on von Mises plasticity with linear isotropic hardening. The sensitivity analysis is carried out analytically using the adjoint method. However, this might not be the case for other plasticity models. We present a novel topology optimization scheme based on the level-set method. Our approach leverages the computational power of COMSOL Multiphysics to solve nonlinear finite element problems. Additionally, the automatic differentiation capabilities of COMSOL are used to compute sensitivities for the objective function. This integration enables topology optimization for path-dependent material properties, including elasto-plastic models. Initially, COMSOL graphic user interface is used to create the finite element model, specifying the design domain, boundary conditions, material model, and objective function. Then, the main optimization loop is defined in a MATLAB script. At each iteration, the COMSOL model is used to solve the nonlinear finite element analysis and to compute the sensitivities through automatic differentiation. We will investigate a wide range of plasticity models and their influences on topology optimization and the optimized designs. This approach not only broadens the scope of material models applicable to topology optimization, but also streamlines the implementation of nonlinear analyses, paving the way for a more comprehensive exploration of plasticity effects in the optimization process.