A particle-in-cell method is proposed for history-dependent materials, combining the advantages of Eulerian and Lagrangian schemes. The method tracks material points through the entire deformation history, avoiding mesh tangling and enabling accurate tracking of history-dependent variables. A fixed Eulerian grid provides spatial gradients, while material points are mapped to the grid to avoid numerical errors. The method handles elastic and elastic-plastic impacts without special algorithms, ensuring no slip at interfaces. Numerical examples demonstrate the robustness of the method, showing accurate reproduction of elastic behavior and handling of inelastic impacts. The algorithm is efficient, avoiding mesh distortion and remeshing. The method is applied to various problems, including rotation tests, vibrating cylinders, and impact scenarios, showing good performance in terms of energy and momentum conservation. The approach is effective for both elastic and inelastic materials, with the ability to handle complex deformation histories. The method is implemented using a mixed weak form of governing equations, ensuring symmetry and accuracy in the solution. The algorithm is efficient and robust, making it suitable for a wide range of engineering problems involving history-dependent materials.A particle-in-cell method is proposed for history-dependent materials, combining the advantages of Eulerian and Lagrangian schemes. The method tracks material points through the entire deformation history, avoiding mesh tangling and enabling accurate tracking of history-dependent variables. A fixed Eulerian grid provides spatial gradients, while material points are mapped to the grid to avoid numerical errors. The method handles elastic and elastic-plastic impacts without special algorithms, ensuring no slip at interfaces. Numerical examples demonstrate the robustness of the method, showing accurate reproduction of elastic behavior and handling of inelastic impacts. The algorithm is efficient, avoiding mesh distortion and remeshing. The method is applied to various problems, including rotation tests, vibrating cylinders, and impact scenarios, showing good performance in terms of energy and momentum conservation. The approach is effective for both elastic and inelastic materials, with the ability to handle complex deformation histories. The method is implemented using a mixed weak form of governing equations, ensuring symmetry and accuracy in the solution. The algorithm is efficient and robust, making it suitable for a wide range of engineering problems involving history-dependent materials.