The present work suggests a new stabilization scheme for void and low density elements of geometrical non-linear topology optimization. Frequently, certain localized regions in the geometrical non-linear finite element analysis of the topology optimization have excessive artificial distortions due to the low stiffness of the void and low density elements. The present stabilization approach presented in [1] applies a hyperelastic constitutive material model for the numerical stabilization that is associated with the condition number of the deformation gradient. Thereby, the stabilizing material model is associated with the numerical conditioning of the mapping between the current configuration and the reference configuration of the underlying continuum mechanics at the material integration points for the constitutive material model. The stabilization method is independent upon the topology design variables during the optimization iterations. Numerical parametric studies show that the parameters for the constitutive hyperelasticity material of the new stabilization scheme are governed by the stiffness of the constitutive model of the initial physical system. The parametric studies also show that the stabilization scheme is independently upon the type of constitutive model of the physical system and the element types applied for the finite element modelling. The stabilization scheme is numerically verified using both academic reference examples and industrial applications. The numerical examples show that the number of optimization iterations is significantly reduced compared to the stabilization approaches previously reported in the literature.