Dynamics of irregular hyperelastic substrate under the impact of moving load

This work delves into the study of stresses induced in a non-homogeneous pre-stressed nearly incompressible elastic substrate with irregularity as a result of a normal load moving on its rough surface. The irregularity on the free surface of the substrate is considered in the form of parabolic irregularity. The solution methodology features the applicability of perturbation method along with substitution method to obtain the displacement components. The expressions of the induced shear and normal stresses have been established in closed form, and their expressions for special cases of the considered problem have also been deduced, which concur well with the existing literature. The influences of affecting parameters viz., non-homogeneity, frictional coefficient, irregularity factor, irregularity depth, hydrostatic stress and depth of the substrate on shear and normal stresses have been depicted graphically by means of numerical computation. The computational results have been manifested for distinct cases of irregularity zone involving parabolic as well as rectangular irregularities present in the considered geometrical model. It has been figured out that the presence of non-homogeneity in the irregular substrate has significant impact on the developed stresses.