Modeling of the contact between a rigid indenter and a heterogeneous viscoelastic material

• 3D contact model for viscoelastic material containing ellipsoidal inclusion(s) is proposed.
• The heterogeneous inclusion can be either isotropic or anisotropic, of any orientation.
• Potential applications include composite materials.
• The numerical technique is based on semi-analytical methods (SAM), close to the boundary element method (BEM).
• With numerical summation of elementary analytical solutions instead of solving numerically integral function, making the numerical technique very fast.

In this paper, the contact problem between a rigid indenter and a viscoelastic half space containing either isotropic or anisotropic elastic inhomogeneities is solved. The model presented here is 3D and based on semi-analytical methods. To take into account the viscoelastic properties of the matrix, contact and subsurface problem equations are discretized in the spatial and temporal dimensions. A conjugate gradient method and the fast Fourier transform are used to solve the normal problem, contact pressure, subsurface problem and real contact area simultaneously. The Eshelby’s formalism is applied at each step of the temporal discretization to account for the effect of the inhomogeneity on pressure distribution and subsurface stresses. This method can be seen as an enrichment technique where the enrichment fields from heterogeneous solutions are superimposed to the homogeneous viscoelastic problem solution. Note that both problems are fully coupled. The model is validated by comparison with a Finite Element Model. A parametric analysis of the effect of elastic properties and geometrical features of the inhomogeneity is proposed. The model allows to obtain the contact pressure distribution disturbed by the presence of inhomogeneities as well as subsurface and matrix/inhomogeneity interface stresses at every step of the temporal discretization.