Relative Pore Volume Under Indentation of Porous Materials

Abstract

Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.