The adhesive contact of a flat punch on a hyperelastic substrate subject to a pull-out force or a bending moment

Abstract

In the last decade, instrumented macro- and nano-indentation tests have become useful tools for probing mechanical properties of materials. In this context, little in-depth work has been done for soft bio-materials like biofilms, tissues, gels, cells, etc. Such materials show large elastic strains when subjected to relatively fast loading (excluding viscoelastic phenomena). The present work focuses on the adhesive contact of such materials. Flat punches of circular imprint are used and are subjected to pullout normal forces or bending moments. The materials are modeled as hyperelastic (fast-testing conditions), using the Mooney–Rivlin (M–R) strain energy density function. We examine both incompressibility and compressibility issues. The contact problem of half-space materials interacting with rigid indenters is solved explicitly for moderate deformations and is compared with finite element results. Experiments are conducted with an artificial material (gel, reinforced with talc powder) that is modeled as a hyperelastic material. The present work is expected to extend indentation testing to important technologies like medical applications (health monitoring of tissues) and food industries (quality control of various production stages). It is concluded that the adhesive contact can be used to estimate the initial elastic modulus of soft substrates, but not all the material constants required by the hyperelastic models.