Experimental and numerical analyses of indentation in finite-sized isotropic and anisotropic rubber-like materials

Indentation tests perpendicular to the major plane of a material have been proposed as a means to index some of its in-plane mechanical properties. We showed the feasibility of such tests in myocardial tissue and established its theoretical basis with a formulation of small indentation superimposed on a finitely stretched half-space of isotropic materials. The purpose of this study is to better understand the mechanics of indentation with respect to the relative effects of indenter size, indentation depth, and specimen size, as well as the effects of material properties. Accordingly, we performed indentation tests on slabs of silicone rubber fabricated with both isotropic, as well as transversely isotropic, material symmetry. We performed indentation tests in different thickness specimens with varying sizes of indenters, amounts of indentation, and amounts of in-plane stretch. We used finite-element method simulations to supplement the experimental data. The combined experimental and modeling data provide the following useful guidelines for future indentation tests in finite-size specimens: (i) to avoid artifacts from boundary effects, the in-plane specimen dimensions should be at least 15 times the indenter size; (ii) to avoid nonlinearities associated with finite-thickness effects, the thickness-to-radius ratio should be >10 and thickness to indentation depth ratio should be >5; and (iii) we also showed that combined indentation and in-plane stretch could distinguish the stiffer direction of a transversely isotropic material.