Characterization of soft materials with cylindrical cavity pores via indentation technique

Soft materials with designed pore structures often exhibit superior properties, becoming increasingly important in advanced applications such as metamaterials and soft robotics. Quantitative characterization of the intrinsic mechanical properties of defect-containing soft materials is crucial for optimizing their performance. This study investigates spherical indentation for soft materials with cylindrical cavity defects. In contrast to the response of bulk materials, a critical load P₁ is identified from the load–displacement curve of the indentation test, at which the insertion-induced instability occurs. This is followed by a load decay and subsequent stabilization to P₂ in regions sufficiently remote from the cavity termini. By combining dimensional analysis with finite element method, the explicit expressions relating P₁ and P₂ to material parameters and friction coefficients are determined. An indentation method is subsequently developed to evaluate the shear modulus μ₀ and friction coefficient f simultaneously. Optimal parameter space of normalized cavity radius R̄_h and f is preliminarily determined to provide guidance for the indentation tests and avoid the absence of P₁ or the phenomenon of self-contact. The effectiveness of the proposed method is validated experimentally. By combining finite element analysis with theory of contact mechanics, we analyze the evolution of the load P during indentation process. Experiments on specimens with multiple cavities show that the method remains reasonably effective for specimens containing multiple cavities. Through the incorporation of the Ogden hyperelastic model into finite element simulations, the method's sensitivity to strain hardening is evaluated, confirming its robust performance for typical soft materials. Finally, an approximate expression for the stabilized load P₂ under low-friction conditions is derived, and the adhesive stress is further considered in the indentation method for cases involving low friction and relatively small adhesive stress.