Constitutive formulation and analysis of heel pad tissues mechanics

Abstract

This paper presents a visco-hyperelastic constitutive model developed to describe the biomechanical response of heel pad tissues. The model takes into account the typical features of the mechanical response such as large displacement, strain phenomena, and non-linear elasticity together with time-dependent effects. The constitutive model was formulated, starting from the analysis of the complex structural and micro-structural configuration of the tissues, to evaluate the relationship between tissue histology and mechanical properties. To define the constitutive model, experimental data from mechanical tests were analyzed. To obtain information about the mechanical response of the tissue so that the constitutive parameters could be established, data from both in vitro and in vivo tests were investigated. Specifically, the first evaluation of the constitutive parameters was performed by a coupled deterministic and stochastic optimization method, accounting for data from in vitro tests. The comparison of constitutive model results and experimental data confirmed the model's capability to describe the compression behaviour of the heel pad tissues, regarding both constant strain rate and stress relaxation tests. Based on the data from additional experimental tests, some of the constitutive parameters were modified in order to interpret the in vivo mechanical response of the heel pad tissues. This approach made it possible to interpret the actual mechanical function of the tissues.