Viscoelastic Models of Tissues. Mathematical Background and Hysteresis Loops

Abstract

Abstract Human, animal, and plant tissues are typically viscoelastic, meaning their mechanical response lies between purely viscous and purely elastic behaviour. These tissues exhibit both viscous and elastic properties, modeled using viscoelastic frameworks. The mechanical behaviour of viscoelastic materials is determined by the relationship between stress σ and strain ε, referred to as the constitutive equation. In viscoelastic models, both stress and strain are functions of time. These models are often constructed using parallel or serial combinations of elementary components: Hookean elastic elements (H)and Newtonian viscous elements (N). The configurations formed through these combinations yield specific geometric equations which, when combined with physical equations, determine the corresponding global constitutive relations. This study presents an analysis and theoretical results related to an approximate viscoelastic model for aponeurosis, specifically represented by the Burgers model.