A Simple Formulation for Visco-Hyperelastic Behavior for Soft Materials Suitable for Different Loading Types

Abstract

Soft materials, and especially soft biological tissues, have a complex highly nonlinear behavior both for quasielastic (slow) and viscous loading. In partiular, the cyclic behavior is different depending on the loading speed, number of cycles, and their magnitude. Furthermore, different soft materials and soft tissues have different particularities in their behavior. Therefore, a phenomenological proposal capable of accurately capturing all these singularities with few, easy to obtain parameters based on experimental data, is valuable. In this study, a visco-hyperelastic one-dimensional formulation to characterize different biological tissues is proposed, which has proven to be capable of capturing the response of numerous soft biological tissues (brain tissue, coronary arteries, tendons, tongue tissues, abdominal muscle, cells...) under pure and combined loading modes, including tension, compression, simple shear and the combination of the latter one with tension and compression. One of the main advantages of the proposed model is its simplicity, being that the formulation is calibrated with four simple parameters (two of them for the hyperelastic component and four for dealing with the different viscous aspects) obtained from the uniaxial loading. The formulation, based on a combination of Maxwell and Kelvin-Voigt rheological models has proven to represent to very good accuracy the behavior of a wide range of materials under different types of loadings, including effects like preconditioning and cycle stabilization. In all these cases, under different monotonic and cyclic loading, all aspects of the viscous and elastic behavior are accurately captured. Thanks to its structure, this model incorporates strain-level dependent nonequilibrium viscoelasticity and it may be easily incorporated to 3D nonlinear finite strains formulations.