Viscoelasticity of Articular Cartilage and Ligament: Constitutive Modeling and Experiments

Articular cartilage and ligament are soft fibrous connective tissues with apparent viscoelastic behavior. An anisotropic visco-hyperelastic constitutive model for these tissues has been proposed in this study based on the short-term and long-term internal variables. The constitutive model was particularized for both tissues, numerically implemented into the finite element software package ABAQUS and the material parameters were identified using the available experimental data. The constitutive model was able to capture both the short-term and long-term time-dependent response of these tissues with less difficulty in material characterization process. Due to the lack of the desired tensile experimental results on articular cartilage, the mechanical behavior of this tissue was also examined experimentally. The tensile stiffness of articular cartilage was found to be rate-dependent. It has been shown by numerical simulations that the strain-rate dependent tensile stiffness of collagen fibers can also contribute to the highly rate-dependent compressive response of articular cartilage, besides the fluid-driven viscoelasticity.12 month

Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables

Publisher version of article deposited according to publisher policy posted on BioMed Central, May 13, 2015. http://www.biomedcentral.com/authors/licenseBackground Differential-type and integral-type formulations are two common approaches in modeling viscoelastic materials. A differential-type theory is often derived from a Helmholtz free energy function and is usually more suitable for the prediction of strain-rate dependent mechanical behavior during rapid loading, while an integral-type theory usually captures stress relaxation more efficiently than a differential-type theory. A modeling approach is needed to predict the viscoelastic responses during both rapid loading and relaxation phases. Methods A constitutive modeling methodology based on the short and long-term internal variables was proposed in the present study in order to fully use the better features of the two types of theories. The short-term variables described the loading rate, while the long-term variables involving time constants characterized loading history and stress relaxation. Results The application of the methodology was demonstrated with particular formulations for ligament and articular cartilage. Model parameters were calibrated for both tissues with experimental data from the literature. It was found that the proposed model could well predict a wide range of strain-rate dependent load responses during both loading and relaxation phases. Conclusion Introducing different internal variables in terms of their time scales reduced the difficulties in the material characterization process and enabled the model to predict the experimental data more accurately, in particular at high strain-rates.Funding provided by the Open Access Authors Fund

Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables

Abstract Background: Differential-type and integral-type formulations are two common approaches in modeling viscoelastic materials. A differential-type theory is often derived from a Helmholtz free energy function and is usually more suitable for the prediction of strain-rate dependent mechanical behavior during rapid loading, while an integral-type theory usually captures stress relaxation more efficiently than a differential-type theory. A modeling approach is needed to predict the viscoelastic responses during both rapid loading and relaxation phases