[Paper Review] A novel study of temperature effects on the viscoelastic behavior of articular cartilage

Reza Behrou, Hamid Foroughi+1 more|arXiv (Cornell University)|Oct 16, 2017

Osteoarthritis Treatment and Mechanisms17 references3 citations

TL;DR

This study develops a finite element model to investigate the coupled thermo-poro-viscoelastic behavior of articular cartilage under varying temperatures. Using biphasic mixture theory with temperature-dependent material properties and the generalized Maxwell model, it demonstrates that temperature significantly influences early-stage deformation, fluid pressure dissipation, and thermal response—particularly under unconfined and partially loaded conditions—before elastic equilibrium is restored as temperature equilibrates.

ABSTRACT

This paper presents a new approach to study the effects of temperature on the poro- elastic and viscoelastic behavior of articular cartilage. Biphasic solid-fluid mixture theory is applied to study the poro-mechancial behavior of articular cartilage in a fully saturated state. The balance of linear momentum, mass, and energy are considered to describe deformation of the solid skeleton, pore fluid pressure, and temperature distribution in the mixture. The mechanical model assumes both linear elastic and viscoelastic isotropic materials, infinitesimal strain theory, and a time-dependent response. The influence of temperature on the mixture behavior is modeled through temperature dependent mass density and volumetric thermal strain. The fluid flow through the porous medium is described by the Darcy's law. The stress-strain relation for time-dependent viscoelastic deformation in the solid skeleton is described using the generalized Maxwell model. A verification example is presented to illustrate accuracy and efficiency of the developed finite element model. The influence of temperature is studied through examining the behavior of articular cartilage for confined and unconfined boundary conditions. Furthermore, articular cartilage under partial loading condition is modeled to investigate the deformation, pore fluid pressure, and temperature dissipation processes. The results suggest significant impacts of temperature on both poro- elastic and viscoelastic behavior of articular cartilage.

Motivation & Objective

• To develop a thermo-poro-viscoelastic finite element model that captures the coupled mechanical, fluid flow, and thermal behavior of articular cartilage.
• To investigate how temperature variations affect the viscoelastic and poroelastic responses of articular cartilage under different loading and boundary conditions.
• To evaluate the influence of temperature-dependent mass density and volumetric thermal strain on deformation, pore pressure, and thermal dissipation.
• To verify the model’s accuracy using analytical solutions and assess its performance across confined, unconfined, and partially loaded configurations.

Proposed method

• Employs biphasic solid-fluid mixture theory to model fully saturated articular cartilage with coupled mass, momentum, and energy balances.
• Uses the generalized Maxwell model to describe time-dependent viscoelastic behavior of the solid matrix under infinitesimal strain.
• Applies Darcy’s law to model fluid flow through the porous matrix, with temperature-dependent fluid viscosity and thermal strain effects.
• Incorporates temperature-dependent mass density and volumetric thermal strain to capture thermal expansion and density changes.
• Discretizes governing equations using the implicit backward Euler scheme in time and the Galerkin finite element method in space.
• Validated against analytical reference solutions to ensure accuracy and efficiency in 2D simulations.

Experimental results

Research questions

• RQ1 How does temperature influence the viscoelastic and poroelastic response of articular cartilage during mechanical loading?
• RQ2 What is the role of temperature-dependent material properties (density and thermal strain) in altering deformation and fluid pressure evolution?
• RQ3 How do different boundary conditions (confined, unconfined, partial loading) affect the thermal and mechanical response of articular cartilage?
• RQ4 What is the temporal evolution of pore fluid pressure and temperature dissipation, particularly at early loading stages?
• RQ5 To what extent does thermal coupling alter the transient behavior before steady-state elastic response is recovered?

Key findings

• Temperature has a significant influence on the early-stage mechanical response of articular cartilage, with higher temperatures leading to lower pore fluid pressures and larger vertical displacements.
• At early loading times, thermal effects dominate, causing rapid dissipation of temperature and fluid pressure, particularly in unconfined and partially loaded models.
• The model shows that as temperature and fluid pressure dissipate, the system recovers to a linear elastic response, indicating thermal effects are transient but impactful.
• In unconfined and partially loaded configurations, expansion occurs at the top middle due to free displacement boundary conditions, with pronounced displacement and pressure drops observed in early stages.
• The finite element framework accurately replicates analytical solutions, confirming its reliability for modeling complex thermo-poro-viscoelastic behavior in 2D.
• The framework is extendable to 3D and finite strain regimes, suggesting broad applicability for future biomechanical studies of articular cartilage.