AuthorKerem Ün
TitleA Penetration-Based Finite Element Method for Hyperelastic
EditorSchool of Engineering
SchoolRensselaer Polytechnic Institute

Advancements in theoretical, computational and experimental methods have enabled researchers to develop more refined and realistic models for articular cartilage. A realistic numerical simulation of cartilage mechanics under in vivo conditions requires the tissue layers to be modeled in contact, undergoing large deformation.

The objective of the current research is to develop an efficient finite element procedure for numerical simulation of three-dimensional (3-D) biphasic cartilage layers in contact. To achieve that objective, the penetration method is developed as a preprocessing technique that makes use of experimentally measured joint kinematic data to derive approximate contact boundary conditions. This process eliminates the nonlinearity associated with contact mechanics, and enables independent analyses of the contacting tissues. The derived boundary conditions provide the input to a finite element procedure where the material and geometric nonlinearities, as well as the straindependent permeability, of the tissue layers are taken into account through a biphasic continuum model.

The linear and nonlinear versions of penetration-based biphasic finite element analyses are critically evaluated using canonical problems, then applied to a physiological example, namely the glenohumeral joint of the shoulder. This work represents the first attempt to analyze contacting biphasic articular cartilage layers on physiological geometries under finite deformation. This is a numerically challenging problem and requires that conventional nonlinear solution procedures be improved. The research therefore included an examination of alternate linearizations of the nonlinear problem and line search techniques to stabilize the iterative solution scheme.

Both linear and nonlinear versions of this formulation have been implemented into the object-oriented analysis framework, Trellis, of the Scientific Computation Research Center at Rensselaer Polytechnic Institute using the C++ programming language.

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