Finite elastic wrinkling deformations of incompressible fiber-reinforced plates.

A two-dimensional plate theory, valid for finite elastic deformations with small strains, is derived for incompressible, fiber-reinforced materials. Single-layer plates and two-layer laminates are considered. Numerical simulations illustrate the substantial effect that fiber reinforcement has on wrinkling patterns in the sheet.

Design of Bioprosthetic Aortic Valves using biaxial test data.

Bioprosthetic Aortic Valves (BAVs) do not have the serious limitations of mechanical aortic valves in terms of thrombosis. However, the lifetime of BAVs is too short, often requiring repeated surgeries. The lifetime of BAVs might be improved by using computer simulations of the structural behavior of the leaflets. The goal of this study was to develop a numerical model applicable to the optimization of durability of BAVs. The constitutive equations were derived using biaxial tensile tests. Using a Fung model, stress and strain data were computed from biaxial test data. SolidWorks was used to develop the geometry of the leaflets, and ABAQUS finite element software package was used for finite element calculations. Results showed the model is consistent with experimental observations. Reaction forces computed by the model corresponded with experimental measurements when the biaxial test was simulated. As well, the location of maximum stresses corresponded to the locations of frequent tearing of BAV leaflets. Results suggest that BAV design can be optimized with respect to durability.

Influences of the depth-dependent material inhomogeneity of articular cartilage on the fluid pressurization in the human knee.

The material properties of articular cartilage are depth-dependent, i.e. they differ in the superficial, middle and deep zones. The role of this depth-dependent material inhomogeneity in the poromechanical response of the knee joint has not been investigated with patient-specific joint modeling. In the present study, the depth-dependent and site-specific material properties were incorporated in an anatomically accurate knee model that consisted of the distal femur, femoral cartilage, menisci, tibial cartilage and proximal tibia. The collagen fibers, proteoglycan matrix and fluid in articular cartilage and menisci were considered as distinct constituents. The fluid pressurization in the knee was determined with finite element analysis. The results demonstrated the influences of the depth-dependent inhomogeneity on the fluid pressurization, compressive stress, first principal stress and strain along the tissue depth. The depth-dependent inhomogeneity enhanced the fluid support to loading in the superficial zone by raising the fluid pressure and lowering the compressive effective stress at the same time. The depth-dependence also reduced the tensile stress and strain at the cartilage-bone interface. The present 3D modeling revealed a complex fluid pressurization and 3D stresses that depended on the mechanical contact and relaxation time, which could not be predicted by existing 2D models from the literature. The greatest fluid pressure was observed in the medial condyle, regardless of the depth-dependent inhomogeneity. The results indicated the roles of the tissue inhomogeneity in reducing deep tissue fractures, protecting the superficial tissue from excessive compressive stress and improving the lubrication in the joint.

Recent advances in computational mechanics of the human knee joint.

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.

Altered knee joint mechanics in simple compression associated with early cartilage degeneration.

The progression of osteoarthritis can be accompanied by depth-dependent changes in the properties of articular cartilage. The objective of the present study was to determine the subsequent alteration in the fluid pressurization in the human knee using a three-dimensional computer model. Only a small compression in the femur-tibia direction was applied to avoid numerical difficulties. The material model for articular cartilages and menisci included fluid, fibrillar and nonfibrillar matrices as distinct constituents. The knee model consisted of distal femur, femoral cartilage, menisci, tibial cartilage, and proximal tibia. Cartilage degeneration was modeled in the high load-bearing region of the medial condyle of the femur with reduced fibrillar and nonfibrillar elastic properties and increased hydraulic permeability. Three case studies were implemented to simulate (1) the onset of cartilage degeneration from the superficial zone, (2) the progression of cartilage degeneration to the middle zone, and (3) the progression of cartilage degeneration to the deep zone. As compared with a normal knee of the same compression, reduced fluid pressurization was observed in the degenerated knee. Furthermore, faster reduction in fluid pressure was observed with the onset of cartilage degeneration in the superficial zone and progression to the middle zone, as compared to progression to the deep zone. On the other hand, cartilage degeneration in any zone would reduce the fluid pressure in all three zones. The shear strains at the cartilage-bone interface were increased when cartilage degeneration was eventually advanced to the deep zone. The present study revealed, at the joint level, altered fluid pressurization and strains with the depth-wise cartilage degeneration. The results also indicated redistribution of stresses within the tissue and relocation of the loading between the tissue matrix and fluid pressure. These results may only be qualitatively interesting due to the small compression considered.