Total meniscectomies are commonly thought to cause progressive degenerative arthrosis pathology in articular cartilage in a period of a few years because of alteration of the biomechanical environment including increased joint instability. This concern has lead to a preference for partial meniscectomies, although lateral partial meniscectomies sometimes lead to catastrophic results. We performed a three-dimensional finite element model of the human tibiofemoral joint to examine the effect of lateral meniscectomy on knee biomechanics. The results were compared to those from modeling a medial meniscectomy. Under axial femoral compressive loads, the peak contact stress and maximum shear stress in the articular cartilage increased 200% more after a lateral than a medial meniscectomy. These increased stresses could partly explain the higher cartilage degeneration observed after a lateral meniscectomy. ß
The long-term dynamic response of non-linear geometrically exact rods under-going finite extension, shear and bending, accompanied by large overall motions, is addressed in detail. The central objective is the design of unconditionally stable time-stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum, the total angular momentum and, for the Hamiltonian case, the total energy. This objective is accomplished in two steps. First, a class of algorithms is introduced which conserves linear and angular momentum. This result holds independently of the definition of the algorithmic stress resultants. Second, an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved. Conventional schemes exhibiting no numerical dissipation, symplectic algorithms in particular, are shown to lead to unstable solutions when the high frequencies are not resolved. Compared to conventional schemes there is little, if any, additional computational cost involved in the proposed class of energy-momentum methods. The excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations. J. C. SIMO. N. TARNOW AND M. DOBLARE class of mechanical systems incorporates finite rotations and large deformations without restrictions placed on the allowable flexibility, and furnishes the canonical model problem for nonlinear structural dynamics.Rod models of the type considered here are fairly classical. In fact, the local balance of momentum equations are essentially contained in the works of Euler, Clebch, Maxwell, Kirchhoff and others (see e.g. Reference 2). Extensions to incorporate effects such as transverse shear deformation and warping distortion have been addressed by a number of authors from different perspectives; see References 3-7 and references therein. The key point from a numerical analysis perspective concerns the specific choice of parametrization employed in the mathematical description of the kinematics of the rod. The parametrization adopted here, introduced in Reference 5, renders a form of the momentum equations which strongly resembles the classical Euler equations of rigid body dynamics and is well suited both for mathematical and numerical analysis (see References 8-10 and the work of Mielke.") The same parametrization is adopted in Reference 12; alternative approaches are discussed in References 13 and 14.The preceding non-linear rod model can be shown to define an infinite dimensional Hamiltonian system.' Energy-momentum schemes for finite dimensional Hamiltonian systems with a linear configuration space have been considered by a number of authors, see e.g. References 16-18 for the case of classical particle mechanics. However, considerable difficulties arise when the configuration manifold is non-linear, as in the case of rigid body mechanic^,'^*^^ or for the infinite dimensional case which is the situation of interest here...
Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.
SUMMARYIn this paper we present a fully three-dimensional finite-strain damage model for fibrous soft tissue. Continuum damage mechanics is used to describe the softening behaviour of soft tissues under large deformation. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. We considered the internal variables associated to damage to correspond to separated contributions of the matrix and fibres. In order to show clearly the performance of the constitutive model, we present 3D simulations of the behaviour of the human medial collateral ligament and of a coronary artery. Results show that the model is able to capture the typical stress-strain behaviour observed in fibrous soft tissues and seems to confirm the soundness of the proposed formulation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.