Swelling of a polymer gel is a kinetic process coupling mass transport and mechanical deformation. A comparison between a nonlinear theory for polymer gels and the classical theory of linear poroelasticity is presented. It is shown that the two theories are consistent within the linear regime under the condition of a small perturbation from an isotropically swollen state of the gel. The relationships between the material properties in the linear theory and those in the nonlinear theory are established by a linearization procedure. Both linear and nonlinear solutions are presented for swelling kinetics of substrate-constrained and freestanding hydrogel layers. A new procedure is suggested to fit the experimental data with the nonlinear theory. A nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on nonlinear continuum theories for hydrogels with compressible and incompressible constituents. The incompressible instantaneous response of the aggregate imposes a constraint to the finite element discretization in order to satisfy the LBB condition for numerical stability of the mixed method. Three problems of practical interests are considered: constrained swelling, flat-punch indentation, and fracture of hydrogels. Constrained swelling may lead to instantaneous surface instability. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, and is compared with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson’s ratio and loading rate are discussed. On the study of hydrogel fracture, a method for calculating the transient energy release rate for crack growth in hydrogels, based on a modified path-independent J-integral, is presented. The transient energy release rate takes into account the energy dissipation due to diffusion. Numerical simulations are performed for a stationary center crack loaded in mode I, with both immersed and non-immersed chemical boundary conditions. Both sharp crack and blunted notch crack models are analyzed over a wide range of applied remote tensile strains. Comparisons to linear elastic fracture mechanics are presented. A critical condition is proposed for crack growth in hydrogels based on the transient energy release rate. The applicability of this growth condition for simulating concomitant crack propagation and solvent diffusion in hydrogels is discussed. / text

Not available / text

Not available / text

Not available / text

Not available / text

Not available / text

Not available / text

We present an algorithm for fully automatic hp-adaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse grids, and a corresponding sequence of fine grids, such that the energy norm of error decreases exponentially with respect to the number of degrees of freedom in either sequence. At each step, we employ a discrete optimization algorithm to determine the refinements for the current coarse grid such that the projection-based interpolation error for the current fine grid solution decreases with an optimal rate with respect to the number of degrees of freedom added by the refinement. The refinements are restricted only by the requirement that the resulting mesh is at most 1-irregular, but they may be anisotropic in both element size h and order of approximation p. While we cannot prove that our method converges at all, we present numerical evidence of exponential convergence for a diverse suite of model problems from acoustic and electromagnetic scattering. In particular we show that our method is well suited to the automatic resolution of exterior problems truncated by the introduction of a perfectly matched layer. To enable and accelerate the solution of these problems on commodity hardware, we include a detailed account of three critical aspects of our implementations, namely an efficient implementations of sum factorization, several interfaces to the direct multi-frontal solver MUMPS, and some fast direct solvers for the computation of a sequence of nested projections. / text

After Total Knee Arthroplasty, contact stresses at the surface and stresses at the implant-cement-bone interface are directly related to the joint contact forces. These stresses are a major factor in wear and fatigue, aseptic loosening, stress shielding and osteoporosis. Implant contact stresses influence the wear and fatigue damage of the Ultra High Molecular Weight Polyethylene (UHMWPE) articulating surface, decreasing the longevity of the implant. The contact stresses are influenced by the kinematics, the bearing congruency of the articulating surfaces and insert thickness. Thus, various studies have focused on the prediction and optimization of kinematics at the joint interface, contact areas, and stresses in different knee implant designs. As a result, the successful total knee replacement designs depend on joint kinematics and the contact stresses. The objective of this study was to perform contact stress analysis on a newly designed surface guided knee implant, in order to evaluate the design with respect to the potential of polyethylene wear. In order to test the performance of this design, Finite Element Modeling (FEM) was used as a good medium to analyze the design’s specifications, and to evaluate the results of the stress analysis of the design. For validation and also comparison with previous studies, results of this study were compared with those of related work with similar loading and constraints. Based on the gathered data from FE analysis of the design, it can be concluded that the new surface guided knee implant shows lower peak contact pressure than other previously evaluated implants. / October 2015

Accurate assessment of hip fracture risk is very important to prevent hip fracture and to monitor the effect of a treatment. A subject-specific QCT-based finite element model was constructed to assess hip fracture risk at the critical locations of femur during the single-leg stance and the sideways fall. The aim of this study was to improve the prediction of hip fracture risk by introducing a more proper failure criterion to more accurately describe bone failure mechanism. Hip fracture risk index was defined using the strain energy criterion, which is able to integrally consider information such as stresses, strains and material properties in bone failure. It was found that the femoral neck and the intertrochanteric region have higher fracture risk than other part of the femur, probably owing to the larger content of cancellous bone in these regions. The study results also suggested that women are more prone to hip fracture than men. The effects of different parameters such as age, body height, weight, and BMI on hip fracture risk were also investigated in this study. The findings in this study have a good agreement with those clinical observations reported in the literature. The main contributions from this study include: (1) introducing an algorithm for hip fracture risk assessment at the critical locations of femur using the strain energy criterion and QCT-based finite element modeling, (2) theoretically more reasonable definition of hip fracture risk index based on the strain energy criterion, and (3) a semi-automatic finite element analysis and automatic calculation of hip fracture risk index at the critical locations of femur using in-house developed computer codes. The proposed hip fracture risk index based on the strain energy criterion will be a promising tool for more accurate assessment of hip fracture risk. However, experimental validation should be conducted before its clinical applications. / October 2015