Modeling calcium dynamics in neurons with endoplasmic reticulum: existence, uniqueness and an implicit-explicit finite element scheme.

Like many other biological processes, calcium dynamics in neurons containing an endoplasmic reticulum is governed by diffusion-reaction equations on interface-separated domains. Interface conditions are typically described by systems of ordinary differential equations that provide fluxes across the interfaces. Using the calcium model as an example of this class of ODE-flux boundary interface problems, we prove the existence, uniqueness and boundedness of the solution by applying comparison theorem, fundamental solution of the parabolic operator and a strategy used in Picard's existence theorem. Then we propose and analyze an efficient implicit-explicit finite element scheme which is implicit for the parabolic operator and explicit for the nonlinear terms. We show that the stability does not depend on the spatial mesh size. Also the optimal convergence rate in H 1 norm is obtained. Numerical experiments illustrate the theoretical results.

Prediction of Cutting Force and Chip Formation from the True Stress-Strain Relation Using an Explicit FEM for Polymer Machining.

In the present work, an explicit finite element (FE) model was developed for predicting cutting forces and chip morphologies of polymers from the true stress-strain curve. A dual fracture process was used to simulate the cutting chip formation, incorporating both the shear damage failure criterion and the yield failure criterion, and considering the strain rate effect based on the Johnson-Cook formulation. The frictional behaviour between the cutting tool and specimen was defined by Coulomb's law. Further, the estimated cutting forces and chip thicknesses at different nominal cutting depths were utilized to determine the fracture toughness of the polymer, using an existing mechanics method. It was found that the fracture toughness, cutting forces, and chip morphologies predicted by the FE model were consistent with the experimental results, which proved that the present FE model could effectively reflect the cutting process. In addition, a parametrical analysis was performed to investigate the effects of cutting depth, rake angle, and friction coefficient on the cutting force and chip formation, which found that, among these parameters, the friction coefficient had the greatest effect on cutting force.

A comparison between dynamic implicit and explicit finite element simulations of the native knee joint.

The finite element (FE) method has been widely used to investigate knee biomechanics. Time integration algorithms for dynamic problems in finite element analysis can be classified as either implicit or explicit. Although previously both static/dynamic implicit and dynamic explicit method have been used, a comparative study on the outcomes of both methods is of high interest for the knee modeling community. The aim of this study is to compare static, dynamic implicit and dynamic explicit solutions in analyses of the knee joint to assess the prediction of dynamic effects, potential convergence problems, the accuracy and stability of the calculations, the difference in computational time, and the influence of mass-scaling in the explicit formulation. The heel-strike phase of fast, normal and slow gait was simulated for two different body masses in a model of the native knee. Our results indicate that ignoring the dynamic effect can alter joint motion. Explicit analyses are suitable to simulate dynamic loading of the knee joint in high-speed simulations, as this method offers a substantial reduction of the computational time with a similar prediction of cartilage stresses and meniscus strains. Although mass-scaling can provide even more gain in computational time, it is not recommended for high-speed activities, in which inertial forces play a significant role.

An analysis of the contact between the stent and the artery using tube hydroforming simulation.

Stents for angioplasty have been extensively used to treat coronary diseases. The aim of this study is to analyze the expansion of the stent and the contact with the artery using tube hydroforming simulation. In the simulation, the contact stress and the final shape of the artery after stent expansion process using the Stampack (®;) software will be studied. A model of a commercial stent made of 316L stainless steel was modeled by using an elastic-plastic constitutive law with isotropic hardening. The artery was modeled as a cylinder and made of hyperelastic material. The stent model studied in this work presented a good performance according to the results obtained. After expansion, any region of the stent's structure with strong risk of wrinkling, thinning, or buckling was not observed. In the forming limit diagram, all points were far from the Keeler-Goodwin diagram. Furthermore, the expanded stent model has a good conformability. In conclusion, our data show that the proposed methodology is a useful tool to check if the stent model implanted in the artery may cause restenosis after angioplasty; thus, our tests provided a reliable tool to analyze this risk.