Performance assessment of the augmented finite element method for the modeling of weak discontinuities

This paper investigates the convergence properties of the augmented finite element method (AFEM). The AFEM is here used to model weak discontinuities independently of the underlying mesh. One noticeable advantage of the AFEM over other partition of unity methods is that it does not introduce additional global unknowns. Numerical 2D experiments illustrate the performance of the method and draw comparisons with the finite element method (FEM) and the non conforming FEM. It is shown that the AFEM converges with an error of O(ℎ0.5) in the energy norm. The non-conforming FEM shares the same property while the FEM converges at O(ℎ). Yet, the AFEM is on par with the FEM for certain homogenization problems

Carbon

We present a combined experimental and computational study of the elastic behavior of a series of highly anisotropic pyrocarbons, with crystallite sizes La in the 2–10 nm range, under a-axis compressive load. The materials include a rough laminar and a regenerative laminar pyrocarbon, as-prepared by chemical vapor deposition and after various heat treatments up to 2600 °C, for which a-axis nanoindentation experiments have been performed, showing a significant decrease in the indentation modulus and hardness with increasing La (or heat treatment temperature). To rationalize this behavior, molecular dynamics simulations of the uniaxial compression of accurate atomistic models of the materials as well as pristine graphite were performed, unraveling significant out-of-plane deformations in the models with increasing compressive strain, leading to elastic softening. More precisely, significant kinks were observed around extended screw dislocation-like defects in the most disordered pyrocarbon at rather large strain levels (∼ 3%). Conversely, graphite rather shows the formation of extended buckles, starting at very low strain values. Finite element modelling shows that such kinking/buckling transitions should take place in a large area under the indenter tip within usual nanoindentation conditions. Both finite element calculation and analytical approximation of the indentation modulus predict the correct trend of decreasing modulus with increasing La when applied with the elastic tensors computed after the buckling/kinking transitions, certainly proving the importance of the latter in the observed experimental indentation moduli

Structural Optimization of Dental Restorations using the Principle of Adaptive Growth

ABSTRACT Fracture of restored teeth is a problem in restorative dentistry since it has been estimated that 92 percent of fractured teeth have been previously restored. In a restored tooth, the stresses that occur at the tooth-restoration interface during loading could become large enough to fracture the tooth and/or restoration. The tooth preparation process for a dental restoration is therefore a classical optimization problem: tooth reduction must be minimized to preserve tooth tissue whilst stress levels must be kept low to avoid fracture of the restored tooth. The objective of the present study was to propose alternative optimized designs for a second upper premolar cavity preparation by means of structural shape optimization based on the finite element method and biological adaptive growth. Restored tooth models using the optimized cavity shapes exhibited significant reduction of stresses along the tooth-restoration interface. In the best case, the maximum stress value was reduced by more than 50 percent

Synthesis and optimization of low-pressure chemical vapor deposition-silicon nitride coatings deposited from SiHCl3 and NH3

Stoichiometric silicon nitride films were deposited by low-pressure chemical vapor deposition from the SiHCl3-NH3-H2-Ar system in a hot wall reactor at pressures ranging from 0.3 to 2 kPa. The films are amorphous for deposition temperatures up to 1000 °C and crystalline, in the α-form, at 1200 °C and above. A method for evaluating the internal stresses based on the curvature of the silicon substrate wafer and the resulting silicon Raman peak shift was developed. Some amorphous films exhibit high internal tensile stresses that can lead to cracking during deposition depending on the mechanism and effective precursors involved. Residual stresses can thus be reduced and cracking avoided by, in descending order of importance, reducing the concentration of reactive gases through dilution, increasing the deposition temperature and decreasing the total pressure. The effects of these parameters on the intrinsic stresses were related to the amount of residual hydrogen successively incorporated and thermally released during the growth of the coating according to the Noskov's model

Journal of the European Ceramic Society

We propose a multi-physics numerical model for a self-healing ceramic matrix mini-composite under tensile load. Crack averaged PDEs are proposed for the transport of oxygen and of all the chemical species involved in the healing process and studied in the dimensionless form to perform the most appropriate discretization choices concerning time integration, and boundary conditions. Concerning the fibres’ degradation, a slow crack growth model explicitly dependent on the environmental parameters is calibrated using a particular exact solution and integrated numerically in the general case. The tow failure results from the statistical distribution of the fibres’ initial strength, the slow crack growth kinetics, and the load transfer following fibres breakage. The lifetime prediction capabilities of the model, as well as the effect of temperature, spatial variation of the statistical distribution of fibres strength, and applied load, are investigated highlighting the influence of the diffusion/reaction processes (healing) on the fibre breakage scenarios.Composites Auto-Cicatrisants Virtuels pour la Propulsion Aéronautiqu

Feasibility of a weakly intrusive Generalized Finite Element Method implementation in a commercial code: Application to Ceramic Matrix Composite micro-structures

As the development of new grades of Ceramic Matrix Composites (CMC) for civil aviation grows, different manufacturing processes have been perfected and several of them can be used successively in order to obtain different types of micro-structures and a variable material quality. Consequently a versatile model should be developed in order to compare these materials and create a tool to help engineers to predict the mechanical behavior at the fiber scale. Here the Generalized Finite Element Method (GFEM) is proposed. It consists in enriching the classical Finite Element (FE) approached displacement by numerical functions to deliver an accurate description of the fiber-scale structure while limiting the number of degrees of freedom compared to a classical finite element description. A pattern-based description of the microscale is depicted using an industrial code for an engineering purpose. Four main difficulties are highlighted (i) the choice of the enrichment functions regarding the literature (ii) their stiffness matrix computation in a commercial code (iii) the construction of the pattern-based structure and (iv) the post-processing. Two GFEM strategies are presented and demonstrate the feasibility of an enriched kinematics within a classical finite element modeler. The selection of such modeler is conditioned by the possibility of weakly intrusive automation of the various stages of construction of the enriched patterns with the help of an external scripting language

Compos B Eng

Carbon/Carbon composites used in rocket propulsion contain many process-related pores and have a porosity-dependent oxidation recession rate. A 1D analytical model has been developed to describe this behavior and assess the structure-reactivity relationship for the oxidation of such composites. The model has been compared to experiments for validation. Oxidation experiments have been carried out using samples featuring individually different matrix fractions in a thermogravimetric analysis apparatus under dry air. Post-test morphologies were characterized with X-ray micro-computerized tomography and a 3D-image correlation technique. Finally, guidelines are given for the design and optimization of porous C/C composites with respect to oxidation resistanc