Noriko Katsube

A hybrid finite element method for heterogeneous materials with randomly dispersed elastic inclusions

Abstract A new hybrid finite element method is presented for the mechanical analysis of heterogeneous materials with randomly dispersed inclusions. A special n-sided polygonal element with an elastic inclusion is developed on the basis of the Hellinger-Reissner principle. The element formulations are derived by decomposing the original problem into inclusion and matrix problems and relating each other through consistency conditions at their interface. For circular inclusions, the proposed method is verified against simple analytical solutions and shown to be suitable even for extreme cases such as porous materials and materials with rigid inclusions. It is also demonstrated that the effect of random packing of inclusions on stress concentration factors can be easily evaluated using the proposed method.

Contact damage in model dental multilayers: an investigation of the influence of indenter size.

This paper presents a combined experimental and computational study of the influence of indenter ball size on contact damage in model multilayered structures with equivalent elastic properties to bonded dentin/crown structures. Following a brief description of restored tooth structures, prior work on the development of model dental multilayered structures is reviewed. The effects of indentation ball size are investigated within a combined experimental and computational/analytical framework. The observed cracking patterns at the onset of crack nucleation are shown to be associated with principal stress contours computed using finite element analysis. The implications of the results are discussed for the design of dental multilayers that are more resistant to crack nucleation and propagation.

Residual interface tensile strength of ceramic bonded to dentin after cyclic loading and aging.

STATEMENT OF PROBLEM To guard against the potential risk of cusp fracture, esthetic onlay restorations have been advocated for teeth with large restorations. The influence of the adhesive resin cement is believed to play a role in strengthening these restorations. The durability of this tooth/adhesive/ceramic interface is critical to ensure clinical longevity. PURPOSE The purpose of this study was to assess the effects of cyclic loading and environmental aging on the residual interface strength of a ceramic bonded to dentin structure. MATERIAL AND METHODS Eighteen simple trilayer specimens were fabricated, consisting of a 1.5-mm-thick ceramic plate (ProCAD) bonded to a flattened human molar tooth with exposed coronal dentin. The ceramic plates were bonded using resin cement (Nexus 2) and manufacturer-recommended bonding techniques. The specimens were divided into 3 equal groups and were stored in water at 37 degrees C for 10 weeks as a control group (CT), 9 months as an aging group (AG), or placed in water at 37 degrees C while being subjected to 10 million vertical loading cycles between 20 N to 200 N, as a fatigue group (FG). After the specimens were subjected to the experimental conditions, they were sectioned perpendicular to the flat ceramic surface into 1 x 1-mm sticks. The mean residual interface microtensile bond (MTB) strength was determined for each specimen using only those sticks which contained ceramic bonded to dentin. The MTB strength data were analyzed using Weibull analysis methods to determine differences between groups. All subsequent failed specimen surfaces were evaluated under a stereomicroscope at x10 magnification to determine the apparent failure modes. Some specimens were selected from each failure mode category for surface evaluation under a scanning electron microscope (SEM). RESULTS The characteristic Weibull means for the 3 groups were CT, 19.2, FG, 14.7, and AG, 11.7. The bond strength of group CT was significantly greater than both AG (P=.007) and FG (P=.014). Light microscopic categorization of the failure modes suggests that adhesive failure at the ceramic/cement interface was the most common (65%) for all 3 groups. SEM evaluation of failed surfaces of select specimens from each group could not distinguish any interface appearance differences. CONCLUSIONS For indirect adhesive-retained ceramic restorations, both cyclic masticatory loading and hydrolytic degradation may contribute to a weakening of the interface bond. The ceramic/resin interface may be more susceptible to these changes over the time frame of this investigation than the dentin/resin interface.

A constitutive model for thermomechanical response of decomposing composites under high heating rates

Abstract The thermomechanical response model of chemically decomposing composites is established. Mass loss due to thermochemical decomposition is modeled by the Arrhenius equation. Phenomenological shrinkage models are proposed and the pore formation due to mass loss is examined from a micro-mechanical point of view. The effect of gas pore pressure caused by decomposition on the deformation of the composite is considered based on the thermal effective stress laws for linearly poroelastic composites. The coupling between the thermochemical decomposition and thermomechanical deformation is made clear throughout the formulation. The results of laboratory tests known as free thermal expansion tests and restrained thermal growth tests are theoretically predicted by the obtained model.

Hybrid crack-tip element and its applications

Abstract A hybrid crack-tip element with a distribution of traction along the crack surfaces is developed. Following the Hellinger–Reissner variational principle, the reduced form of functional that involves only line integral is used. Linear superposition and approximate functions based on the linear elasticity theory are employed in the formulation. The accuracy of the developed special crack-tip element is demonstrated through comparison with the analytical results for a crack in an infinite (large) plate. The efficiency of the method is verified against numerical results obtained by ABAQUS through an edge-crack boundary value problem. The developed crack-tip element is also applied to problems involving interaction of a main crack with random arrays of micro-cracks subjected to a constant traction on the crack surfaces. The effect of constant traction on the stress intensity factors of the main crack is analyzed.

A thermomechanical model for chemically decomposing composites—I. Theory

In this work, a thermostructural model for chemically decomposing composites with moisture is obtained based on the mixture theory by Green and Naghdi. Balance laws of mass, linear momentum, and energy in the mixture theory are expressed in terms of physically measurable quantities. The formulation includes moisture vaporization, thermochemical decomposition, thermomechanical deformation, gas flow, and heat transfer. It is shown that the usual form of equilibrium equation and Darcys equation, widely used in literature, need modification when the phase change occurs. Moisture vaporization is incorporated in mass and energy balance, and vaporization rate at each point of a continuum can be theoretically predicted.

The anisotropic thermomechanical constitutive theory for a fluid-filled porous material with solid/fluid outer boundary

Abstract The anisotropic theromechanical constitutive theory for a fluid-filled porous material with a solid/fluid outer boundary is constructed along the same lines as in the author’s previous work. The notion that a representative volume element may be considered as a superposition of the porous solid material and the porous fluid material is employed. The constitutive theory with a uniform temperature increase is constructed by use of superposition. The thermal effective stress laws for various kinematical quantities are obtained.

3D statistical failure analysis of monolithic dental ceramic crowns.

For adhesively retained ceramic crown of various types, it has been clinically observed that the most catastrophic failures initiate from the cement interface as a result of radial crack formation as opposed to Hertzian contact stresses originating on the occlusal surface. In this work, a 3D failure prognosis model is developed for interface initiated failures of monolithic ceramic crowns. The surface flaw distribution parameters determined by biaxial flexural tests on ceramic plates and point-to-point variations of multi-axial stress state at the intaglio surface are obtained by finite element stress analysis. They are combined on the basis of fracture mechanics based statistical failure probability model to predict failure probability of a monolithic crown subjected to single-cycle indentation load. The proposed method is verified by prior 2D axisymmetric model and experimental data. Under conditions where the crowns are completely bonded to the tooth substrate, both high flexural stress and high interfacial shear stress are shown to occur in the wall region where the crown thickness is relatively thin while high interfacial normal tensile stress distribution is observed at the margin region. Significant impact of reduced cement modulus on these stress states is shown. While the analyses are limited to single-cycle load-to-failure tests, high interfacial normal tensile stress or high interfacial shear stress may contribute to degradation of the cement bond between ceramic and dentin. In addition, the crown failure probability is shown to be controlled by high flexural stress concentrations over a small area, and the proposed method might be of some value to detect initial crown design errors.

An Energy Balance Method for the Numerical Simulation of Inertia Welding

Abstract This paper presents the results of numerical simulations and experimental measurements of temperature distributions in heat-affected zones formed during inertia welding. These were obtained from the inertia welding of Inconel 718 (IN718) toIN718 and the inertia welding of IN718 to 1045 Steel. Microstructures of the heat-affected zone are presented along with microhardness profiles for similar and dissimilar inertia welds. The measured temperature profiles are compared with numerical/finite element predictions of temperature distributions in the heat-affected zone. The effects of friction welding parameters on the temperature distributions in the heat-affected zone are modeled using the finite element method. The experimental results are compared with predictions from numerical analysis. The implications of the results are then discussed.

Survival Predictions of Ceramic Crowns Using Statistical Fracture Mechanics

This work establishes a survival probability methodology for interface-initiated fatigue failures of monolithic ceramic crowns under simulated masticatory loading. A complete 3-dimensional (3D) finite element analysis model of a minimally reduced molar crown was developed using commercially available hardware and software. Estimates of material surface flaw distributions and fatigue parameters for 3 reinforced glass-ceramics (fluormica [FM], leucite [LR], and lithium disilicate [LD]) and a dense sintered yttrium-stabilized zirconia (YZ) were obtained from the literature and incorporated into the model. Utilizing the proposed fracture mechanics–based model, crown survival probability as a function of loading cycles was obtained from simulations performed on the 4 ceramic materials utilizing identical crown geometries and loading conditions. The weaker ceramic materials (FM and LR) resulted in lower survival rates than the more recently developed higher-strength ceramic materials (LD and YZ). The simulated 10-y survival rate of crowns fabricated from YZ was only slightly better than those fabricated from LD. In addition, 2 of the model crown systems (FM and LD) were expanded to determine regional-dependent failure probabilities. This analysis predicted that the LD-based crowns were more likely to fail from fractures initiating from margin areas, whereas the FM-based crowns showed a slightly higher probability of failure from fractures initiating from the occlusal table below the contact areas. These 2 predicted fracture initiation locations have some agreement with reported fractographic analyses of failed crowns. In this model, we considered the maximum tensile stress tangential to the interfacial surface, as opposed to the more universally reported maximum principal stress, because it more directly impacts crack propagation. While the accuracy of these predictions needs to be experimentally verified, the model can provide a fundamental understanding of the importance that pre-existing flaws at the intaglio surface have on fatigue failures.