Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

A numerical study of pore-fluid, thermal and mass flow iu fluid-saturated porous rock basins

We present a numerical methodology for the study of convective pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. lit particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore-fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore-fluid flow and mass transport in fluid-saturated hydrothermal basins; (2) Convective pore-fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence off the distribution patterns of convective pore;fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore-fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. (C) 2003 Elsevier B.V. All rights reserved.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

A numerical study of effect of grain boundaries on elastic and plastic properties in nanocomposite materials

Nanocomposite materials have received considerable attention in recent years due to their novel properties. Grain boundaries are considered to play an important role in nanostructured materials. This work focuses on the finite element analysis of the effect of grain boundaries on the overall mechanical properties of aluminium/alumina composites. A grain boundary is incorporated into the commonly used unit cell model to investigate its effect on material properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the ''effective'' plastic property of the grain boundary is estimated. In addition, the strengthening mechanism is also discussed based on the Estrin-Mecking model.

Understanding Contradictory Data in Contraction Stress Tests

The literature shows contradictory results regarding the role of composite shrinkage and elastic modulus as determinants of polymerization stress. The present study aimed at a better understanding of the test mechanics that could explain such divergences among studies. The hypothesis was that the effects of composite shrinkage and elastic modulus on stress depend upon the compliance of the testing system. A commonly used test apparatus was simulated by finite element analysis, with different compliance levels defined by the bonding substrate (steel, glass, composite, or acrylic). Composites with moduli between 1 and 12 GPa and shrinkage values between 0.5% and 6% were modeled. Shrinkage was simulated by thermal analogy. The hypothesis was confirmed. When shrinkage and modulus increased simultaneously, stress increased regardless of the substrate. However, if shrinkage and modulus were inversely related, their magnitudes and interaction with rod material determined the stress response.

Measuring Bond Strength Between Fiber Post and Root Dentin: A Comparison of Different Tests

Purpose The aim of this study was to evaluate the ability of bond strength tests to accurately measure the bond strength of fiber posts luted into root canals Materials and Methods The test methods studied were hourglass microtensile (HM), push-out (PS), modified push out (MP) and pull out (PL) The evaluated parameters were bond strength values, reliability (using Weibull analysis), failure mode (using confocal microscopy), and stress distribution (using finite element analysis) Forty human intact single rooted and endodontically treated teeth were divided into four groups Each group was assigned one of the test methods The samples in the HM and PS groups were 1 0 +/- 0 1 mm thick, the HM samples were hourglass shaped and the PS samples were disk shaped For the PL and MP groups, each 1 mm dentin slice was luted with a fiber post piece Three dimensional models of each group were made and stress was analyzed based on Von Mises criteria Results PL provided the highest values of bond strength followed by MP both of which also had greater amounts of adhesive failures PS showed the highest frequency of cohesive failures MP showed a more homogeneous stress distribution and a higher Weibull modulus Conclusion The specimen design directly influences the biomechanical behavior of bond strength tests

Can Fiber Posts Increase Root Stresses and Reduce Fracture?

The clinical success of fiber posts has been attributed to their lower elastic modulus. The tested hypothesis was that fiber posts could lead to lower risk of post debonding and lower risk of root fracture, despite an increase in root stresses. Stress analyses were carried out with a 3D finite element model of a premolar restored with a metallic or a fiber post. Bonded and non-bonded post/cement interface conditions were simulated. We calculated risk-of-fracture indices by determining the highest principal stress values divided by the tensile strength. Shear stresses along the post/cement interface were analyzed for the bonded models. Compared with the premolar restored with a metallic post, the fiber post generated lower stresses along the interface and higher stresses in the root. However, with the fiber post, fracture was less likely to occur in the root, since its core and post fracture indices were higher.

Direct comparison of the bond strength results of the different test methods: A critical literature review

Objective. The goal of this paper is to undertake a literature search collecting all dentin bond strength data obtained for six adhesives with four tests ( shear, microshear, tensile and microtensile) and to critically analyze the results with respect to average bond strength, coefficient of variation, mode of failure and product ranking. Method. A PubMed search was carried out for the years between 1998 and 2009 identifying publications on bond strength measurements of resin composite to dentin using four tests: shear, tensile, microshear and microtensile. The six adhesive resins were selected covering three step systems ( OptiBond FL, Scotch Bond Multi-Purpose Plus), two-step (Prime & Bond NT, Single Bond, Clear. l SE Bond) and one step (Adper Prompt L Pop). Results. Pooling results from 147 references showed an ongoing high scatter in the bond strength data regardless which adhesive and which bond test was used. Coefficients of variation remained high (20-50%) even with the microbond test. The reported modes of failure for all tests still included high number of cohesive failures. The ranking seemed to be dependant on the test used. Significance. The scatter in dentin bond strength data remains regardless which test is used confirming Finite Element Analysis predicting non-uniform stress distributions due to a number of geometrical, loading, material properties and specimens preparation variables. This reopens the question whether, an interfacial fracture mechanics approach to analyze the dentin - adhesive bond is not more appropriate for obtaining better agreement among dentin bond related papers. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Elastic modulus of posts and the risk of root fracture

The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts` elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (sigma(max)) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (processing). Load of 100 N was applied, varying the directions (0 degrees, 45 degrees and 90 degrees) in relation to the post`s long axis. The magnitude and direction of the sigma(max) were recorded. At the 45 degrees and 90 degrees loading, the highest values of sigma(max) were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0 degrees loading, the highest values of sigma(max) were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the sigma(max) generated on the root was dependent on the loading direction.