The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
J. N. Reddy - One of the best experts on this subject based on the ideXlab platform.
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Large strained fracture of nearly Incompressible hyperelastic materials: enhanced assumed strain methods and energy decomposition
Journal of the Mechanics and Physics of Solids, 2020Co-Authors: Lu-wen Zhang, J. N. ReddyAbstract:Abstract Tracking crack propagation at large strains of hyperelastic solids is a challenging task due to the high nonlinearity, nearly incompressibility and ordered tendency in microstructure of the rubbery material under stretch. On the basis of the diffusive crack model, this work presents a new phase-field model by combining the strain energy decomposition and the enhanced assumed strain method. The proposed fracture formulation is indeed Griffith's theory-based framework but further accounting for the coupled effects of the stretches, damage and incompressibility to predict the crack growth in both compressible and Incompressible hyperelastic solids. There are three innovations contained in this study: (i) The developed phase-field framework is capable to capture the effect of hole collapse, which is an intrinsic phenomenon of hyperelastic material and difficult to be detected by the others. (ii) The developed energy decomposition method provides a reasonable description of the physical reality that the hyperelastic fracture is driven by the changes in the internal energy of the stretched molecular chains in the polymer network. This continuum description automatically distinguishes the strain energy that really contributes to crack growth at multiaxial stress states, reducing significantly the numerical instability caused by material softening. (iii) By introducing the assumed strain method to the present fracture scheme, the physical consistency of energy decomposition and the mathematical nonnegativeness of strain energy can be satisfied simultaneously for Incompressible Problem. We demonstrate the performance of the enhanced phase-field framework through representative examples and highlight the importance of positive deviatoric energy for Incompressible Problem by comparing with experiments and classical models.
Lu-wen Zhang - One of the best experts on this subject based on the ideXlab platform.
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Large strained fracture of nearly Incompressible hyperelastic materials: enhanced assumed strain methods and energy decomposition
Journal of the Mechanics and Physics of Solids, 2020Co-Authors: Lu-wen Zhang, J. N. ReddyAbstract:Abstract Tracking crack propagation at large strains of hyperelastic solids is a challenging task due to the high nonlinearity, nearly incompressibility and ordered tendency in microstructure of the rubbery material under stretch. On the basis of the diffusive crack model, this work presents a new phase-field model by combining the strain energy decomposition and the enhanced assumed strain method. The proposed fracture formulation is indeed Griffith's theory-based framework but further accounting for the coupled effects of the stretches, damage and incompressibility to predict the crack growth in both compressible and Incompressible hyperelastic solids. There are three innovations contained in this study: (i) The developed phase-field framework is capable to capture the effect of hole collapse, which is an intrinsic phenomenon of hyperelastic material and difficult to be detected by the others. (ii) The developed energy decomposition method provides a reasonable description of the physical reality that the hyperelastic fracture is driven by the changes in the internal energy of the stretched molecular chains in the polymer network. This continuum description automatically distinguishes the strain energy that really contributes to crack growth at multiaxial stress states, reducing significantly the numerical instability caused by material softening. (iii) By introducing the assumed strain method to the present fracture scheme, the physical consistency of energy decomposition and the mathematical nonnegativeness of strain energy can be satisfied simultaneously for Incompressible Problem. We demonstrate the performance of the enhanced phase-field framework through representative examples and highlight the importance of positive deviatoric energy for Incompressible Problem by comparing with experiments and classical models.
Chen Ling - One of the best experts on this subject based on the ideXlab platform.
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Improvement on the 10-node tetrahedral element for three-dimensional Problems
Computer Methods in Applied Mechanics and Engineering, 2000Co-Authors: Chen LingAbstract:By decomposing the strain part of the conforming 10-node tetrahedral element T10 and relaxing the compatibility condition for the constant strain term, the performance of the element can be improved. By introducing the Incompressible condition in the high order strain term, the element can be made very efficient for the analysis of the nearly Incompressible Problem. Numerical results show that the modified element, in general, has better accuracy and reliability compared to the classical displacement-based tetrahedral element T10 for a wide range of structural Problems, including the analysis of thin and slender structures.
I. Frankel - One of the best experts on this subject based on the ideXlab platform.
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On the compressible Taylor-Couette Problem
Bulletin of the American Physical Society, 2006Co-Authors: Avshalom Manela, I. FrankelAbstract:We consider the linear temporal stability of a Couette flow of a Maxwell gas within the gap between a rotating inner cylinder and a concentric stationary outer cylinder both maintained at the same temperature. The neutral curve is obtained for arbitrary Mach (Ma) and arbitrarily small Knudsen (Kn) numbers by use of a ‘slip-flow’ continuum model and is verified via comparison to direct simulation Monte Carlo results. At subsonic rotation speeds we find, for the radial ratios considered here, that the neutral curve nearly coincides with the constant-Reynolds-number curve pertaining to the critical value for the onset of instability in the corresponding Incompressible-flow Problem. With increasing Mach number, transition is deferred to larger Reynolds numbers. It is remarkable that for a fixed Reynolds number, instability is always eventually suppressed beyond some supersonic rotation speed. To clarify this we examine the variation with increasing Ma of the reference Couette flow and analyse the narrow-gap limit of the compressible TC Problem. The results of these suggest that, as in the Incompressible Problem, the onset of instability at supersonic speeds is still essentially determined through the balance of inertial and viscous-dissipative effects. Suppression of instability is brought about by increased rates of dissipation associated with the elevated bulk-fluid temperatures occurring at supersonic speeds. A useful approximation is obtained for the neutral curve throughout the entire range of Mach numbers by an adaptation of the familiar Incompressible stability criteria with the critical Reynolds (or Taylor) numbers now based on average fluid properties. The narrow-gap analysis further indicates that the resulting approximate neutral curve obtained in the (Ma, Kn) plane consists of two branches: (i) the subsonic part corresponding to a constant ratio Ma/Kn (i.e. a constant critical Reynolds number) and (ii) a supersonic branch which at large Ma values corresponds to a constant product Ma Kn. Finally, our analysis helps to resolve some conflicting views in the literature regarding apparently destabilizing compressibility effects.
Mary F. Wheeler - One of the best experts on this subject based on the ideXlab platform.
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A MULTISCALE MORTAR MIXED FINITE ELEMENT METHOD FOR SLIGHTLY COMPRESSIBLE FLOWS IN POROUS MEDIA
Journal of the Korean Mathematical Society, 2007Co-Authors: Mi-young Kim, Eun-jae Park, Sunil G. Thomas, Mary F. WheelerAbstract:We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the Incompressible Problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark Problems are given to show the efficiency and effectiveness of the method.
