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Fracture Problems (fracture + problem)
Selected AbstractsAdvanced Experimental and Simulation Approaches to Meet Reliability Challenges of New Electronics SystemsADVANCED ENGINEERING MATERIALS, Issue 4 2009Dietmar Vogel Abstract This paper focuses on some advanced aspects of physics of failure approaches. Tracing of failure modes under realistic loading is a key issue to separate relevant failure sites to be studied in more detail. In the past design of experiment (DoE) tools have been developed to handle this problem. They allow to optimize design and/or material selection with respect to different failure mechanisms and sites. The application of these methods is demonstrated by optimizations performed for fracture problems. Interface fracture has been chosen as one of the most important failure mechanisms. Finally, local stress and strain measurement tools developed over the past years are presented at the end of the paper. They are tools to validate simulation results and therefore the underlying mechanical modeling. Namely, local stress measurement tools under development are needed to make realistic assumptions of loading conditions and to provide residual stress data for FEA. [source] Mesh adaptation and transfer schemes for discrete fracture propagation in porous materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2007Stefano Secchi Abstract This paper presents a numerical procedure for cohesive hydraulic fracture problems in a multiphase system. The transient problem of crack nucleation and/or advancement, with the ensuing topological changes, is solved by successive remeshing and projection of the field variables required in the time marching scheme. The projection is directly applied to the nodal vector of the previous step and is performed by means of a suitable mapping operator which acts on nodal forces and fluxes. This hence ensures ,a priori' the local fulfilment of the balance equations (equilibrium and mass conservation). The resulting procedure is computationally simple; however checks have to be made on its capability of conserving strain energy of the system. The latter property together with the accuracy of the solution is heuristically assessed on the basis of numerical benchmarks. Copyright © 2007 John Wiley & Sons, Ltd. [source] A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010G. R. Liu Abstract It is well known that the lower bound to exact solutions in linear fracture problems can be easily obtained by the displacement compatible finite element method (FEM) together with the singular crack tip elements. It is, however, much more difficult to obtain the upper bound solutions for these problems. This paper aims to formulate a novel singular node-based smoothed finite element method (NS-FEM) to obtain the upper bound solutions for fracture problems. In the present singular NS-FEM, the calculation of the system stiffness matrix is performed using the strain smoothing technique over the smoothing domains (SDs) associated with nodes, which leads to the line integrations using only the shape function values along the boundaries of the SDs. A five-node singular crack tip element is used within the framework of NS-FEM to construct singular shape functions via direct point interpolation with proper order of fractional basis. The mix-mode stress intensity factors are evaluated using the domain forms of the interaction integrals. The upper bound solutions of the present singular NS-FEM are demonstrated via benchmark examples for a wide range of material combinations and boundary conditions. Copyright © 2010 John Wiley & Sons, Ltd. [source] A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005A. P. Peirce Abstract We present a novel multigrid (MG) procedure for the efficient solution of the large non-symmetric system of algebraic equations used to model the evolution of a hydraulically driven fracture in a multi-layered elastic medium. The governing equations involve a highly non-linear coupled system of integro-partial differential equations along with the fracture front free boundary problem. The conditioning of the algebraic equations typically degrades as O(N3). A number of characteristics of this problem present significant new challenges for designing an effective MG strategy. Large changes in the coefficients of the PDE are dealt with by taking the appropriate harmonic averages of the discrete coefficients. Coarse level Green's functions for multiple elastic layers are constructed using a single dual mesh and superposition. Coarse grids that are sub-sets of the finest grid are used to treat mixed variable problems associated with ,pinch points.' Localized approximations to the Jacobian at each MG level are used to devise efficient Gauss,Seidel smoothers and preferential line iterations are used to eliminate grid anisotropy caused by large aspect ratio elements. The performance of the MG preconditioner is demonstrated in a number of numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Dynamic crack propagation with cohesive elements: a methodology to address mesh dependencyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004F. Zhou Abstract In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three-dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||