SUMMARYThis paper proposes a generalization of the eXtended finite element method (X-FEM) to model dynamic fracture and time-dependent problems from a more general point of view, and gives a proof of the stability of the numerical scheme in the linear case. First, we study the stability conditions of Newmark-type schemes for problems with evolving discretizations. We prove that the proposed enrichment strategy satisfies these conditions and also ensures energy conservation. Using this approach, as the crack propagates, the enrichment can evolve with no occurrence of instability or uncontrolled energy transfer. Then, we present a technique based on Lagrangian conservation for the estimation of dynamic stress intensity factors for arbitrary 2D cracks. The results presented for several applications are accurate for stationary or moving cracks.
A full three dimensional study of a fatigue crack in cast iron is presented. This analysis involves combining various tools, namely, Synchrotron X-ray microtomography
Preprint submitted to Elsevier 4 October 2009of an in situ experiment, image acquisition and treatment, 3D volume correlation to measure 3D displacement fields, extraction of the crack geometry, extended digital image correlation to account for the crack displacement discontinuity, crack modeling in an elastic material exploiting the actual crack geometry, and finally estimation of stress intensity factors. All these different tasks are based on specific multiscale approaches.
SUMMARYA two-scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non-linear due to the non-linearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns.
SUMMARYThe methodology of eXtended Finite Element Method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both on artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path.
SUMMARYThis paper focuses on the introduction of a lumped mass matrix for enriched elements, which enables one to use a pure explicit formulation in X-FEM applications. A proof of stability for the 1D and 2D cases is given. We show that if one uses this technique, the critical time step does not tend to zero as the support of the discontinuity reaches the boundaries of the elements. We also show that the X-FEM element's critical time step is of the same order as that of the corresponding element without extended degrees of freedom.
Abstract. Digital image correlation is a measurement technique that allows one to retrieve displacement fields "separating" two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images.
stephane.roux,firstname.lastname@example.org RÉSUMÉ. Afin de réduire l'incertitude de mesure, une technique de mesure de champ de déplacement est proposée. Elle associe à la corrélation d'images numériques une pénalisation supplémentaire sur l'écart du champ de déplacement à sa projection dans l'espace des solutions élastiques. Cette application s'effectue dans le cadre de la méthode des élément finis étendus qui permet d'introduire des discontinuités indépendamment du maillage. Une application à l'analyse
SUMMARYConstitutive parameter identification has been greatly improved by the achievement of full-field measurements. In this context, noise sensitivity has been shown to be of great importance. It is crucial to incorporate noise sensitivity minimization in the design of robust identification procedures. In this paper, we investigate noise sensitivity reduction techniques for constitutive parameter identification based on Finite Element Model Updating. After examining the existing strategies, we propose a single step algorithm based on a mixed optical/mechanical cost function. The key point of this novel procedure is that no boundary conditions are needed. A first example on a real case illustrates the advantages of the proposed methodology in terms of noise sensitivity. A second example shows its capabilities to identify a non-linear consitutive law.
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