Phase-field models, sometimes referred to as gradient damage or smeared crack models, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical ...results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’ criterion. For a one-dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter be identified with the material’s internal or characteristic length. In this article, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.
Our main claim, supported by validation and verification in a broad range of materials and geometries, is that crack nucleation can be accurately predicted by minimization of a nonlinear energy in variational phase field models, and does not require the introduction of ad-hoc criteria.
In this article, we focus on the validation of Francfort and Marigo’s variational approach to fracture based on some classical fracture experiments. We show that this approach can be used to ...faithfully account for unknown crack paths even for complex loadings and geometry. We revisit the backtracking algorithm, aimed at avoiding some spurious local minimizers of the total fracture energy and introduce a variant: the deep backtracking algorithm.
BCG vaccine has shown consistently high efficacy against childhood tuberculous meningitis and miliary tuberculosis, but variable efficacy against adult pulmonary tuberculosis and other mycobacterial ...diseases. We assess and compare the costs and effects of BCG as an intervention against severe childhood tuberculosis in different regions of the world.
We calculated the number of tuberculous meningitis and miliary tuberculosis cases that have been and will be prevented in all children born in 2002, by combining estimates of the annual risk of tuberculosis infection, the proportion of infections that lead to either of these diseases in unvaccinated children, the number of children vaccinated, and BCG efficacy.
We estimated that the 100·5 million BCG vaccinations given to infants in 2002 will have prevented 29 729 cases of tuberculous meningitis (5th–95th centiles, 24 063–36 192) in children during their first 5 years of life, or one case for every 3435 vaccinations (2771–4177), and 11 486 cases of miliary tuberculosis (7304–16 280), or one case for every 9314 vaccinations (6172–13 729). The numbers of cases prevented would be highest in South East Asia (46%), sub-Saharan Africa (27%), the western Pacific region (15%), and where the risk of tuberculosis infection and vaccine coverage are also highest. At US$2–3 per dose, BCG vaccination costs US$206 (150–272) per year of healthy life gained.
BCG vaccination is a highly cost-effective intervention against severe childhood tuberculosis; it should be retained in high-incidence countries as a strategy to supplement the chemotherapy of active tuberculosis.
This continues the study of the effective toughness of layered materials started in Hossain et al. (2014) and Hsueh et al. (2018), with a focus on anisotropy. We use the phase-field model and the ...surfing boundary condition to propagate a crack macroscopically at various angles to the layers. We study two idealized situations, the first where the elastic modulus is uniform while the toughness alternates and a second where the toughness is uniform and the elastic modulus alternates. We find that in the first case of toughness heterogeneity the effective toughness displays ‘anomalous isotropy’ in that it is independent of the propagation direction and equal to that of the tougher material except when the crack propagation is parallel to the layers. In the second case of elastic heterogeneity, we find the behavior more anisotropic and consistent with the toughening effects of stress fluctuation and need for crack renucleation at the compliant-to-stiff interface. In both cases, the effective toughness is not convex in the sense of interfacial energy or Wulff shape reflecting the fact that crack propagation follows a critical path. Further, in both cases the crack path is not straight and consistent with a maximal dissipation principle. Finally, the effective toughness depends on the contrast and pinning, rather than on the extent of crack fluctuation.
Effective toughness of heterogeneous media Hossain, M.Z.; Hsueh, C.-J.; Bourdin, B. ...
Journal of the mechanics and physics of solids,
11/2014, Letnik:
71
Journal Article
Recenzirano
We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The ...key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to evolve as it chooses. The approach is verified and used to study examples in brittle fracture. We demonstrate that effective toughness is different from effective or weighted surface area of the crack set. Furthermore, we demonstrate that elastic heterogeneity can have a profound effect on fracture toughness: it can be a significant toughening mechanism and it can lead to toughness asymmetry wherein the toughness depends not only on the direction but also on the sense of propagation. The role of length-scale is also discussed.
It has been established that contrast in the elastic properties can lead to enhancement of fracture toughness in heterogeneous materials. Focussing on layered materials as a model system, we show ...that this enhancement is a result of two distinct phenomena – first, fluctuations in stress leading to regions where the stress intensity at the crack is considerably smaller than that of the macroscopically applied value; and second, the lack of stress intensity when a crack is at a compliant to stiff interface thereby requiring renucleation. Using theoretical, computational and experimental methods, we study two geometries – a layered material and a layered material with a narrow channel – to separate the two phenomena. The stress fluctuation is present in both, but renucleation is present only in the layered medium. We provide quantitative estimates for the enhanced toughness.
Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a ...medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture-when unavoidable-can be guided through predesigned paths to minimize loss of critical components.
We address the problem of fracture in homogenous linear elastic thin films using a variational model. We restrict our attention to quasi-static problems assuming that kinetic effects are minimal. We ...focus on out-of-plane displacement of the film and investigate the effect of bending on fracture. Our analysis is based on a two-dimensional model where the thickness of the film does not need to be resolved. We derive this model through a formal asymptotic analysis. We present numerical simulations in a highly idealized setting for the purpose of verification, as well as more realistic micro-indentation experiments.
•Variational approach to fracture mechanics is extended to thin-film fracture.•Fracture of thin-films subject to out-of-plane loading is studied.•Crack patterns corresponding to experimental observations are predicted.
We study fracture and debonding of a thin stiff film bonded to a rigid substrate through a thin compliant layer, introducing a two-dimensional variational fracture model in brittle elasticity. ...Fractures are naturally distinguished between transverse cracks in the film (curves in 2D) and debonded surfaces (2D planar regions). In order to study the mechanical response of such systems under increasing loads, we formulate a dimension-reduced, rate-independent, irreversible evolution law accounting for both transverse fracture and debonding. We propose a numerical implementation based on a regularized formulation of the fracture problem via a gradient damage functional, and provide an illustration of its capabilities exploring complex crack patterns, showing a qualitative comparison with geometrically involved real life examples. Moreover, we justify the underlying dimension-reduced model in the setting of scalar-valued displacement fields by a rigorous asymptotic analysis using Γ-convergence, starting from the three-dimensional variational fracture (free-discontinuity) problem under precise scaling hypotheses on material and geometric parameters.
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•We study fracture of thin films with a variational approach.•A variational asymptotic analysis allows to establish a two-dimensional model.•The limit system naturally discriminates between transverse and debonding cracks.•We perform numerical experiments, extending a classical regularization approach.•The experiments capture complex evolving patterns, including hexagonal crack networks.
Basalt columns, septarias, and mud cracks possess beautiful and intriguing crack patterns that are hard to predict because of the presence of cracks intersections and branches. The variational ...approach to brittle fracture provides a mathematically sound model based on minimization of the sum of bulk and fracture energies. It does not require any
a priori
assumption on fracture patterns and can therefore deal naturally with complex geometries. Here, we consider shrinkage cracks obtained during unidirectional drying of a colloidal suspension confined in a capillary tube. We focus on a portion of the tube where the cross-sectional shape cracks does not change as they propagate. We apply the variational approach to fracture to a tube cross-section and look for two-dimensional crack configurations minimizing the energy for a given loading level. We achieve qualitative and quantitative agreement between experiments and numerical simulations using a regularized energy (without any assumption on the cracks shape) or solutions obtained with traditional techniques (fixing the overall crack shape a priori). The results prove the efficiency of the variational approach when dealing with crack intersections and its ability to predict complex crack morphologies without any a priori assumption on their shape.
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