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M Adda-Bedia

Publications and source records attributed to M Adda-Bedia.

11 recordsLinked to original sources
PubMed2006

A statistical approach to close packing of elastic rods and to DNA packaging in viral capsids.

We propose a statistical approach for studying the close packing of elastic rods. This phenomenon belongs to the class of problems of confinement of low dimensional objects, such as DNA packaging in viral capsids. The method developed is based on Edwards' approach, which was successfully applied to polymer physics and to granular matter. We show that the confinement induces a configurational phase transition from a disordered (isotropic) phase to an ordered (nematic) phase. In each phase, we derive the pressure exerted by the rod (DNA) on the container (capsid) and the force necessary to inject (eject) the rod into (out of) the container. Finally, we discuss the relevance of the present results with respect to physical and biological problems. Regarding DNA packaging in viral capsids, these results establish the existence of ordered configurations, a hypothesis upon which previous calculations were built. They also show that such ordering can result from simple mechanical constraints.

Capsid↗
PubMed2006

Spiral patterns in the packing of flexible structures.

Spiral patterns are found to be a generic feature in close-packed elastic structures. We describe model experiments of compaction of quasi-1D sheets into quasi-2D containers that allow simultaneous quantitative measurements of mechanical forces and observation of folded configurations. Our theoretical approach shows how the interplay between elasticity and geometry leads to a succession of bifurcations responsible for the emergence of such patterns. Both experimental forces and shapes are also reproduced without any adjustable parameters.

Elasticity↗
PubMed2006

Second-order variation in elastic fields of a tensile planar crack with a curved front.

We derive the second-order variation in the local static stress intensity factor of a tensile crack with a curved front. We then discuss the relevance of this result to the stability analysis of such fronts, and propose an equation of motion of planar crack fronts in heterogeneous media that contains two main ingredients--irreversibility of the propagation of the crack front and nonlinear effects.

Journal Article↗
PubMed2005

Hierarchical crack pattern as formed by successive domain divisions. II. From disordered to deterministic behavior.

Hierarchical crack patterns, such as those formed in the glaze of ceramics or in desiccated layers of mud or gel, can be understood as a successive division of two-dimensional domains. We present an experimental study of the division of a single rectangular domain in drying starch and show that the dividing fracture essentially depends on the domain size, rescaled by the thickness of the cracking layer e. Utilizing basic assumptions regarding the conditions of crack nucleation, we show that the experimental results can be directly inferred from the equations of linear elasticity. Finally, we discuss the impact of these results on hierarchical crack patterns, and in particular the existence of a transition from disordered cracks at large scales--the first ones--to a deterministic behavior at small scales--the last cracks.

Journal Article↗
PubMed2004

Path prediction of kinked and branched cracks in plane situations.

Using the asymptotic expansion of the stress field ahead a curved extension of a straight crack, some general results on the paths selected by kinked and branched cracks are derived. When dealing with the dynamic branching instability of a single propagation crack, the experimentally observed shape of the branches is recovered without introducing any adjustable parameter. It is shown that the length scale introduced by the curved extension of the branches is given by the geometrical length scale of the experiment. The theoretical results agree quantitatively with the experimental findings.

Journal Article↗
PubMed2003

Morphologies resulting from the directional propagation of fractures.

When growing in a stress gradient, cracks have a directional growth. We investigate here this type of instability in the case of a colloidal gel deposited on a substrate and left to dry. The use of various materials reveals the existence of two distinct types of dynamics. When the crack nucleation is easy a well known situation is reached: an array of periodic fractures forms, which grow parallel to each other and move quasistatically with the stressed region. In contrast, in materials where the crack nucleation is difficult, a subcritical process is observed with the retarded formation of isolated cracks which move faster and which display an arch shaped trajectory. This type of process appears to be generic in all cases where there is delayed nucleation. This is confirmed by experiments on the directional propagation of cracks in thermally stressed glass.

Journal Article↗
PubMed2001

Fracture spacing in layered materials.

We perform an elastostatic analysis of a periodic array of cracks under constant loading. We give an analytical solution and show that there is a limitation to the fracture spacing, due to a transition from an opening to a compressive loading. For this configuration, the threshold of the fracture spacing depends on neither the applied strain nor the elastic parameters of the material. This result shows that, in the general case of layered materials, the physical mechanism that is responsible for the limitation in the density of fractures is related mainly to the geometry of the problem. This is in agreement with observations and with recent numerical results.

Journal Article↗
PubMed1999

Generalized Griffith criterion for dynamic fracture and the stability of crack motion at high velocities.

We use Eshelby's energy momentum tensor of dynamic elasticity to compute the forces acting on a moving crack front in a three-dimensional elastic solid [Philos. Mag. 42, 1401 (1951)]. The crack front is allowed to be any curve in three dimensions, but its curvature is assumed small enough so that near the front the dynamics is locally governed by two-dimensional physics. In this case the component of the elastic force on the crack front that is tangent to the front vanishes. However, both the other components, parallel and perpendicular to the direction of motion, do not vanish. We propose that the dynamics of cracks that are allowed to deviate from straight line motion is governed by a vector equation that reflects a balance of elastic forces with dissipative forces at the crack tip, and a phenomenological model for those dissipative forces is advanced. Under certain assumptions for the parameters that characterize the model for the dissipative forces, we find a second order dynamic instability for the crack trajectory. This is signaled by the existence of a critical velocity V(c) such that for velocities V V(c) it is governed by K(II) not equal to 0. This result provides a qualitative explanation for some experimental results associated with dynamic fracture instabilities in thin brittle plates. When deviations from straight line motion are suppressed, the usual equation of straight line crack motion based on a Griffiths-like criterion is recovered.

Journal Article↗