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Publication# Dynamic crack propagation with phase-field approach

Abstract

This project aims at studying the non-unicity of crack paths in materials using the phase-field approach. The energy functional to be minimized in the variational phase-field modelling of brittle fracture is not convex. Hence, multiple local minima can coexist and could be interpreted as multiple solutions associated with various crack patterns. Recent work on the subject revealed and illustrated this fact. By introducing perturbations in the model, it is possible to trigger some variability in the crack patterns. It is applied here by small variations of the geometry, leading to distinct crack paths with associated probabilities computed using the Monte Carlo method. Moreover, in this context, the Monte Carlo method allows drawing expectation maps of the damage. Thus, starting from a previous publication on stochastic phase-field modelling of brittle fracture, this piece of work explores the variability of mode 1 crack in static. It is observed here that slight changes in geometry yields considerable variations in the expectation maps. The physical properties of the material seem also to influence significantly the variability of the damage field. Finally, the same experiment is made once more, but this time with dynamic resolution. Varying the velocity at which the load is applied to the model allows observing changes in variability of fissure patterns according to the loading speed. Even for low velocities, the experiments in this project show differences between results in static and in dynamic. One notable difference is that the variability disappears with very low or very high speeds. At high velocities, some branching can also be witnessed, but no variability associated with it is observed. Globally, in all the experiment, the variability of the crack patterns seems to be highly sensitive to slight changes in the geometry, modification of the physical properties of the material or, in the dynamic case, to the loading velocity. And, considering that even low velocities in dynamic resolution have shown to lead to results distinct from the experiment in static, studying only the static case in not sufficient to have a global insight of the plausible crack paths.

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Related concepts (5)

Geometry

Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

Velocity

Velocity is the speed and the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.

High-speed rail

High-speed rail (HSR) is a type of rail network utilizing trains that run significantly faster than those of traditional rail, using an integrated system of specialised rolling stock and dedicated tracks. While there is no single standard that applies worldwide, lines built to handle speeds above or upgraded lines in excess of are widely considered to be high-speed. The first high-speed rail system, the Tōkaidō Shinkansen, began operations in Japan in 1964. The system also became known by its English nickname the bullet train.