Spectral method for fundamental 3D dynamic fracture problems

Objectives

Method description

Advantages of the method

The convolution kernels are non-singular and are well-behaved oscillating and decaying functions;
The numerical scheme allows for the incorporation of almost any type of rate- and state-dependent cohesive failure and friction models to simulate spontaneous crack propagation;
The numerical method is easily adapted to massively parallel computing environments, allowing for the investigations of very large problems. Recent efforts in the parallel implementation of the spectral scheme have allowed us to investigate problems involving more than 16,000,000 sampling points on the fracture plane and over 20,000 time steps. The spectral scheme is undoubtedly the most efficient numerical scheme available to date to study fundamental dynamic fracture problems.

Graduate students and postdoctoral research associates involved in this project

Michael J. Danyluk

M. Scot Breitenfeld

Dr. Changyu Hwang

Examples - Illustrations

Sudden uniform pressure loading of an elliptical crack

Evolution of the shape of an elliptical crack embedded
in an elastic medium and subjected to a sudden uniform
tensile loading (mode I). The pictures clearly show the
dynamic overshoot characteristic of this type of problems.
Note also how the Rayleigh waves emanating from the edge
of the crack move toward the center, generating a complex
wave pattern.

To better visualize this dynamic fracture problem, have a look at these two mpeg movies

the first movie (292k) shows the evolution of the crack shape;
the second movie (471k) presents the evolution of the crack opening velocity. Note the complex motion of the Rayleigh waves as they converge toward the center of the crack.

Interaction of a moving tensile (mode I) crack front with a row of circular asperities

Interaction of an initially straight tensile crack front with a row of circular asperities.
The crack propagates dynamically (at a speed approximately equal to 60% of the Rayleigh wave speed)
from the back to the front of the picture. The elevation corresponds to the crack opening displacement
and the color to the stress level, showing how dynamic stresses build up in the vicinity of the asperities.
The asperities eventually break in a snapping mode, and the crack front resumes its propagation.

Click here

Off-plane stress computation for a dynamically propagating mode III interfacial crack

Stress wave emanating from a stationary interfacial mode III crack subjected
to a sudden uniform loading. The stiffer material is at the bottom, the more compliant one on top.
Note the presence of the stress concentrations in the vicinity of the two crack tips.

In these three snapshots, we show the stress field in the vicinity of a spontaneously propagating and arresting dynamic mode III interfacial crack. The right crack tip is propagating from left to right (the left crack tip is stationary). As apparent from the wave pattern, the stiffer material (in which the shear wave speed is higher) is located in the top half plane, while the more compliant material occupies the bottom half space. The second picture presents the stress field at the instant at which the right crack tip is arrested, showing the sudden appearence of the dynamic stress. A few instants later (third picture), the stress field includes the presence of an arrest wave propagating away from the right crack tip.