Modeling and numerical simulation of the path of a single crack in an elastic material submitted to a stress gradient

This work starts the phase field modeling that is a linearized elastodynamics model coupling the phase theory, the material is intact by φ =1 and crack by φ = 0 . This problem is solved by the numerical methods and FORTRAN program. Firstly we simulate a simple case only the displacement loading and the results are straight crack and symmetric branched crack under the different amplitude of displacement. Then, the main works are simulations of quasistatic under the thermal loading. There are straight propagation and oscillating propagation with different amplitude of the temperature. Those results fit other experimental and numerical research. The wavelength of oscillating is about 60 and amplitude of oscillating is 25. When the g = 545, the oscillating crack would propagate a little back and it is going on oscillating propagation. matrix and saturated porous matrix.