An arbitrary Lagrangian description of 2D and 3D cracked structures Original Research Article

An arbitrary Lagrangian description is proposed for the moving crack analysis. The method is based on the use of a mapping of the moving domain to the initial stationary one (boundaries, shape and conditions may be very general). In the framework of elasticity, the energy release rate is expressed as surface integrals on the fixed domain, explicitly related to the current crack growth (or crack shape in 3D) parameter. Numerical results of an energy release rate analysis are presented for a large range of 2D and 3D crack extension. The advantages of this method are: firstly, it avoids remeshing or introducing special numerical parameters such as relaxation forces to simulate the crack growth or performing parametric analysis for different crack shape; secondly, to obtain exact derivatives of the potential energy.