Crack growth as a standard dissipative system

The crack propagation problem for LEFM has been studied by several authors exploiting its analogy with standard dissipative systems [1]. Minimum theorems were derived in [2] in terms of crack front “ quasi-static velocity" for the 3D LEFM. They are reminiscent of Ceradini’s theorem in plasticity and provide crack front velocity as the minimum of constrained quadratic functionals. Such minimum theorems have been recently rephrased in terms of weight functions [3] moving from the cornerstone work of Rice [4] on weight functions theory for the 3D case. Weight functions are displacements analytical solutions, in a distributional sense, of the LEFM boundary value problem. Their closed form is available for a very limited set of geometries and load cases. The need to supply a high quality approximation for the weight functions in all cases for which they are not available in closed form has lead to the formulation of a novel algorithm, based on the definition of weight function itself. An implicit and effective 3D crack tracking algorithm is therefore allowed. It is based on a Newton-Raphson numerical strategy for the Griffith-Maximum Energy Release Rate condition, which is endowed with a variational formulation [5] at every iteration and computationally handles the constraint via the penalty method.