Numerical simulations of fracture propagation in a 2-dimensional isotropic strain gradient continuum

In this presentation we exploit a specific result in the theory of irreversible phenomena, treated in a variational context, to address the study of quasi-static brittle fracture propagation in a 2-dimensional isotropic continuum. The elastic strain energy density of the body has been assumed to be geometrically non-linear and to depend upon the strain gradient. These materials possess an intrinsic length scale, which determines the size of internal boundary layers. In particular, the non-locality conferred by this internal length scale avoids the concentration of deformations, which is usually observed when dealing with local models and which leads to mesh-dependency. Besides, a scalar Lagrangian damage field, ranging from zero to one, is introduced to describe the internal state of structural degradation of the material. Standard Lamé and second gradient elastic coefficients are all assumed to decrease as damage increases and to be locally zero if the value attained by damage is one. This last situation is associated with crack formation and/or propagation. Numerical solutions of the model will be provided in the case of an obliquely notched rectangular specimen subject to monotonous tensile and shear loading tests and brittle fracture propagation is discussed.