Nonlinear, Finite-Strain Fracture Mechanics

Linear elasticity theory, on which LEFM is based, is not valid when the strains are large or when the stress-strain curves are nonlinear. To cope with this situation, various alternative formulations of fracture mechanics have been developed. 

Since the sheet thickness is h, the energy released per unit area of crack growth is 

If the crack just propagates, the energy consumed per unit area, d, must equal the energy available (released) from the stress field. Thus the fracture mechanics parameter, S, is given by Eq. (6) with the critical value of Wq inserted. Thus 

A second approach is that of Rice,(3) who defined a path-independent integral around a crack and denoted it J. It turns out that, for a nonlinear elastic solid, the integral is equivalent to the energy released from the stress field for unit propagation of the crack and is thus essentially the same as the more empirical parameter of Rivlin and Thomas.(2) 

FIGURE 1. Edge crack in sheet under load showing relaxed region shaded. 

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For refined finite element analysis, the fracture behavior of concrete and masonry can be simulated with continuum elements based on the nonlinear fracture mechanics concept. In these elements, cracks are modeled in a smeared fashion, i.e., with a material stress—strain law representing distributed crack development in... 

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