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Mechanics of fracture in heterogeneous media

Fracture affects an extensive range of technologies. While successes in the field over the decades are impressive, it is also impressive how much remains unknown, both at macroscale and nanoscale, particularly under heterogeneous conditions. For example, although heterogeneity is prevalent in almost all solids at some lengthscales, it remains a challenging task to characterize the relation between heterogeneity and macroscopic ability of a solid to resist fracture failure. The goal of this work is to develop a comprehensive meaning of effective toughness that is applicable at multiple lengthscales under multiphysical material conditions.

Employing the basic definition of Eshelby's energy-momentum tensor, we define effective toughness as the maximum driving force that we would need to apply at the macroscopic boundary for a crack to propagate through a heterogeneous domain.

It is found that the macroscopic toughness is very different from the weighted surface area of the crack set. Results also indicate that elastic heterogeneity alone can enhance toughening, and it can induce toughening asymmetry.

Figure The domain has uniform Gc but a contrast in E. Although the crack remains in material-1, the effective toughness of the domain is higher than Gc -- a phenomena that is inaccessible through widely used weighted-averaging approach. 

Further reading:
[1] M. Z. Hossain, C-J. Hsueh, B. Bourdin, K. Bhattacharya, 'Effective toughness of heterogeneous media', J. of Mech. and Phys. of Solids 71, 15 (2014)
[2] M. Z. Hossain, B. Bourdin, K. Bhattacharya, 'Role of interface and anisotropy on effective toughness in solids', in prep (2014)
[3] M. Z. Hossain,  B. Bourdin, K. Bhattacharya, 'Rate-dependence and crack propagation in heterogeneous media', in prep (2014)