Effective elastic moduli in solids with high density of cracks

Abstract

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precursors of percolation. For a parallel alignment of cracks, where percolation does not occur, we analytically predict a power-law decay of the effective elastic constants for high crack densities, and confirm this result numerically.

Scaling Shift in Multicracked Fiber Bundles

“…We remark that we observed this shift behavior also with nonlocal couplings among the fibers. It is interesting to note that similar regimes were observed in multicracked bulk solid materials [45][46][47], for which it was separately found that randomly oriented cracks lead to an exponential degradation, while parallel cracks lead to a power-law decay of the effective properties.…”

“…Although the progressive damage originated by the load redistribution is a relevant effect largely studied within the FBM [10,11], we have not included this feature in order to isolate the statistical behavior induced by the random fractures within the interacting fibers. Under this respect, the problem belongs to the field of homogenization theories [43][44][45][46][47]. In particular, our approach allows us to demonstrate the existence of a marked shift in the scaling law of the effective Young's modulus of the fiber bundle: the elastic modulus decays with an exponential scaling, expð−N=MÞ at small N, and goes into a power-law scaling 1=N 2 at increasing values of N. The threshold N Ã between the exponential and the power-law regime is a decreasing function of the lateral coupling k. This "slowing-down" shift has therefore important practical implications, in that the yielding of a fiber-bundle material could be postponed to longer times upon increasing the amount of lateral coupling in the bundle.…”

Brittle fracture in viscoelastic materials as a pattern-formation process

“…This method is especially advantageous due to its high versality to study quite complicated crack patterns as well as multicrack situations [55]. Nowadays, phase field models capture many known features of cracks [44][45][46]56].…”

Fracture as a pattern formation process

“…During the past years, phase field modeling has emerged as a promising approach to model crack propagation by continuum methods (see [26] for a recent review). This method is especially advantageous due to its high versality to study quite complicated crack patterns as well as multi crack situations [55]. Nowadays, phase field models capture many known features of cracks [44][45][46]56]; However, a significant attribute of most of these descriptions is that the scale of the growing patterns is always set by the phase field interface width, which is a purely numerical parameter and not directly connected to physical properties; therefore these models do not possess a valid sharp interface limit.…”