Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts

TLDR

Effective moduli of cracked solids are critically reviewed, highlighting deficiencies of approximate schemes linked to the inadequacy of conventional crack density parameters and situating the problem within damage mechanics. The study proposes an alternative crack density parameter that is sensitive to the mutual positions of cracks. The authors discuss various approaches, assess their predictions against deterministic array results, and propose an alternative crack density parameter sensitive to crack mutual positions. Computer experiments reveal that the non‑interacting crack approximation remains valid over a wider range than expected, yet the study finds no direct quantitative link between microcracking progression and stiffness loss, indicating that effective moduli may not reliably signal damage.

Abstract

The problem of effective moduli of cracked solids is critically reviewed. Various approaches to the problem are discussed; they are further assessed by comparing their predictions to results for sample deterministic arrays. These computer experiments indicate that the approximation of non-interacting cracks has a wider than expected range of applicability. Some of the deficiencies of various approximate schemes seem to be related to inadequacy of the conventionally used crack density parameter (insensitive to mutual positions of cracks). An alternative parameter that has this sensitivity, is suggested. Finally, the problem of effective moduli is discussed in the context of “damage mechanics”. It is argued that, contrary to the spirit of many damage models, there is no direct quantitative correlation between progression of a microcracking solid towards fracture and deterioration of its stiffness; thus, the effective moduli may not always serve as a reliable indicator of damage.