Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

John Waldridge, The Leaven of the Ancients: Suhrawardi and the Heritage of the Greeks, SUNY Series in Islam (Albany: State University of New York Press, 1999). Pp. 323

In the Leaven of the Ancients, John Walbridge studies the appropriation of non–Peripatetic philosophical ideas by an anti–Aristotelian Islamic philosopher, Shihab al-Din al-Suhrawardi (d. 1191). He proposes a comprehensive explanation of the origin of Suhrawardi's philosophical system, a revival of the “wisdom of the Ancients” and its philosophical affiliations “grounded” in Greek philosophy (p. xiii). Walbridge attempts to uncover the reasons for Suhrawardi's rejection of the prevailing neo–Aristotelian synthesis in Islamic philosophy, Suhrawardi's knowledge and understanding of non–Aristotelian Greek philosophy, the ancient philosophers Suhrawardi was attempting to follow, the relationship between Suhrawardi's specific philosophical teachings (logic, ontology, physics, and metaphysics), and his understanding of non–Aristotelian ancient philosophy and the relationship between Suhrawardi's system and the major Greek philosophers, schools, and traditions—in particular the Presocratics, Plato, and the Stoics (p. 8). Copyright © 2003 Cambridge University Press