The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain-gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant is introduced, in addition to the standard Lamé constants . The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics

Post-Arab Spring: The Arab World Between the Dilemma of the Nation-State and the Rise of Identity Conflicts

The Arab world is one of the most volatile regions in the world suffering from identity conflicts. These conflicts, which revolve around religious, sectarian, ethnic, and tribal issues, represent the other side of the crisis of nation-state building in the Arab world in the postindependence era. Although identity conflicts are not new to the region, they have intensified after the US invasion of Iraq in 2003 and the revolutions of the so-called Arab Spring. These two events revealed the deep crisis of the nation-state, thereby highlighting the failure of the postindependence ruling elites to establish nation states that can maintain a position of legitimacy and effectiveness. Being both legitimate and effective enables a state to include religious, sectarian, ethnic, and tribal pluralism within the framework of its national identity, based on the foundations and principles of citizenship, rule of law, respect for human rights, minority rights, and social justice.Additionally, identity conflicts are linked to two other factors that escalated after the US invasion of Iraq and the events of the “Arab spring.” First, was the increased politicization of religious, sectarian, and tribal affiliations, which was used to serve political ends, either by ruling regimes, political parties, or non-state actors. Second, is the current expansion of the political polarization between the forces of political Islam which rose rapidly after the “Arab spring” on one hand and the liberal, leftist, and national civil forces on the other hand. This polarization reflects the deep gap between the advocates of the “religious state” and the advocates of the “civil state.” The purpose of this chapter is to analyze and interpret the dimensions of the relationship between the deep crisis of the nation–state and identity conflicts in the post-Arab spring era