Nonlocal Theory for Fracturing of Quasibrittle Materials

摘要

The failure of quasibrittle materials, which include concrete, rock, high-performance ceramics and fiber composites, cannot be treated according to the classical theories of plasticity or fracture mechanics because growth of zones of strain softening damage due to cracking must be considered. The mathematical treatment involves difficulties with spurious excessive localization. To remedy them, the nonlocal continuum concept was previously introduced, however, without theoretical foundation. The principal objective of the research has been to formulate the nonlocal damage concept on the basis of micromechanics of systems of growing and interacting cracks. This has led to a new model in which the nonlocal interactions are based on a smeared crack influence function, are tensorial and directional, and directional, and exhibit a power-type long-range decay. An iterative method for solving a Fredholm integral equation for the crack interactions in a finite element code has also been formulated. Advances have further been made in several related problems of micro-macro correlation. The applicability limits of the classical Weilbull theory of random micro-strength have been identified and a nonlocal probabilistic generalization derived. The time dependence and rate effect in damage evolution have been described on the basis of the activation theory for bond ruptures. The problems of scaling and size effect associated with damage have been analyzed, both theoretically and experimentally (with tests on concretes, fiber composites and rocks).