Strain gradient elasticity theory for antiplane shear cracks. Part I: Oscillatory displacements

A strain gradient theory of elasticity has been proposed recently to addres s problems involving singularities and discontinuities in materials. Among its capabilities, the theory can eliminate the crack-tip strain singularity while providing structure to the cohesive zone without resorting to extran eous forces as in plastic strip models. Due to the theory's higher-order te rms, additional boundary conditions must be imposed over those of linear el asticity, which affect directly the form of the solution. Various boundary conditions have been used by different investigators resulting in different profiles in crack opening displacement. In this two-part paper the similar ities and differences among the various antiplane crack solutions obtained thus far for this theory are examined. New analytical results are also pres ented in the course of this review. Part I of the paper is devoted to solut ions having crack displacements which are oscillatory in nature; whereas, P art II is dedicated to those which exhibit monotonic behavior. (C) 2000 Els evier Science Ltd. All rights reserved.