Effective anisotropic compliance relationships for wing-cracked brittle materials under compression. (1st December 2016)

• Record Type: Journal Article
• Authors: Liu, Junwei; Graham-Brady, Lori
• Is Part Of: International journal of solids and structures. Volume 100/101(2016)
• Page Start: 151
• Page End: 168
• Publication Date: 2016-12-01
• Subjects: Compressive compliance of damaged brittle materials -- Damage induced anisotropy -- Wing-crack modeling -- Periodic unit cell; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2016.08.012
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: The failure mechanism for brittle materials under compressive loading is generally assumed to be dominated by the development of wing-cracks. Due to the preferential direction of the wing-crack development, material damaged in this mode exhibits damage induced anisotropy and volume dilatancy. The effective compliance of such wing-crack damaged materials is important for developing micromechanics-based constitutive models. This work addresses the scenario of a brittle material with periodically distributed wing-cracks under uniaxial compressive load. Closed form expressions for the instantaneous anisotropic compliance tensor with respect to the key physical parameters of the wing-cracks (the number density of cracks, the pre-existing flaw orientations and flaw sizes, the instantaneous length of wing-cracks, and the friction coefficient on the flaw surfaces) are derived through a kinematic approach. Accordingly, finite element models with perturbing compressive loads and periodic boundary conditions are carried out based on the above ideological wing-crack model, in order to verify and parameterize the analytically-based model. Good agreement is found between the finite element results and the analytical expression.