A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy

Abstract

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such materials, there is lack of consistent failure criteria to support their applications in engineering structures. A general quadratic failure criterion tends to leave undetermined coefficients for interactive terms. A rational approach is adopted in this paper based on mathematical and logical considerations to determine these coefficients as the objective of this paper. Considerations are based on the intrinsic characteristics of the quadric surfaces introduced by the quadratic failure criterion. These coefficients must take the values as obtained, leaving no alternatives if logic prevails. The obtained criterion integrates for the first time a range of criteria separately formulated for materials of different degrees of anisotropy, from genuinely orthotropic, through transversely isotropic, cubically symmetric, to completely isotropic ones with different or identical tensile and compression strengths.

Keywords

• failure criterion
• orthotropic materials
• strength
• quadratic failure function
• quadric surface
• Tsai–Wu criterion