LUSAS (United Kingdom)

This paper discusses the use of high-performance incompatible, enhanced-strain and hybrid stress elements for the St Venant torsion and bending of composite prismatic shafts, formulated in terms of the warping function. The properties of the shaft are uniform along its length but piece-wise constant and orthotropic across its cross-section. In order to analyse composite shafts whose microstructural details are difficult to be modelled directly by finite element discretisation, the two-scale asymptotic (or mathematical) homogenisation approach is also discussed; the resulting equilibrium equations can be readily solved by the aforementioned high-performance elements

Abstract This paper discusses the asymptotic fields ahead of mixed mode frictional cohesive cracks in quasi‐brittle materials. These fields have been derived after reformatting the cohesive‐law in a special but universal polynomial containing fractional or integer powers. This special form ensures that the radial and angular variations of the asymptotic fields are separable as in the Williams expansions for a traction‐free crack. The coefficients of the expansions however depend nonlinearly on the softening law and the boundary conditions. As expected, the asymptotic field of a frictional cohesive crack reduces to that of a frictionless cohesive crack with normal cohesive separation when the friction coefficient becomes zero. It is also shown that the asymptotic field of a frictionless cohesive crack can be used to a non‐cohesive crack opened by crack face loading, after including the singular terms corresponding to the eigenvalue 1/2. Furthermore, the coefficients are given explicitly for two special softening laws that are commonly used in practice. The leading terms of the true displacement asymptotic field are also derived explicitly. These are especially useful as the enrichment functions at the tip of a mixed mode cohesive crack for accurate simulation of crack growth in quasi‐brittle materials using the extended finite element (XFEM).