Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part I: Formulation and full-field solution
arXiv:1604.06275 · doi:10.1016/j.ijsolstr.2016.01.027
Abstract
An infinite class of nonuniform antiplane shear fields is considered for a linear elastic isotropic space and (non-intersecting) isotoxal star-shaped polygonal voids and rigid inclusions perturbing these fields are solved. Through the use of the complex potential technique together with the generalized binomial and the multinomial theorems, full-field closed-form solutions are obtained in the conformal plane. The particular (and important) cases of star-shaped cracks and rigid-line inclusions (stiffeners) are also derived. Except for special cases (addressed in Part II), the obtained solutions show singularities at the inclusion corners and at the crack and stiffener ends, where the stress blows-up to infinity, and is therefore detrimental to strength. It is for this reason that the closed-form determination of the stress field near a sharp inclusion or void is crucial for the design of ultra-resistant composites.
arXiv comment19 pages, 6 figures, 1 table
References in corpus (4)
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- Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials
- Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part II: Singularities, annihilation and invisibility
Cited by in corpus (3)
- Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction
- Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part II: Singularities, annihilation and invisibility
- Torsion of elastic solids with sparse voids parallel to the twist axis