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For a long time, direct and indirect BEM/BIEMs were always unified and seemed equivalent in real implementation for ensuring the solution. Regarding the solution space and the numerical aspects in linear algebra, it is interesting to find that they are not fully equivalent. To demonstrate this finding, antiplane shear problems containing the elliptical rigid inclusion and hole as well as rigid-line inclusion and line crack were given to demonstrate the non-equivalence between the direct and indirect BEM/BIEMs. It is interesting to find that nonunique boundary densities may yield the unique field solution in both analytical derivation and numerical implementation. The mechanism was analytically studied and numerically performed by using the degenerate kernel and the singular value decomposition technique, respectively. Besides, the Fredholm alternative theorem was employed to examine the solvability condition in both the indirect boundary integral equation method and indirect boundary element method. For continuous system and discrete system, we can explain why the boundary density does not match the exact solution but the field solution is always acceptable when setting ξ 0 = 0 in the beginning of the derivation of BIE. Two approaches, direct and indirect BEM/BIEMs, show the non-equivalence of solution in case of degenerate boundary and degenerate scale. [ABSTRACT FROM AUTHOR]

The derivation of the boundary conditions is the most challenging part of the asymptotic techniques underlying low-dimensional models for thin elastic structures. At the moment, these techniques do not take into consideration the effect of the environment, e.g., a Winkler foundation, when tackling boundary conditions, and have to be amended. In this paper as an example we consider an antiplane problem for a thin elastic strip contacting with a relatively compliant Winkler foundation. Refined boundary conditions at an edge loaded by prescribed stresses are established using a properly adjusted Saint-Venant's principle. They appear to be useful for advanced structure modelling including analysis of the static equilibrium under self-equilibrated loading. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive numerical analysis of daughter crack localization in pure antiplane shear. Although antiplane shear fracture is important in various industrial applications, understanding the morphology of the resulting fragmentation remains challenging. The paper develops innovative phase-field models to induce the facets using a small spatial variation in the toughness field and examines the impact of numerical and material parameters on the newly formed daughter cracks' shape and spacing. Through meticulous comparison to the coupled criterion, the paper reveals a compelling connection between the internal length-scale of damage regularization, Irwin's length and the facet crack spacing. Furthermore, the effect of Poisson's ratio on the crack form and spacing is investigated: the results reveal a significant influence and showcase comparable initiation distances between the numerical simulations and experimental measurements in pure antiplane loading. • Phase-field models reveal daughter crack morphology in pure antiplane shear. • Link found between regularization length, Irwin's length, and facet crack spacing. • Poisson's ratio's impact on crack form and spacing identified. • Comparisons highlight similar initiation distances to experimental measurements. [ABSTRACT FROM AUTHOR]

A numerical scheme is proposed for simulating dynamic antiplane fracture at an interface between a layer and a half-plane. The scheme is a spectral boundary integral equation method which relates the shear stress and the displacement discontinuity at the interface in the spectral domain. In previous studies, numerical schemes have been developed for fracture problems in unbounded solids. This is the first work where a spectral boundary integral equation method has been developed for a system one of whose constituents is a finite solid, namely, a layer. The spectral scheme involves performing time convolution of the spectral amplitude of the shear stress at the interface of the layer and half-space. Numerically, conversion between the spectral domain and spatial domain is done by the Fast Fourier Transform. The numerical scheme is validated through comparison with known solutions of model problems. Use of the numerical method is illustrated by simulating 2D antiplane slip rupture propagation wherein the spectral boundary integral equation is coupled with a slip-weakening friction law. We illustrate the role of initial stress distribution on the modes of rupture propagation at the interface, which can be crack-like or pulse-like. The effect of the layer thickness on the critical nucleation size for dynamic rupture propagation is also studied numerically. [ABSTRACT FROM AUTHOR]

Abstract: An interfacial crack in an anisotropic bimaterial wedge under antiplane shear is investigated. An interfacial wedge crack in an isotropic bimaterial with concentrated forces is first solved by using the Mellin transform and the Wiener–Hopf technique. The solution of an interfacial crack in an anisotropic composite wedge is then derived from the isotropic solution based on a linear transformation method. An expression for the stress intensity factor for the interfacial crack is obtained. The asymptotic problem of an interfacial wedge crack is also analyzed. The stress intensity factor is obtained in terms of the stress intensity factor of a wedge without cracks. Numerical calculations of the stress intensity factor are carried out for various wedge types such as symmetric and asymmetric wedges as well as wedges with edge cracks and kinked cracks. [Copyright &y& Elsevier]

Abstract: A crack emanating from the apex of an infinite wedge in an anisotropic material under antiplane shear is investigated. An isotropic wedge crack subjected to concentrated forces is first solved by using the conformal mapping technique. The solution of an anisotropic wedge crack is obtained from that of the transformed isotropic wedge crack based on a linear transformation method. Expressions for the stress intensity factor for the anisotropic wedge crack with both concentrated and distributed loads are derived. The stress intensity factors are numerically calculated for generally orthotropic wedge cracks with various crack and wedge angles as well as anisotropic parameters. [Copyright &y& Elsevier]

Abstract: We consider an anisotropic elastic inclusion of arbitrary shape embedded inside an infinite dissimilar anisotropic elastic medium (matrix) subjected to a uniform antiplane shear loading at infinity. In contrast to the corresponding results from linear isotropic elasticity, we show that for certain anisotropic materials, despite the limitation of perfect bonding between the inclusion and its surrounding matrix, it is possible to design an arbitrarily shaped (not necessarily elliptic) inclusion so that the interior stress distribution is uniform provided the shear stress in the matrix (of dissimilar anisotropic material) is also uniform. Further, in the case when the bonding between the inclusion and the matrix is assumed to be imperfect, we show that for the stress distribution inside the inclusion to be uniform, the inclusion must be elliptical. [Copyright &y& Elsevier]