1,720,967 research outputs found
Integral representations at the boundary for Stokes flow and related symmetric Galerkin formulation
No full textA SYMMETRIC GALERKIN boundary element formulation is given for the first time for two-dimensional, steady and incompressible flow. The formulation requires the derivation of certain integral representations (whose importance extends beyond the present application) for velocity gradient and pressure at the flow boundary; these turn out to be coupled at angular points of the contour profile
A boundary element technique for incremental, non-linear elasticity. Part II: Bifurcation and shear bands
No full textIncremental elastic deformations superimposed upon a given homogeneous strain are analyzed employing the boundary element technique developed in Part I of this study. As a consequence of the fact that the formulation fully embodies non-linear effects, the proposed approach yields bifurcation loads and associated deformation modes. In particular, bifurcations of elastic structures are investigated, including cracked bodies and multilayers. As special cases of instability not involving length scales, surface bifurcations and shear bands are analyzed and they are both found to occur within the elliptic range, as induced by perturbations
Interactions between multiple rigid lamellae in a ductile metal matrix: Shear band magnification and attenuation in localization patterns
No full textA ductile matrix material containing an arbitrary distribution of parallel and stiff lamellar ('rigid-line') inclusions is considered, subject to a prestress state provided by a simple shear aligned parallel to the inclusion lines. Because the lamellae have negligible thickness, the simple shear prestress state remains uniform and its amount can be high enough to drive the matrix material on the verge of ellipticity loss. Close to this critical stage, a uniform remote Mode I perturbation realizes shear band formation, growth, interaction, thickening or thinning. This two-dimensional problem is solved through the derivation of specific boundary integral equations, holding for a nonlinear elastic matrix material uniformly prestressed; the related numerical treatment is specifically tailored to capture the stress singularity present at the inclusion tips. Results show how complex localized deformation patterns form, so explaining features related to the failure mechanisms of ductile materials reinforced with stiff and thin inclusions. In particular, the influence of the inclusion distribution on the shear bands pattern is disclosed. Conditions for the magnification (the attenuation) of the localized deformations are revealed, fostering the progress (the setback) of the failure process
A boundary element technique for incremental, non-linear elasticity. Part I: Formulation
No full textIncremental elastic deformations superimposed upon a given homogeneous strain are analyzed with a boundary element technique. This is based on a recently-developed Green’s function for non-linear incremental elastic deformations. Plane strain perturbations are considered of a broad class of incompressible material behaviours (including hyper-, hypoelastic and Navier–Stokes constitutive equations) within the elliptic range. Numerical treatment of the problem is detailed. A possibility of employing the method in the fully non-linear range is outlined, which yields a boundary element approach where the use of domain integrals is avoided, at least in a conventional sense. The methods for bifurcation and shear band analyses will be reported in Part II
- …
