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In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be used as test specimens for measuring the lengths that enter the constitutive equations of gradient elasticity. It is then useful to be able to apply approximate solutions for the extension, shear and flexure of slender bodies. Such approach requires the existence of some form of the Saint-Venant principle. The present work presents a statement of the Saint-Venant principle in the context of linear strain gradient elasticity. A reciprocity theorem analogous to Betti's theorem in classic elasticity is provided first, together with necessary restrictions on the constitutive equations and the body forces. It is shown that the order of magnitude of displacements are in accord with the Sternberg's statement of the Saint-Venant principle. The cases of stretching, shearing and bending of a beam were examined in detail, using two-dimensional finite elements. The numerical examples confirmed the theoretical results.

Background: The duodenum is a common site for diverticulum formation. Most of the duodenal diverticula are asymptomatic, incidental findings. Perforation is a rare but potentially lethal complication of duodenal diverticular disease. Surgery remains the mainstay of treatment for perforated duodenal diverticula. In recent years, a few cases were successfully managed either conservatively or with endoscopy. Case presentation: We present two cases of female patients treated in our department for duodenal diverticulum perforation. The first case was treated surgically with a diverticulectomy. The second case was managed conservatively with bowel rest and intravenous antibiotics. Both patients had an uncomplicated postoperative course and were discharged home. Conclusions: Both surgical and conservative treatments are viable options for a perforated duodenal diverticulum in selected patients. Patients with a contained duodenal diverticular perforation can be managed conservatively at the outset. Possibly, the introduction of a classification system for duodenal diverticulum perforation may help clinicians in making essential therapeutic decisions.