Batra [1] used a linear relationship between the second Piola-Kirchhoff stress tensor S and the Green-St. Venant strain tensor E to study finite simple shearing and finite simple extension deformations of an elastic body. In each case he found that the tangent modulus (i.e. the slope of the shear stress vs. the shear strain curve or the slope of the axial stress vs. the axial stretch curve) is ...

A layer-wise third order shear and normal deformable plate/shell theory (TSNDT) incorporating a cohesive zone model (CZM) is used to study the initiation and growth of delamination in straight and curved laminated beams. Upon satisfaction of the delamination criteria at a point on the interface between two layers, displacements there of two abutting points on the interface between the two layer...

A nonlinearly elastic shell is modeled either by the nonlinear threedimensional shell model or by a nonlinear two-dimensional shell model. We show how such two-dimensional shell models can be derived from the minimization problem associated with the nonlinear three-dimensional shell model. For shells made of a Saint Venant-Kirchhoff material, we obtain in particular the nonlinear shell models o...

We study a simple one-dimensional (1-D) toy model for landslides-generated nonlinear water waves. The landslide is modeled as a rigid bump translating down the side of the bottom while the water motion is modeled by the Saint-Venant system of shallow water equations. The resulting system is numerically solved using a well-balanced positivity preserving central-upwind scheme. The obtained numeri...

In this paper a suitable Laplacian preconditioner is proposed for the numerical solution of the nonlinear elasto-plastic torsion problem. The aim is to determine the tangential stress in cross-sections under a given torsion, for which the physical model is based on the Saint Venant model of torsion and the single curve hypothesis for the connection of strain and stress. The proposed iterative s...

This paper deals with the regulation problem of a class of irrigation canals using the Saint-Venant partial differential equations (pde). The Internal Model Boundary Control (IMBC) approach is used and the multireaches case is considered (several reaches in cascade). Perturbation theory of exponential semigroup used for control synthesis is extended here to nonhomogeneous hyperbolic systems, as...