The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform a...

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elast...

The aim of this paper is to extend, to the linear elasticity system, the asymptotic analysis by compensated compactness previously developed by the authors for the linear diffusion equation. For simplicity, we restrict ourselves to stratified media. In the case of sole homogenization we recover the classical result of W.H. Mc Connel, deriving explicitly the effective elasticity tensor for strat...

Ultrasound elastography is the method of obtaining relative stiffness information of biological tissue, which plays an important role in early diagnosis. Generally, a gradient-based strain imaging algorithm assumes that motion only occurs in an axial direction. However, because tissue has different relative stiffness, the scatter presents lateral motion under high freehand compression. Therefor...