This article presents a method for measuring three-dimensional mechanical displacement and strain fields using stimulated echo MRI. Additional gradient pulses encode internal displacements in response to an externally applied deformation. By limiting the mechanical transition to the stimulated echo mixing time, a more accurate static displacement measurement is obtained. A three-dimensional ela...

The multi-mode propagation and diffusion properties are crucial informations when studying complex waveguides. In this paper, firstly, the three-dimensional modeling of micro-sized structures is introduced by using second strain gradient theory. constitutive relation deduced while six quintic Hermite polynomial shape functions employed for displacement field. weak formulations including element...

A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with firstorder strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of t...

The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first...