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...

A mode III crack problem in a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ` and `′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived ass...

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...

This paper first considers the approximation of peridynamics by strain-gradient models in the linear, one-dimensional setting. Strain-gradient expansions that approximate the peridynamic dispersion relation using Taylor series are compared to strain-gradient models that approximate the peridynamic elastic energy. The dynamic and energetic expansions differ from each other, and neither captures ...

A method is proposed herein to build beam equations for materials featuring higher-grade elasticity. As it based on the minimization of constitutive equation gap, static admissibility conditions are taken into account so that naturally converges usual resulting from Cauchy elasticity when dimensions large enough. The exemplified, Euler–Bernoulli beams, first-strain gradient and second-strain el...

It is well known that glassy polymer nanocomposites (PNC) exhibit heterogeneous mechanical properties, with a distinct polymer/nanoparticle (NP) interfacial region. The interphase rigidity in particular can significantly influence the overall response of PNCs. Continuum theories typically describe behavior such to depend only on deformation and, thus, they discard strong internal gradients with...