Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity

Abstract

International audienceThis letter presents a three-dimensional model to describe the complex behavior of nonlinear mesoscopic elastic materials such as rocks and concrete. Assuming isotropy and geometric contraction of principal stress axes under dynamic loading, the expression of elastic wave velocity is derived, based on the second-order elastic constants (λ,μ), third-order elastic constants (l, m, n), and a parameter α of nonclassical nonlinear elasticity resulting from conditioning. We demonstrate that both softening and recovering of the elastic properties under dynamic loading is an isotropic effect related to the strain tensor. The measurement of the conditioning is achieved using three polarized waves. The model allows the evaluation of the third-order elastic constants uncoupled from conditioning and viscoelastic effects. The values obtained are similar to those reported in the literature using quasi-static loading

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

“…largest strain amplitude A L ). This effect from the Poisson's ratio was already observed by Lott et al [40]. During the slow relaxation (e.g., at time t 2 ), the induced anisotropy remains.…”

“…More recently, Lott et al [40,41] have proposed an extension of Hughes and Kelly's formulation [29] by taking into account the softening of geomaterials under dynamic vibration. This new formulation starts from a volume of material that is small enough to fit within the assumption of continuum mechanics but large enough to contain a relatively large number of defects.…”

“…Likewise, the HF pulses used to probe the elastic state of the material is no longer restricted to (compressional) P waves but extended to (shear) S waves. The experimental findings are compared to theoretical predictions from the approach proposed by Lott et al [40].…”

Damage detection and localization from linear and nonlinear global vibration features in concrete slabs subjected to localized thermal damage

“…Recently, it has been demonstrated that the linear frequency–strain amplitude dependency observed in hysteretic materials could be modeled in three-dimensional (3D) structures by a single parameter (again, the hysteretic parameter α which relates to the λ n parameters obtained herein). 45 Such a model applies to uniform micro-damaged media (say, isotropically oriented defects), for example, concrete, thermally damaged concrete, and certain rock types. 46 An important finding of these studies 45,46 is that the different slopes λ n at the undamaged state become alike if the precise strain–acceleration conversion for every mode is considered.…”

“…45 Such a model applies to uniform micro-damaged media (say, isotropically oriented defects), for example, concrete, thermally damaged concrete, and certain rock types. 46 An important finding of these studies 45,46 is that the different slopes l n at the undamaged state become alike if the precise strain-acceleration conversion for every mode is considered. Herein, we use the relative variations of l n instead of the values of a n to overcome an acceleration to strain the conversion of every mode.…”