The nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the nonlocal modified gradient theory of elasticity. The equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced. The size-dependent effects of the dilatation gradient, deviatoric stretch gradient, and symmetric rotation gradient in addition to the nonlocality are beneficially captured in the flexure problem of nano-beams. The well posedness of the proposed nonlocal modified gradient problem is demonstrated via analytical examination of the elastostatic flexure and the wave dispersion phenomenon in nano-beams. The dispersive behavior of flexural waves is verified in comparison with the molecular dynamics simulation. The dominant stiffening effect of the gradient characteristic parameters associated with the nonlocal modified gradient elasticity is confirmed. Both the stiffening and softening responses of nano-structured materials are effectively realized in the framework of the introduced augmented elasticity theory. The conceived nonlocal modified gradient elasticity theory can accordingly provide a practical approach for nanoscopic study of the field quantities.

Contribution of nonlocal integral elasticity to modified strain gradient theory

Fractures enhance secondary porosity and permeability of tight sandstone and in turn promote fluid migration and well recovery. The developmental characteristics and dominant factors of tight sandstone reservoir fractures in the lower Permian Shanxi Formation, southern Qinshui Basin, were systematically studied by combining qualitative observations, quantitative characterizations, logging interpretations, and tectonic analysis. The results show that fractures are extensively developed in the Shanxi Formation tight sandstone. The primary factors controlling these fractures include tectonic position, proximity to faulting, rock brittleness, single sand body thickness, formation anisotropy, and diagenesis. In crest or flank portions of the anticline and the bottom or low regions or well-developed faults, the fracture density is generally greater than 2 per meter. The scale and intensity of faulting both have a significant impact on the fracture development. Near some faults, “crushed zones” or “weak zones” were observed in the cores. These areas have a moderate- to low-angle or near-horizontal dips of less than 15° and widths of less than 50 cm. The rock rupture of the crushed zone typically occurred in a certain direction. It was found that the first fractures to form in a tight sandstone reservoir are related to tensile failure or shear-tensile failure. A negative exponential correlation exists between the linear fracture density and the single sand body thickness. When the single sand body thickness is less than 3 m, the linear fracture density is generally higher than 4 per meter; when the single sand body thickness is greater than 6 m, the fracture density is generally lower than 2 m−1. The influence of fracture density on rock anisotropy is stronger than that of the geostress. Minerals with unstable chemical properties, such as carbonate cements and feldspar, provide favorable conditions for the migration of acidic fluids and the formation of dissolution fractures.

Developmental characteristics and dominant factors of fractures in marine–continental transitional facies tight sandstone reservoirs in heavily deformed areas: a case study

The work is concerned with the wave propagation at the interface of isolated exponentially graded couple stress thermoelastic media under initial stress and gravity. We analyse the influence of initial stress and gravity on reflection and refraction coefficients for both upper and lower couple stress thermoelastic half-spaces. Further, we found there are three waves, viz. quasi-SV and set of two longitudinal waves propagating with different speeds. The phase speeds, equation of motions, reflection and refraction coefficients are calculated in closed form. The impact of gravity and initial stress parameter has also been calculated numerically and shown graphically.

Plane wave propagation in functionally graded isotropic couple stress thermoelastic solid media under initial stress and gravity

The solution of static elastic deformation of a homogeneous, orthotropic elastic uniform half-space with rigid boundary due to a non-uniform slip along a vertical strike-slip fault of infinite length and finite width has been studied. The results obtained here are the generalisation of the results for an isotropic medium having rigid boundary in the sense that medium of the present work is orthotropic with rigid boundary which is more realistic than isotropic and the results for an isotropic case can be derived from our results. The variations of displacement with distance from the fault due to various slip profiles have been studied to examine the effect of anisotropy on the deformation. Numerically it has been found that for parabolic slip profile, the displacement in magnitude for isotropic elastic medium is greater than that for an orthotropic elastic half-space, but, in case of linear slip, the displacements in magnitude for an orthotropic medium is greater than that for the isotropic medium.

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Static elastic deformation in an orthotropic half-space with rigid boundary model due to non-uniform long strike slip fault

Plane wave propagation and fundamental solution in non-local couple stress micropolar thermoelastic solid medium with voids

This work is concerned with the propagation of plane wave in an infinite isotropic nonlocal couple stress thermoelastic solid. Two problems have been evaluated by making incidence of (i) a longitudinal displacement wave and (ii) a set of coupled transverse waves. All these waves are dispersive in nature. Reflection phenomenon of an incident coupled longitudinal wave from stress free boundary surface of a nonlocal thermoelastic solid has also been studied. The dispersion curves of various waves of Magnesium crystal are calculated numerically and shown graphically. The effect of nonlocality has also been observed and shown graphically.

Wave propagation in nonlocal couple stress thermoelastic solid

A study of plane waves and fundamental solution in isotropic non-local couple stress micropolar thermoelastic solid without energy dissipation is undertaken. We observe that there exist four waves,...

Ravinder Kumar Sahrawat

Papers

Plane wave propagation in functionally graded isotropic couple stress thermoelastic solid media under initial stress and gravity

Static elastic deformation in an orthotropic half-space with rigid boundary model due to non-uniform long strike slip fault

Plane wave propagation and fundamental solution in non-local couple stress micropolar thermoelastic solid medium with voids

Wave propagation in nonlocal couple stress thermoelastic solid

Plane wave and fundamental solution in non-local couple stress micropolar thermoelastic solid without energy dissipation