Related papers: A variational approach for the deformation of a sa…
It is stated in the main in essence new approach to mechanics of the stressed state of the solid body from statistically isotropic material and the homogeneous liquid dynamics. The approach essence is in the detected property of the…
Fluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Variational principle is the main approach to obtain complete and self-consistent field equations in gravitational theories. This method works well in pure field cases such as $f(R)$ and Horndeski gravities. However, debates exist in the…
Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…
The occurrence of heterogeneous perturbations of fluid mass density and solid elastic strain of a porous continuum, as a consequence of its undrained response is a very important topic in theoretical and applied poromechanics. The classical…
Hysteresis in the relation between the capillary pressure and the moisture content in unsaturated porous media, which is due to surface tension at the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation.…
The instant Lagranian coordinator system is used to describe the fluid material motion. By this way, the instant deformation gradient (expressed by spatial velocity gradient) concept is established. Based on this geometrical understanding,…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
The turbulence field is stacked on the laminar flow. In this research, the laminar flow is described as a macro deformation which forms an instant curvature space. On such a curvature space, the turbulence is viewed as a micro deformation.…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
The problem of surface effects at a fluid boundary created by the force field of finite value is investigated. A classical simple fluid with a locally introduced field imitating a permeable solid is considered. The cases of micro- and…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
This paper is concerned with the diffusion of a fluid through a viscoelastic solid undergoing large deformations. Using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
Fluid diffusion in unsaturated porous media manifests strong hysteresis effects due to surface tension on the liquid-gas interface. We describe hysteresis in the pressure-saturation relation by means of the Preisach operator, which makes…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model ``dust'', provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is…