Related papers: A variational approach for the deformation of a sa…
A sponge subjected to an increase of the outside fluid pressure expands its volume but nearly mantains its true density and thus gives way to an increase of the interstitial volume. This behaviour, not yet properly described by solid-fluid…
Second gradient theories have to be used to capture how local micro heterogeneities macroscopically affect the behavior of a continuum. In this paper a configurational space for a solid matrix filled by an unknown amount of fluid is…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
The equation of motions and the conditions on surfaces and edges between fluids and solids in presence of non-constant surface energies, as in the case of surfactants attached to the fluid particles at the interfaces, are revisited under…
Second gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…
Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…
Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example,…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the…
Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has…
The time evolution of the pore size distributions and mechanical properties of amorphous solids at constant pressure is studied using molecular dynamics simulations. The porous glasses were initially prepared at constant volume conditions…
We study the existence and infinite-speed propagation of solutions to models arising in porous media, when the mobility is highly degenerate (inverse power law). The approach is based on maximum principles for the fractional Laplacian, and…
Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…
Hysteresis in the pressure-saturation relation in unsaturated porous media, which is due to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. Solutions to such degenerate…
A covariant formulation of the virtual power principle based on Lie derivatives is proposed. The Lie covariant approach does not require an inner product and the Cauchy deformation tensor to start, but, at first order in a Galilean…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a 'solid' and a 'broken' component. The 'solid' part is the one that is capable of transferring stress, whereas the…
The role of porous structure and glass density in response to compressive deformation of amorphous materials is investigated via molecular dynamics simulations. The disordered, porous structures were prepared by quenching a high-temperature…
This study is an introduction to the theory of three-dimensional consolidation. The point of departure in the description are the basic equations of elasticity (i.e. constitutive law, equations of equilibrium in terms of stresses, and the…