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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 mixture theories, is studied here by using the Principle of Virtual Power with the most simple dependence of the free energy as a function of the partial apparent densities of the solid and the fluid. The model is capable of accounting for the above mentioned dilatational behaviour, but in order to isolate its essential features more clearly we compromise on the other aspects of deformation. Comment: 20 pages

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... In fact, permeability measurements Cosenza et al. 1999; Stormont 1997 in the immediate vicinity of the cavern walls disclose a dilatation of the pores within a relatively small boundary layer of the polycrystalline salt. The origin of this disturbed rock zone is still somewhat debatable; however, a microstructured theory of solid–fluid mixtures was recently proposed Sciarra 2002; Sciarra et al. 2001 Sciarra et al. , 2003 dell'Isola et al. 2000 that offered a means of explaining, in the framework of an elastic model, the occurrence of the apparently counterintuitive expansion of the pore-space by the increase in internal cavern pressure. In our initial publication on this sub- ject Sciarra et al. 2001, second-gradient effects for the deformed porous salt matrix, which was filled with an ideal fluid, were claimed to be essential. ...

... The origin of this disturbed rock zone is still somewhat debatable; however, a microstructured theory of solid–fluid mixtures was recently proposed Sciarra 2002; Sciarra et al. 2001 Sciarra et al. , 2003 dell'Isola et al. 2000 that offered a means of explaining, in the framework of an elastic model, the occurrence of the apparently counterintuitive expansion of the pore-space by the increase in internal cavern pressure. In our initial publication on this sub- ject Sciarra et al. 2001, second-gradient effects for the deformed porous salt matrix, which was filled with an ideal fluid, were claimed to be essential. Our present understanding tells us that second-gradient effects yield dominant qualitative behavior of the dilatancy deformation of the salt-fluid mixture only for specific simple load configurations, while in general it affects the deformation field only quantitatively, for instance by altering the dimension of dilatancy boundary layers. ...

... These results imply almost by default that, for p 01 = p 02 , s = 0 for all r a , . This is indeed the result that motivated us to improve the first-gradient model by a second-gradient model in our earlier paper Sciarra et al. 2001 to recover dilatancy effects also in the wall-near boundary layer when p 01 = p 02 . The monotonic behavior exhibited by the graphs of Fig. 2prevails for all prestress conditions p 01 and p 02 . ...

Afluid filled cylindrical cavern of circular cross section in a homogeneous infinite salt formation under a hydrostatic stress is set under internal pressure that differs from the confining pressure. The fluid in the cavern and in the mixture is treated as ideal and the solid as elastic. The initial state of stress is a consequence of the outside pressure and the cavern pressure. Perturbing the cavern pressure induces small changes in the solid and fluid densities.We compute these fields as functions of the radial distance from the cavern centre and show that depending on the relative stress levels the (salt) formation experiences either a dilatation or a compaction that is concentrated in a boundary layer near the cavern wall.

... Another application is related to the modeling of residual stresses in metamorphic rocks [14][15][16]. Further investigations could be focused on the computation of effective properties within the framework of the couple stress theory [34] and the homogenization of fluid-structure interaction [5,29,31]. ...

The article considers an approach for multiscale geomechanical modeling under finite strains. A mathematical model, methods and algorithms for the multiscale numerical estimation of the effective elastic and thermal properties of the preloaded heterogeneous porous materials under finite strains are presented. The developed algorithms were applied to the problem of the estimation of the effective properties of core samples. The digital models obtained from computed tomography scan data of core samples are used. An initial voxel representation of the digital core sample is transformed into an unstructured mesh, thus reducing the number of unknowns by orders of magnitude and requiring computational resources accordingly. The mesh convergence tests demonstrated the efficiency and correctness of the developed algorithms. The calculations of the effective elastic and thermal properties of preloaded porous materials are performed with CAE Fidesys using finite element method. The numerical results demonstrate the significant impact of pre-loading by internal pressure on the effective properties of porous materials.

... This representation of the coupling term is very close to the common expression used in porous materials (see e.g. [7, 18] and more recently [74, 32, 64]), even if in this case, we use II devE instead of the trace of the small strain tensor; this choice is dictated by our physical interpretation of ϕ; the exchange of energy between the bulk and the microstructure is related to a deformation at macro level that induces a sliding on micro-cracks. In Eq. (12) the microstructure elastic force is assumed to be nonlinear. ...

In this paper, a micromorphic, non-linear 3D model aiming to describe internal friction phenomena in concrete is considered. A reduced two-degrees-of-freedom model is employed for the sake of easy handling to explain dissipative loops which have been observed in some concrete specimens tested under cyclic uniaxial compression loading with different frequencies and having various amplitudes but never inducing large strains. As (linear or non-linear) viscoelastic models do not seem suitable to describe neither qualitatively nor quantitatively the measured dissipation loops, we propose to introduce a multi-scale micromechanism of Coulomb-type internal dissipation associated to the relative motion of the faces of the microcracks present in the material and to the asperities inside the microcracks. We finally present numerical simulations showing that the proposed model is suitable to describe some of the available experimental evidence.

... Indeed, this results, rather obvious, is obtained in exactly the same way in [15], Remark 3, pag. 48 and systematically exploited in the applications of second gradient theory presented in [19], [48] . Some interesting consideration about this point are already available in [51] togheter with some consideration about third gradient ‡uids. ...

The investigated work analytically addresses the diffraction of horizontally polarised shear wave by a rigid strip in a pre-stressed transversely isotropic poroelastic infinite medium. The far field solution for the diffracted displacement of shear wave has been established in closed form. The diffraction patterns for displacement in the said medium have been computed numerically and its dependence on wave number has been depicted graphically. Further, the study also delineates the pronounced influence of various affecting parameters viz. anisotropy parameter, porosity parameter, speed of the shear wave, and incident angle on the diffracted displacement of the propagating wave. The effects of horizontal as well as vertical compressive and tensile pre-stresses on diffracted displacement of propagating wave have been examined meticulously in a comparative manner. It can be remarkably quoted that porosity prevailing in the medium disfavors the diffracted displacement of the propagating wave. In addition, some special cases have been deduced from the determined expression of the diffracted displacement of shear wave at a large distance from the strip.

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
gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour
of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and
related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the clas-
sical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the
surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently
assuming that the strain work rate functional depends on the porosity and strain gradients.
According to classical thermodynamics suitable restrictions for stresses and second gradient internal actions (hyper-
stresses) are recovered, so as to determine a suitable extended form of the constitutive relation and Darcy’s law.
Finally a numerical application of the envisaged model to one-dimensional consolidation is developed; the obtained
results generalize those by Terzaghi; in particular interesting phenomena occurring close to the consolidation external sur-
face and the impermeable wall can be described, which were not accounted for previously.

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

The development of basic relations in the classical era: the stress concept, the elasticity law, the fundamental laws of Delesse, Fick, and Darcy, the foundation of the mixture theory by Maxwell and Stefan, as well as the foundation of thermodynamics, all these had provided enough background material in order to treat empty or fluid-saturated porous solids. Indeed, in this century, the theory of porous media has been at last firmly established based on the achievements of the nineteenth century.

A mixture theory attributing distinct velocity fields to the separate
constituents is adopted to describe the deformations and motions of a
fluid-saturated porous solid. Constitutive laws for the partial stresses
are related to the response of the respective constituents as single
continuums in terms of effective stress and effective deformation. A
simple multiplicative decomposition of the deformation gradient tensor
with emphasis on finite deformation is introduced; this decomposition
allows a definition of effective dilatation by appropriate scaling while
leaving the isochoric (shear measure) part unchanged. The interrelation
between the constitutive laws for the different constituents arises in
the scaling functions. This description is theoretically possible for
mixtures of any simple materials, but the concepts have most appeal when
one constituent is a freely diffusing fluid. The cases of
water-saturated elastic and elastic-plastic solids are illustrated, and
the uniaxial strain response is examined. The extent to which a single
interaction scaling function can be determined by isotropic pressure
data is shown, and in illustration the scheme is applied to data for a
saturated tuff.

This work is concerned with the formulation of a constitutive model for a saturated or unsaturated, single-temperature mixture of n (≥2) heat-conducting, isotropic viscous materials, the first m≤n of which possess a variable true mass density. To do this, we extend the Müller-Liu approach to the formulation and exploitation of the mixture entropy inequality. This approach yields, among other things, a generalized Gibbs’ relation for such a mixture, as well as integrability conditions for the mixture entropy, and “extra” entropy flux, densities. Reduction of these general results to results comparable to those obtained in the standard approach necessitates two further constitutive assumptions: (1) the constraint field (“Lagrange multiplier”) associated with the mixture reduced energy balance in the entropy inequality is equal to the mixture absolute coldness, and (2) that associated with the constituent momentum balance in the entropy inequality is equal to the negative of the mixture absolute coldness times are corresponding diffusion velocity. On this bases, for example, the inner parts of the mixture specific internal and Helmholtz free energies, as well as the mixture specific entropy, depend only on the mixture absolute temperature, the constituent true mass densities of the m “compressible” constituents, the volume densities of the first r constituents (with r=n in the unsaturated, and r=n-1 in the saturated, case), and the constituent left Cauchy-Green deformation tensors. In the context of thermodynamic equilibrium, the entropy inequality yields, among other things, the interesting result that the constituent equilibrium thermodynamic pressure depends in a saturated mixture directly on the mixture saturation constraint field, but not on that associated with the evolution relations for the constituent (infinitesimal) volume fractions. As such, the so-called “closure problem” in volume-fraction-based mixture theory does not arise in the current formulation.

Fundamental conceptionsAssumptions involved in the theories of consolidationDifferential equation of the process of consolidation of horizontal beds of ideal clayThermodynamic analogue to the process of consolidationExcess hydrostatic pressures during consolidationSettlement due to consolidationApproximate methods of solving consolidation problemsConsolidation during and after gradual load applicationEffect of gas content of the clay on the rate of consolidationTwo- and three-dimensional processes of consolidation

This work is concerned with an extension of classical mixture theory to the case in which the mixture contains an evolving non-material surface on which the constituents may interact, as well as be created and/or annihilated. The formulation of constituent and mixture jump balance relations on/across such a non-material surface proceed by analogy with the standard volume or bulk constituent and mixture balance relations. On this basis, we derive various forms of the constituent mass, momentum, energy and entropy balances assuming (1), that the constituent in question is present on both sides of the moving, non-material surface, and (2), that it is created or annihilated on this surface, as would be the case in a phase transition. In particular, we apply the latter model to the transition between cold and temperate ice found in polythermal ice masses, obtaining in the process the conditions under which melting or freezing takes place at this boundary. On a more general level, one of the most interesting aspects of this formulation is that it gives rise to certain combinations of the limits of constituent and mixture volume fields on the moving mixture interface which can be interpreted as the corresponding surface form of these fields, leading to the possibility of exploiting the surface entropy inequality to obtain restrictions on surface constitutive relations.