Double poroelasticity derived from the microstructure

We derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient $$\bar{\mathcal {M}}$$ M ¯ is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.

Unequal order T-spline meshes for fracture in poroelastic media

Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different meshes with different orders of interpolation are normally used for the various fields in order to avoid spurious oscillations. When including discontinuities in these meshes, there exist several options for the discretisation. Herein we will discuss two options which use T-splines, one aiming at a minimum number of degrees of freedom around the crack tip, the other trying to maximise this number. Both meshes retain a higher-order continuity along the fracture, but the mesh which maximises the number of degrees of freedom mesh introduces two additional degrees of freedom around the crack tip to allow for a sharper crack. The two discretisations are used to simulate a pressurised fracture inside a poroelastic material and the results are compared to results obtained using a Non-Uniform Rational B-Spline (NURBS) mesh. A comparison between the two discretisations shows the effect of including additional degrees of freedom close to the crack tip. However, both meshes yield similar results further away from the crack tip. It is shown that both T-spline meshes capture a fully closed discontinuity at the fracture tip, whereas the NURBS mesh retains a small opening due to the discontinuity which exists for the cracked as well as the intact elements. A fully closed fracture aperture results in T-splines with a lower discontinuity pressure compared to NURBS, making T-splines more suitable for simulations in which the fracture propagation is limited by the fluid transport within the fracture.

Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

SOUND TRANSMISSION LOSS ACROSS A FINITE CLAMPED DOUBLE-LAMINATED COMPOSITE PLATE WITH POROELASTIC MATERIAL

A theoretical study of sound transmission loss across a clamped double-laminated composite plate filled with poroelastic material is formulated. Biot’s theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method. The analytical model is validated against previous experimental results of a single sound wave under normal incidence. The numerical results suggest that the density of poroelastic material, the type of composite materials and the composite plies arrangement have significant effects on the sound transmission loss of considered structure.

A GL Model on Thermo-Elastic Interaction in a Poroelastic Material Using Finite Element Method

The purpose of this study is to provide a method to investigate the effects of thermal relaxation times in a poroelastic material by using the finite element method. The formulations are applied under the Green and Lindsay model, with four thermal relaxation times. Due to the complex governing equation, the finite element method has been used to solve these problems. All physical quantities are presented as symmetric and asymmetric tensors. The effects of thermal relaxation times and porosity in a poro-thermoelastic medium are studied. Numerical computations for temperatures, displacements and stresses for the liquid and the solid are presented graphically.

SOUND TRANSMISSION LOSS ACROSS A FINITE CLAMPED DOUBLE-LAMINATED COMPOSITE PLATE WITH POROELASTIC MATERIAL

A theoretical study of sound transmission loss across a clamped double-laminated composite plate filled with poroelastic material is formulated. Biot’s theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method. The analytical model is validated against previous experimental results of a single sound wave under normal incidence. The numerical results suggest that the density of poroelastic material, the type of composite materials and the composite plies arrangement have significant effects on the sound transmission loss of considered structure.