A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples. Part 2

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.

An Improved Tunnel-Track Model in Saturated Poroelastic Soils to a Moving Point Load

To predict the mechanical response of a circular cavity/tunnel buried in saturated poroelastic soils to a moving point load, a semianalytical model is provided in this work. The soils are governed by Biot’s theory that describes the wave propagations for saturated poroelastic materials. The displacement and stress vectors for the solid skeleton and pore-water fluid are represented by scalar and vectorial potentials. The governing equations for the tunnel and surrounding soils are solved in the frequency domain with the aid of separation of variables and Fourier transformations. To check the feasibility of the present analytical model, the solution is compared with other available results calculated for the ring load case. The good agreement shows the correctness of the present model. Numerical results suggest that the mechanical response from a moving point load in a tunnel for two-phase poroelastic materials is quite different from that in single-phase elastic materials. The critical velocity of the tunnel-soil system is around the shear wave speed of soils while the second one introduced into the track-tunnel-soil system with very high value is around the critical velocity of the track structure itself.

Simulations of poroelastic materials in a complex acoustic system using frequency-dependent parameters in the mid-frequency range

Efficiency requirements prompt manufacturers to develop ever lighter acoustic packages in vehicles. Poroelastic materials are essential to achieve the desired interior noise level targets and thus the simulation of their effects is of utmost importance in NVH analyses. However, it is challenging to achieve good validation between finite element method (FEM) based simulation results and measurements in the mid-frequency range (400-1000 Hz). One possible reason could be the lack of using frequency-dependent Biot-paremeters describing the poroelastic materials (PEM) characteristics of trims. The present research aims to employ frequency-dependent Biot-parameters for the PEM materials to investigate the acoustic response of a scaled car-like steel structure composed of flat plates and U-section stiffeners enclosing an air cavity. Porous acoustic material is applied to the walls of the cavity. The focus of the study is to understand the effect of applying frequency-dependent Young's modulus and damping values for the PEM parameters in the 100-1000 Hz range. Simulation results obtained from ESI VPS FEM solver are compared with measurements, with particular focus on the interior sound pressure levels. The simulation methodology, including discretization techniques, structural damping and fluid damping applications are described in detail.

NUMERICAL WAVE FIELDS QUASISTATIC MODELING IN FLUID-FILLED POROELASTIC MEDIA

This paper presents a numerical algorithm to simulate low-frequency loading of fluid-filled poroelastic materials and estimate the effective frequency-dependent strain-stress relations for such media. The algorithm solves Biot equation in quasi-static state in the frequency space. As a result a system of linear algebraic equations have to be solved for each temporal frequency. We use the direct solver, based on the $LU$ decomposition to resolve the SLAE. According to the presented numerical examples the suggested algorithm allows reconstructing the stiffness tensor within a wide Frequency range.

Analytical Investigation of Transient Wave Propagation in One-Dimensional Unsaturated Poroelastic Materials

As a dynamic response, the wave propagation phenomenon usually varies with different media. In this study, the dynamic response of unsaturated poroelastic materials to an impulse load has been analytically investigated. The governing equations, in the Laplace domain, of the unsaturated poroelastic soil in terms of the variables us (solid displacement), pf (pore fluid pressure), and pa (pore air pressure) will be derived. These equations will be simplified in a one-dimensional form. The solutions that include the dynamic response to the vertical displacement of solid particles and to the variations of fluid and air pressures will be provided which are applicable for an arbitrary loading form. The solutions were validated with the results for saturated soil presented in the literature. The effect of material parameters on dynamic response was analysed through a series of parameter studies. It was found that increasing the porosity or fluid saturation effectively increases the amplitude of fluid and air pressures as well as the wave velocity. Although increasing the fluid saturation leads to solid displacement gradually decreases gradually, it results in increasing the amplitude of fluid and air pressure. The fluid saturation increasing above 0.9 results in wave travels faster significantly. The variation of fluid intrinsic permeability has little influence on the soil dynamic response until it reaches a high level. The findings of this study can help for better understanding of one-dimensional wave propagation in unsaturated soil.