Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.     

一阶速度-应力Biot双相各向同性介质弹性波

提出一种等价的一阶双曲型速度一应力Biot双相各向同性介质弹性波波动方程,以实现双相介质混合波场中纯快慢纵波和纯横波波场分离的问题.应用散度和旋度理论证明双相介质等价方程波场分离的可行性,采用高阶交错网格有限差分法构建高精度正演算子,推导其PML吸收边界条件和稳定性条件,并对均匀双相介质和层状非均匀双相介质模型进行数值...     

A note on anisotropic,inhomogeneous, poro‐elastic media

A modification of the material law associated with the well‐known Biot system as suggested by Murad and Cushman (Int. J. Eng. Sci. 1996; 34(3):313–338) and first investigated by Showalter (J. Math. Anal. Appl. 2000; 251(1):310–340) is reconsidered, generalized and analysed in the light of a new approach to a comprehensive class of evolutionary problems. The framework allows a uniform approach to problems involving general anisotropic, inhomogeneous, non‐smooth media thus covering, for example, transmission problems in layered materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Drained and Undrained Poroelastic Properties of Healthy and Pathological Bone: A Poro-Micromechanical Investigation

Poro-micromechanics allows for the quantification of poroelastic properties such as the Biot and Skempton coefficients, once a continuum micromechanics model for the material under consideration has been developed and validated. Employing such a model for the transversely isotropic elasticity of cortical and trabecular bone, we determine the tensors of Biot and Skempton coefficients as functions of the volume fractions of mineral, collagen, and the micropore space (Haversian and Volkmann canals, and the inter-trabecular space). Increase of microporosity, as experienced in osteoporosis, as well as decrease of mineral content, as experienced in osteomalacia, lead to an increase of Biot and Skempton coefficients, i. e. to magnification of the mechanical role of the marrow filling the micropore space. For quantification of the marrow pressure rise upon downfall, undrained conditions are appropriate, as can be shown by model predictions of non-destructive impact experiments.     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

Discontinuous Galerkin method for the coupled Stokes‐Biot model

In this paper, a semi‐discrete scheme and a fully discrete scheme of the Stokes‐Biot model are proposed, and we analyze the semi‐discrete scheme in detail. First of all, we prove the existence and uniqueness of the semi‐discrete scheme, and a‐priori error estimates are derived. Then, we present the same conclusions for the fully discrete scheme. Finally, under both matching and non‐matching meshes some numerical tests are given to validate the analysis of convergence, which well support the theoretical results.     

Development of boundary element method to dynamic problems for porous media

Biot's consolidation theory is extended to a general class of viscoelastic bodies defined by Riemann-Stieltjes integral convolutions. From a new reciprocity theorem, proved for the governing equations including the inertia terms, the basic integral representations of the displacement fields and pore pressure are obtained. It is shown that, in the absence of internal inputs, a formulation of the dynamic problem in terms of the boundary unknown fields only is possible.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

A fully coupled 3-D mixed finite element model of Biot consolidation

The numerical solution to the Biot equations of 3-D consolidation is still a challenging task because of the ill-conditioning of the resulting algebraic system and the instabilities that may affect the pore pressure solution. Recently new approaches have been advanced based on mixed formulations. In the present paper a fully coupled 3-D mixed finite element model is developed with the aim at alleviating the pore pressure numerical oscillations at the interface between materials with different permeabilities. A solution algorithm is implemented that takes advantage of the block structure of the discretized problem. The proposed model is verified against well-known analytical solutions and successfully experimented with in realistic applications of soil consolidation.