An Enriched Biphasic Model for Solute Driven Degradation

Transport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

饱和多孔介质中骨架的应变局部化萌生条件

应用饱和多孔介质控制方程和Liapunov稳定理论,导出了固相应力和有效应力描述的多孔介质骨架应变局部化的萌生条件．不同应力形式表达的多孔介质基体的控制方程,相应的应变局部化萌生条件的表达形式也不尽相同,其原因源于骨架本构中固液两相之间相互作用的不同描述．应用得出的Terzaghi有效应力描述的应变局部化萌生条件,可以理论解释多孔介质中固、液两相不同相对运动出现的破坏方式,如管涌、滑坡和泥石流．应用简单算例说明了应变局部化条件的具体实施方法．     

Phase-Field Modeling of Hydraulic Fracture

Hydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot-type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille-type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp-crack discontinuity, the proposed regularized approach has the main advantage of a straight-forward modeling of complex crack patterns including branching. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Two‐Phasic Flow Problems in Elasto‐Plastic Porous Materials

In the present contribution, the formulation of the governing equations of coupled flow and deformation processes in porous materials is based on the well‐founded Theory of Porous Media (TPM) [2, 3]. Embedded in this concept, the model under consideration represents a triphasic medium of a cohesive‐frictional elasto‐plastic solid skeleton and a binary pore‐fluid, which is composed of a materially incompressible wetting phase (here water) and a materially compressible non‐wetting phase (here air). The unsaturated domain (saturation in terms of liquid saturation) of the porous medium is included in the model by the application of a suitable capillary‐pressure‐saturation relation, which takes into account the interaction of the solid skeleton and the two pore‐fluids. Furthermore, the interaction is described by Darcy's filter law including a relative permeability, which depends on the deformation of the pore space and the degree of saturation.     

A ternary phase bi-scale FE-model for diffusion-driven dendritic alloy solidification processes

It is of high interest to describe alloy solidification processes with numerical simulations. In order to predict the material behavior as precisely as possible, a ternary phase, bi-scale numerical model will be presented. This paper is based on a coupled thermo-mechanical, two-phase, two-scale finite element model developed by Moj et al. [2], where the theory of porous media (TPM) [1] has been used. Finite plasticity extended by secondary power-law creep is utilized to describe the solid phase and linear visco-elasticity with Darcy's law of permeability for the liquid phase, respectively. Here, the microscopic, temperature-driven phase transition approach is replaced by the diffusion-driven 0D model according to Wang and Beckermann [3]. The decisive material properties during solidification are captured by phenomenological formulations for dendritic growth and solute diffusion processes. A columnar as well as an equiaxial solidification example will be shown to demonstrate the principal performance of the presented model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase transition processes of pore fluids in porous materials

Taking a closer look on, e. g., storage processes of greenhouse gases in deep geological aquifers or pressure decreases in dilatant shear bands, the observation can be made that pressure and temperature changes in porous materials can induce phase transition processes of the respective pore fluids. For a numerical simulation of this behaviour, a continuum mechanical model based on a multiphasic formulation embedded in the well-founded framework of the Theory of Porous Media (TPM) is presented in this contribution. The single phases are an elasto-viscoplastic solid skeleton, a materially compressible pore gas consisting of the components air and gaseous pore water (water vapour) and a materially incompressible pore liquid, i. e., liquid pore water. The numerical treatment is based on the weak formulations of the governing equations, whereas the primary variables are the temperature of the mixture, the displacement of the solid skeleton and the effective pressures of the pore fluids. An initial boundary-value problem is discussed in detail, where the resulting system of strongly coupled differential-algebraic equations is solved by the FE tool PANDAS. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surface wave propagation in a liquid-saturated porous solid layer lying over a heterogeneous elastic solid half-space

Dispersion equation is derived for the propagation of Rayleigh type surface waves in a liquid saturated porous solid layer lying over an inhomogeneous elastic solid half-space. Effect of heterogeneity on the phase velocity is studied by taking different numerical values of heterogeneity factor for particular models. Dispersion curves have been drawn showing the effect of heterogeneity on the phase velocity.     

Phase Field Approximation of Dynamic Brittle Fracture

The numerical assessment of fracture has gained importance in fields like the safety analysis of technical structures or the hydraulic fracturing process. The modelling technique discussed in this work is the phase field method which introduces an additional scalar field. The smooth phase field distinguishes broken from undamaged material and thus describes cracks in a continuum. The model consists of two coupled partial differential equations - the equation of motion including the constitutive behaviour of the material and a phase field evolution equation. The crack growth follows implicitly from the solution of this system of PDEs. The numerical solution with finite elements can be accelerated with an algorithm that performs computationally extensive tasks on a graphic processing unit (GPU). A numerical example illustrates the capability of the model to reproduce realistic features of dynamic brittle fracture. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of hydraulic fracture of porous materials using the phase-field modeling approach

In this contribution, the numerical simulation of hydraulic fracture of fluid-saturated porous materials is carried out on a continuum-mechanical scale using the theory of porous media (TPM), extended by a phase-field modeling (PFM) approach. Following this, behaviors such as crack nucleation and propagation, solid matrix deformation and interstitial-fluid flow change from Darcy to Stokes-like flow in the cracked region can be realized. Moreover, permanent changes of the local physics due to occurrence of the crack, such as of the volume fractions and the permeability, are taken into consideration. The mathematical modeling of this problem yields a strongly coupled system of differential algebraic equations (DAE). Thus, special descretization schemes for a stable and efficient solution are needed. To reveal the ability of the proposed model to simulate the important features of hydraulic cracking, a two-dimensional example using the finite element method is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

考虑流固耦合效应的重力坝水力劈裂模拟

裂缝的高压水力劈裂是混凝土高坝安全评估的重要部分,研究其过程中的流固耦合作用是准确预测在各种情况下裂纹扩展路径和危险程度的关键.该文利用扩展有限元法在模拟裂纹扩展方面的优势,对大坝的裂纹进行水力劈裂模拟研究.裂纹中的水压分布模型采用Brühwiler和Saouma水力劈裂试验的成果,体现了水压和裂纹宽度的耦合关系,给出了扩展有限元在裂纹面上施加水压力荷载的实施方法,对一典型重力坝裂纹的水力劈裂进行了数值模拟分析.研究结果表明:采用扩展有限元法模拟水力劈裂,克服了常规有限元法存在的缺点,裂纹扩展时不用重新划分网格,裂纹的实时宽度可以由加强节点的附加自由度得到,裂纹面上水压的施加也变得简单易行.当考虑裂纹内的流固耦合效应时,裂纹的扩展路径相比不考虑耦合效应时的扩展路径(均布全水头水压),扩展角变大,扩展距离变短.