Modeling Large-deformation-induced Microflow in Soft Biological Tissues

The homogenization approach to multiscale modeling of soft biological tissues is presented. The homogenized model describes the relationship between the macroscopic hereditary creep behavior and the microflow in a fluid-saturated dual-porous medium at the microscopic level. The micromodel is based on Biot’s system for quasistatic deformation processes, modified for the updated Lagrangian formulation to account for coupling the fluid diffusion through a porous solid undergoing large deformation. Its microstructure is constituted by fluid-filled inclusions embedded in the porous matrix. The tangential stiffness coefficients and the retardation stress for the macromodel are derived for a time-stepping algorithm. Numerical examples are discussed, showing the strong potential of the model for simulations of deformation-driven physiological processes at the microscopic scale.     

On the Modeling of Extension-Torsion Experimental Data for Transversely Isotropic Biological Soft Tissues

For the problem of torsion superimposed on extension of incompressible nonlinearly elastic transversely isotropic circular cylinders, a simple asymptotic analysis is carried out on using a small parameter that reflects the moderate twisting of slender cylinders, which corresponds to a typical testing regime for biological soft tissue. The analysis is carried out for a subclass of strain-energy densities that reflect transversely isotropic material response. On using a four-parameter polynomial expression for the strain-energy density in terms of certain classical invariants, this analysis is shown to be in excellent agreement with experimental data obtained by other authors for rabbit papillary muscles. An explicit condition on the strain-energy density is obtained that determines whether the stretched cylinder tends to elongate or shorten on twisting. For the special case of pure torsion where no extension is allowed, this condition determines whether the classical or reverse Poynting effect occurs. For the rabbit papillary muscles, the theoretical results predict and the experimental results confirm that a reverse Poynting-type effect occurs where the stretched rabbit muscle tends to shorten on twisting.     

Peculiarities of the Structure and Mechanical Properties of Biological Tissues*

Five basic principles that determine the structure and mechanical behavior of almost any biological tissue have been formulated. They are the principle of hierarchy, principle of helicality, principle of feedback, principle of universality, and principle of an optimum. It is shown that there are also two types of factors – biological and mechanical – that must be taken into account in determining the mechanical properties of biological tissue. As an example of complexity of the mechanical behavior of a biological tissue the data on compact bone tissue are presented.     

Transport of Multi-Electrolytes in Charged Hydrated Biological Soft Tissues

A mechano-electrochemical theory for charged hydrated soft tissues with multi-electrolytes was developed based on the continuum mixture theory. The momentum equations for water and ions were derived in terms of a mechanochemical force (gradient of water chemical potential), electrochemical forces (gradient of Nernst potentials) and an electrical force (gradient of electrical potential). The theory was shown to be consistent with all existing specialized theories. Using this theory, some mechano-electrokinetic properties of charged isotropic tissues were studied. The well-known Hodgkin–Huxley equation for resting cell membrane potential was derived and the phenomenon of electro-osmotic flow in charged hydrated soft tissues was investigated. Analyses show that the tissue fixed charge density plays an important role in controlling the transport of water and ions in charged hydrated soft tissues.     

Multi-scale Structural Modeling of Soft Tissues Mechanics and Mechanobiology

Soft tissues account for a major fraction of the body volume and mass. They are present in all non-skeletal organs, being responsible for protecting the body, maintaining internal homeostasis, and allowing for mobility. Their function in different organs is highly diverse, as are their properties which are optimally suited for their specific tasks. From a mechanical perspective, specificity of structure and properties is acquired via evolutionary adaptation of the tissue composition and multi-scale structure. In modeling tissue mechanics and mechano-biology, it is thus natural to seek the structural determinants of tissues and their evolution (the “structural approach”). Earlier models were exclusively phenomenological, based either on the general principles of non-linear continuum mechanics or alternatively, on empirical mathematical expressions that fit specific response patterns. In the late 1970’s, structural models were introduced to tissue mechanics (Lanir in J. Biomechanics 12(6): 423–436, 1979; Lanir in J. Biomechanics 16(1): 1–12, 1983). Ever since, a gradually increasing number of structural models have been developed for different types of tissues, and today, it is the method of choice (Cowin and Humphrey in J. Elasticity 61: ix–xii, 2000). The structural approach was recently extended to incorporate a mechanistic formulation of mechano-biological pathways by which tissue structures remodel during growth (Lanir in Biomech Model Mechanobiol, 14(2): 245–266, 2015). Here, the characteristic features of soft tissue structures and their constitutive modeling are reviewed. The presentation starts with a brief survey of the multi-scale and multi-phasic soft tissues structure. The global mechanical characteristics of soft tissues and of their constituents are then briefly reviewed. These two aspects form the basis for structural constitutive formulation via the multi-scale structure-function link. Based on established criteria for model validity, predictions of the formulated theory are contrasted against measured response characteristics. Using this structure-function relationship, the evolutionary pathway by which tissue structure and mechanics remodel during growth to adapt to their physiological function, is laid down. The review concludes with an account of the state of the art, the big picture, and future research challenges in tissue mechanobiological modeling.     

Invariants for Rari- and Multi-Constant Theories with Generalization to Anisotropy in Biological Tissues

The rari-constant theory of linear elasticity is based on the assumption that elasticity in solids is caused by only pair potentials with coaxial forces acting between atoms. The strain energy of each pair potential depends on the square of the strain between the atoms in the pair. This strain can be determined by taking the inner product of the strain tensor with a structural tensor that is the tensor product of a unit vector with itself. It is shown that the 15 independent constants in the rari-constant theory can be generated by a complete set of 15 structural tensors. It is also shown that the 6 additional independent constants in the multi-constant theory can be generated by taking the inner product of 6 of these structural tensors with the square of the strain tensor. A generalization of these results for nonlinear elasticity is discussed with reference to recent work which compares the structural and generalized structural tensor approaches to modeling fibrous tissues.     

Accelerating Reactive Transport Modeling: On-Demand Machine Learning Algorithm for Chemical Equilibrium Calculations

Transport in Porous Media - During reactive transport modeling, the computing cost associated with chemical equilibrium calculations can be 10 to 10,000 times higher than that of fluid flow, heat...     

Fe-Ni基高温自润滑复合材料摩擦磨损特性研究

本文中采用滑动磨损试验方法研究了以PbO和WS2为润滑组元的复合材料与440C不锈钢配副在25～600℃温度范围内的摩擦磨损特性.通过X射线衍射仪分析发现复合材料中含有铬的硫化物等高温润滑物质生成.使用扫描电镜和金相显微镜进一步分析了材料摩擦表面形貌.结果表明:在500 ～ 600℃范围内,PbWO4、CrxSx+1等各种金属化合物在摩擦表面形成了较完整的润滑膜,产生了自润滑能力,具有优良的减摩耐磨性能.润滑膜材料可向摩擦对偶表面转移,在一定程度上阻止了复合材料与440C不锈钢对摩材料的直接接触,显著降低了材料摩擦系数和磨损率,实现了高温自润滑性能.本文进一步探索了单一润滑组元润滑膜和两种润滑组元润滑膜的承载能力,发现两种固体润滑组元产生的协同润滑效应显著改善了润滑膜的润滑性能.     

Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows

We present a pore network model to determine the permeability of shale gas matrix. Contrary to the conventional reservoirs, where permeability is only a function of topology and morphology of the pores, the permeability in shale depends on pressure as well. In addition to traditional viscous flow of Hagen–Poiseuille or Darcy type, we included slip flow and Knudsen diffusion in our network model to simulate gas flow in shale systems that contain pores on both micrometer and nanometer scales. This is the first network model in 3D that combines pores with nanometer and micrometer sizes with different flow physics mechanisms on both scales. Our results showed that estimated apparent permeability is significantly higher when the additional physical phenomena are considered, especially at lower pressures and in networks where nanopores dominate. We performed sensitivity analyses on three different network models with equal porosity; constant cross-section model (CCM), enlarged cross-section model (ECM) and shrunk length model (SLM). For the porous systems with variable pore sizes, the apparent permeability is highly dependent on the fraction of nanopores and the pores’ connectivity. The overall permeability in each model decreased as the fraction of nanopores increased.     

Spatial Estimates for the Constrained Anisotropic Elastic Cylinder

This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone.     

Correction to: Accelerating Reactive Transport Modeling: On-Demand Machine Learning Algorithm for Chemical Equilibrium Calculations

Transport in Porous Media - In the original publication of the article, Table 2 was published incorrectly.     

Multiblock Pore-Scale Modeling and Upscaling of Reactive Transport: Application to Carbon Sequestration

In order to safely store CO₂ in depleted reservoirs and deep saline aquifers, a better understanding of the storage mechanisms of CO₂ is needed. Reaction of CO₂ with minerals to form precipitate in the subsurface helps to securely store CO₂ over geologic time periods, but a concern is the formation of localized channels through which CO₂ could travel at large, localized rates. Pore-scale network modeling is an attractive option for modeling and understanding this inherently pore-level process, but the relatively small domains of pore-scale network models may prevent accurate upscaling. Here, we develop a transient, single-phase, reactive pore-network model that includes reduction of throat conductivity as a result of precipitation. The novelty of this study is the implementation of a new mortar/transport method for coupling pore networks together at model interfaces that ensure continuity of pressures, species concentrations, and fluxes. The coupling allows for modeling at larger scales which may lead to more accurate upscaling approaches. Here, we couple pore-scale models with large variation in permeability and porosity which result in initial preferential pathways for flow. Our simulation results suggest that the preferential pathways close due to precipitation, but are not redirected at late times.     

On the Three Phase Mixtures in Martensitic Transformations of Shape Memory Alloys: Thermodynamical Modeling and Characteristic Temperatures

We study here the thermally-induced martensitic transformation process of shape memory alloys. Taking the internal energy of phase mixtures as the potential function and introducing coherency energies between martensite and austenite and between different variants of the martensitic phase, we are able to use thermodynamical arguments to obtain hysteresis diagrams which could be measured experimentally. The characteristic temperatures for martensitic transformation, (martensite start and finish) and (austenite start and finish) can be identified explicitly and are closely related to the coherency parameters of the coherency energies. Received September 12, 1997     

On the Solution of a Boltzmann System for Gas Mixtures

We study the Boltzmann equation for a mixture of two gases in one space dimension with initial condition of one gas near vacuum and the other near a Maxwellian equilibrium state. A qualitative-quantitative mathematical analysis is developed to study this mass diffusion problem based on the Green’s function of the Boltzmann equation for the single species hard sphere collision model in Liu andYu (Commun Pure Appl Math 57:1543–1608, 2004). The cross-species resonance of the mass diffusion and the diffusion-sound wave is investigated. An exponentially sharp global solution is obtained.     

Infiltration of Liquid Metals in Porous Compacts: Modeling of Permeabilities During Reactive Melt Infiltration

Reactive infiltration is a fast and cost-effective technique for manufacturing ceramic-matrix composites (CMCs). CMCs are used in elevated temperature applications like rocket engine casings, jet nozzles, gas turbine blades and nuclear cladding. There is an urgent need for minimizing experimental costs as well as optimizing process parameters during manufacture, so that we have minimized manufacturing costs and reduced infiltration times. Towards this end, the objective of this research was to develop an integrated micro-macro model of reactive flow of molten silicon in a porous preform consisting of carbon-coated silicon carbide fibers and then optimize process parameters computationally. The overall objective of the research was to arrive at a modified equation of Darcy's law for flow through a porous medium with the help of numerical/computational modeling. This paper deals with the flow of silicon through porous carbon at the macro level. The macro flow of silicon was integrated with an available micro model by determining the transient porosity from the micro model and using it in Darcy's law written for the macro flow of silicon. From the results of this study, we recommend suitable process parameters such as initial temperature of the solid reactant and the specific kind of reactants to be used for achieving complete infiltration. These conclusions are drawn after observation of the rate of decrease of permeability with more reaction.