综放极限平衡区顶煤渗透性的计算模型

基于放顶煤开采中顶煤渗透率对工作面安全生产的重要性, 对煤壁前方极限平衡区内顶煤渗透率的变化规律进行了研究. 应用损伤力学和数理统计方法对顶煤垂直和水平应变进行了研究分析, 并建立了数学模型. 以甲烷气体为渗流体, 应用自制三轴实验机对煤样体积应变与渗透率的关系进行了试验研究, 并利用多项式拟合方法对试验结果进行了分段拟合. 结果表明：根据所建立的顶煤应变计算模型, 可以求出综放顶煤内任意点的体积应变, 且顶煤的水平应变与其距底板的高度无关. 依据试验及拟合所得到的煤体体积应变与渗透率的函数关系, 可以求得顶煤内任意点渗透率. 最后对计算模型进行了实践检验.     

标准线性固体材料应变率相关力学行为与内耗现象本质联系探讨

标准线性固体材料应变率相关力学行为与内耗现象本质联系探讨程经毅，周光泉（中国合肥科学技术大学，合肥２３００２６）关键词粘弹性，标准线性固体，应变率敏感性，内耗１引言尽管材料的应变率相关力学行为和内耗现象是材料在不同的加载方式下的不同响应，然而，它们在...     

正常和早期膝骨关节炎的软骨生物力学研究

膝骨关节炎是导致膝关节疼痛和慢性残疾的一种常见的关节疾病. 膝关节的软骨生物力学是评价膝骨关节炎程度的重要指标. 然而, 早期膝骨关节炎的软骨生物力学依然有待研究, 正常、内侧和内外侧早期膝骨关节炎的软骨生物力学差异尚不清楚. 本文基于固?液双相纤维增强的软骨有限元建模方法, 分别建立了正常膝关节模型、内侧早期膝骨关节炎模型和内外侧早期膝骨关节炎模型, 在步态周期中最大载荷时刻和最大屈曲角度时刻下分别对比分析了正常、内侧和内外侧早期膝骨关节炎3种情况下的软骨生物力学差异. 结果表明, 与正常膝关节相比, 内侧早期膝骨关节炎模型的内侧软骨的流体压力减少, 固相等效应力减少以及应变增大; 外侧软骨的结果基本没有差异. 然而, 内外侧早期膝骨关节炎模型的内外侧软骨的流体压力都减少, 固相等效应力都减少以及应变都增大. 早期膝骨关节炎中退变软骨的属性变化会导致软骨的承载能力下降以及变形增大, 从而增加软骨进一步退变的风险. 本文提出的基于双相纤维增强软骨模型的膝关节有限元模型有效预测了正常和关节炎情况下的软骨生物力学差异, 该模型也可以推广应用于髋、踝和脊柱等其他关节生物力学的研究.      

基于均匀化方法的单向纤维增强体渗透率预报

针对具有周期性分布细观结构的纤维增强体，从Stokes方程出发，用均匀化理论建立了预报纤维预制体渗透率的数学模型. 将Stokes方程与线弹性力学中的Lame方程进行类比，给出了用线弹性平面应变问题的有限元分析程序求解Stokes方程的方法. 据该方法编写了FORTRAN程序HAPS求解控制方程，并以此预报单向纤维增强体渗透率，与有关文献的结果进行比较证明了该方法的合理性.     

单轴拉伸过程中双相不锈钢局部微观变形行为的细观力学有限元分析

针对双相不锈钢中奥氏体相和铁素体相分别展开了纳米压痕实验，并通过有限元反演得到两相各自的拉伸应力-应变关系，利用Voronoi Tessellation法生成代表性的微结构体积单元，对双相不锈钢的单轴拉伸行为进行了有限元仿真和模拟，研究了双相不锈钢在拉伸过程中的局部应力、应变分布和演化规律．结果表明，利用Voronoi Tessellation法建立单元模型，结合本文通过纳米压痕实验获取的两相力学性能参数，可以很好地模拟双相不锈钢的整体单拉行为，奥氏体比铁素体软，拉伸载荷下双相不锈钢的应变集中在奥氏体中，应力集中在铁素体中；局部应力应变的分布特征与两相分布特征和晶粒形状有关，最大应变值主要集中在奥氏体晶粒狭长且尖锐的区域，而最大应力则主要发生在铁素体晶粒狭长和尖锐的区域；对于奥氏体和铁素体晶粒占比相当的双相不锈钢，其虽然可以具有较为综合的宏观力学性能，但是其微观应力集中的区域和应力最大值相对较大．研究成果为进一步揭示双相不锈钢局部失效机理奠定了基础．     

软骨组织工程构建中的生物力学

关节软骨是关节表面具有弹性的承重组织,其结构复杂,由固体相和液体相组成.固体相包括胶原纤维、蛋白多糖等,属纤维增强型复合结构;液体相包括水、电解质等.关节软骨提供了一个低磨损和低摩擦的光滑界面,起缓冲振动和传递载荷等支撑作用.由于膝关节承受的运动量大、应力高,关节软骨损伤在临床上较为常见.但软骨内没有血管,代谢缓慢,其损伤后难以实现自我修复.组织工程从理论上建立了一种治疗软骨缺损的理想方法,但尚未成为临床上常规的治疗选择.如何获得结构和功能相匹配,同时适用于临床治疗的工程软骨,至今仍是亟需解决的问题.在体外构建功能化工程软骨,关键在于运用生物反应器对组织施加合适的力学载荷:首先保证工程软骨复合体内信号分子、营养和废物的有效运输;其次对支架内种子细胞产生特定的力学刺激;同时促进细胞外基质结构与功能的适应性发展.本文对力学载荷在软骨组织工程构建中的应用进展加以综述:按照作用于组织层面的力学载荷传递所需的介质属性,将其分为液体介导、固体介导和其他媒质介导三种类型,重点关注不同载荷对工程软骨功能化构建的作用和效果;分析讨论软骨组织工程构建中存在的关键生物力学问题;总结和展望软骨组织工程未来的发展趋势.软骨组织工程体外培养需要考虑力学载荷和生化刺激的耦合作用;在合适的生化条件下进行滚动、滑动和压缩复合加载,将有利于工程软骨的体外功能化构建.     

软骨组织工程构建中的生物力学

关节软骨是关节表面具有弹性的承重组织, 其结构复杂, 由固体相和液体相组成. 固体相包括胶原纤维、蛋白多糖等, 属纤维增强型复合结构; 液体相包括水、电解质等.关节软骨提供了一个低磨损和低摩擦的光滑界面, 起缓冲振动和传递载荷等支撑作用. 由于膝关节承受的运动量大、应力高, 关节软骨损伤在临床上较为常见. 但软骨内没有血管, 代谢缓慢, 其损伤后难以实现自我修复. 组织工程从理论上建立了一种治疗软骨缺损的理想方法, 但尚未成为临床上常规的治疗选择. 如何获得结构和功能相匹配, 同时适用于临床治疗的工程软骨, 至今仍是亟需解决的问题.在体外构建功能化工程软骨, 关键在于运用生物反应器对组织施加合适的力学载荷: 首先保证工程软骨复合体内信号分子、营养和废物的有效运输; 其次对支架内种子细胞产生特定的力学刺激; 同时促进细胞外基质结构与功能的适应性发展.本文对力学载荷在软骨组织工程构建中的应用进展加以综述: 按照作用于组织层面的力学载荷传递所需的介质属性, 将其分为液体介导、固体介导和其他媒质介导三种类型, 重点关注不同载荷对工程软骨功能化构建的作用和效果; 分析讨论软骨组织工程构建中存在的关键生物力学问题; 总结和展望软骨组织工程未来的发展趋势.软骨组织工程体外培养需要考虑力学载荷和生化刺激的耦合作用; 在合适的生化条件下进行滚动、滑动和压缩复合加载, 将有利于工程软骨的体外功能化构建.      

Biomechanics in cartilage tissue engineering

关节软骨是关节表面具有弹性的承重组织, 其结构复杂, 由固体相和液体相组成. 固体相包括胶原纤维、蛋白多糖等, 属纤维增强型复合结构; 液体相包括水、电解质等.关节软骨提供了一个低磨损和低摩擦的光滑界面, 起缓冲振动和传递载荷等支撑作用. 由于膝关节承受的运动量大、应力高, 关节软骨损伤在临床上较为常见. 但软骨内没有血管, 代谢缓慢, 其损伤后难以实现自我修复. 组织工程从理论上建立了一种治疗软骨缺损的理想方法, 但尚未成为临床上常规的治疗选择. 如何获得结构和功能相匹配, 同时适用于临床治疗的工程软骨, 至今仍是亟需解决的问题.在体外构建功能化工程软骨, 关键在于运用生物反应器对组织施加合适的力学载荷: 首先保证工程软骨复合体内信号分子、营养和废物的有效运输; 其次对支架内种子细胞产生特定的力学刺激; 同时促进细胞外基质结构与功能的适应性发展.本文对力学载荷在软骨组织工程构建中的应用进展加以综述: 按照作用于组织层面的力学载荷传递所需的介质属性, 将其分为液体介导、固体介导和其他媒质介导三种类型, 重点关注不同载荷对工程软骨功能化构建的作用和效果; 分析讨论软骨组织工程构建中存在的关键生物力学问题; 总结和展望软骨组织工程未来的发展趋势.软骨组织工程体外培养需要考虑力学载荷和生化刺激的耦合作用; 在合适的生化条件下进行滚动、滑动和压缩复合加载, 将有利于工程软骨的体外功能化构建.     

多孔介质渗透率的一种新分形模型

多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题．基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型．结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε =1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关．将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好．     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为，本文建立了基于微结构演化的塑性本构模型。首先，采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验，并对其在不同应变程度下的微结构演化特征进行了分析。研究发现，影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程，并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响，进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后，根据隐式应力更新算法对新模型进行了有限元实现，并与实验结果进行比较，验证了新模型的合理性和预测精度。     

An analytical poroelastic model for laboratorial mechanical testing of the articular cartilage (AC)

The articular cartilage (AC) can be seen as a biphasic poroelastic material. The cartilage deformation under compression mainly leads to an interstitial fluid flow in the porous solid phase. In this paper, an analytical poroelastic model for the AC under laboratorial mechanical testing is developed. The solutions of interstitial fluid pressure and velocity are obtained. The results show the following facts. (i) Both the pressure and fluid velocity amplitudes are proportional to the strain loading amplitude. (ii) Both the amplitudes of pore fluid pressure and velocity in the AC depend more on the loading amplitude than on the frequency. Thus, in order to obtain the considerable fluid stimulus for the AC cell responses, the most effective way is to increase the loading amplitude rather than the frequency. (iii) Both the interstitial fluid pressure and velocity are strongly affected by permeability variations. This model can be used in experimental tests of the parameters of AC or other poroelastic materials, and in research of mechanotransduction and injury mechanism involved interstitial fluid flow.     

Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids

Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.After the spatial discretization of the governing field equations within the finite element method, a differential algebraic system in time arises due to the incompressibility constraint of both constituents. For the efficient numerical treatment of the strongly coupled nonlinear solid-fluid problem, a consistent linearization of the weak forms of the governing equations with respect to the unknowns must be used.     

Determination of the effective elastic–plastic response of metal–ceramic composites

The mechanical response of metal–ceramic composites is analysed through a homogenization model accounting for the mechanical behaviour of the constituent materials. In order to achieve this purpose a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code. A prescribed homogenized strain state is applied to a unit volume element of a metal–ceramic composite with proportional loading in which all components of the strain tensor are proportional to one scalar parameter. The mechanical response of the material has been modeled by considering a von Mises plasticity model for the metal phase and a Drucker–Prager associative elastic–plastic material model for the ceramic phase. A two stages plasticity has been obtained in which inelastic strain develops in the metal phase followed by a fully plastic response. A comparison with a finite element model of the stress–strain response of an axisymmetric unit cell has been carried out with the purpose to validate the homogenization based modeling presented in the paper. Plastic parameters of a Drucker–Prager yield surface for the homogenized composite have been calculated at different materials compositions. Associative Drucker–Prager plasticity has been found to be accurate for high ceramic content.     

A nonlinear finite element formulation for axisymmetric torsion of biphasic materials

In this paper, we present a finite element formulation for describing the large deformation torsional response of biphasic materials, with specific application to prediction of nonlinear coupling between torsional deformation and fluid pressurization in articular cartilage. Due to the use of a cylindrical coordinate system, a particular challenge arises in the linearization of the weak form. The torsional axisymmetric case considered gives rise to additional geometric terms, which are important for the robustness of the numerical implementation and that would not be present in a Cartesian formulation. A detailed derivation of this linearization process is given, couched in the context of a variational formulation suitable for finite element implementation. A series of numerical parametric studies are presented and compared to experimental measurements of the time dependent response of cartilage.     

A general solution of the axisymmetric contact problem for biphasic cartilage layers

A unilateral axisymmetric contact problem for articular cartilage layers is considered. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like bodies of revolution with arbitrary convex profiles. The obtained closed-form analytical solution is valid over time periods compared with the typical diffusion time and can be used for increasing loading.     

饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

The study on the mechanical characteristics of articular cartilage in simulated microgravity

The microgravity environment of a long-term space flight may induce acute changes in an astronaut’s musculo-skeletal systems. This study explores the effects of simulated microgravity on the mechanical characteristics of articular cartilage. Six rats underwent tail suspension for 14 days and six additional rats were kept under normal earth gravity as controls. Swelling strains were measured using high-frequency ultrasound in all cartilage samples subject to osmotic loading. Site-specific swelling strain data were used in a triphasic theoretical model of cartilage swelling to determine the uniaxial modulus of the cartilage solid matrix. No severe surface irregularities were found in the cartilage samples obtained from the control or tail-suspended groups. For the tail-suspended group, the thickness of the cartilage at a specified site, as determined by ultrasound echo, showed a minor decrease. The uniaxial modulus of articular cartilage at the specified site decreased significantly, from (6.31 ± 3.37)MPa to (5.05 ± 2.98)MPa (p < 0.05). The histology-stained image of a cartilage sample also showed a reduced number of chondrocytes and decreased degree of matrix staining. These results demonstrated that the 14 d simulated microgravity induced significant effects on the mechanical characteristics of articular cartilage. This study is the first attempt to explore the effects of simulated microgravity on the mechanical characteristics of articular cartilage using an osmotic loading method and a triphasic model. The conclusions may provide reference information for manned space flights and a better understanding of the effects of microgravity on the skeletal system.     

用于多种夹层板等效的有限元分析法

针对夹层板力学性能解析法难于计算复杂结构的夹层板且通用性差的问题,本文采用有限元分析法研究了夹层板性能的等效方法。对夹层板的代表体单元模型施加位移约束,模拟弯曲变形时线性独立的应变分量和弯曲内力;根据夹层板内力与应变的本构关系,求出刚度矩阵;最后由刚度矩阵得出宏观等效弹性常数,从而把夹层板等效成连续材料的单层板单元。将该方法与解析法计算结果进行比较得到的夹层板单元四个主要弹性常数误差在0.2%以内,验证了该方法的有效性;另外采用该方法等效三种典型结构夹层板,比较实际模型和等效模型的弯曲响应,得到的误差均在1.4%以内,表明该方法在不考虑复杂多变的夹芯结构时具有通用性。