率相关饱和多孔介质动力响应的数值分析

在基于混合物理论的多孔介质模型的基础上,将固体相视为弹粘塑性体,建立了饱和多孔介质的弹粘塑性模型。模型的基本思想是在无粘弹塑性本构关系中引入-时间参数,使固体骨架具备了粘性效应。利用Galerkin加权残值法推导得到了罚有限元格式,并采用Newmark预估校正法求解率相关饱和多孔介质的非线性有限元动力方程,此算法可以很...     

泡沫金属子弹撞击载荷下多孔金属夹芯板的动态响应

应用泡沫金属子弹撞击加载的方式研究了固支多孔金属夹芯板的塑性动力响应。讨论了多孔金属夹芯板在冲击载荷作用下的破坏模式。结果表明夹芯板的破坏主要表现在前面板的压痕与侵彻失效,芯层压缩和芯层剪切破坏。基于实验研究,应用LS-DYNA 3D非线性动力学有限元分析软件对夹芯板动力响应进行了有限元分析。数值研究结果与实验结果吻合较好。考察了加载冲量、面板厚度、芯层厚度及相对密度对多孔金属夹芯板抗撞击性能的影响。夹芯板的结构响应对其结构配置比较敏感,增加面板厚度或芯层厚度能够明显地减小后面板的挠度,提高夹芯板的抗撞击能力。研究结果对多孔金属夹芯板的优化设计具有一定得参考价值。     

饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。     

饱和多孔介质不同动力耦合形式数值分析EI北大核心CSCD

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

饱和多孔介质不同动力耦合形式数值分析

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

不可压渗流驱动问题混合有限元/间断有限元耦合格式的误差分析

多孔介质中渗流驱动问题与环境污染和油藏开采等问题密切相关,是当今的研究热点.对具有分子扩散和弥散效应的不可压渗流驱动问题,本文用混合有限元/间断有限元耦合格式来求解,即用混合有限元方法求解压力方程,用对称内罚间断有限元方法逼近浓度方程.运用比剪切算子更为便捷的归纳假设和插值投影,导出了先验hp误差估计.     

饱和多孔介质一维瞬态波动问题的解析分析

采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。     

考虑负载影响的阶梯形超声变幅杆动力特性

考虑与加工工件表面高频重复撞击对结构动力特性的影响,基于瞬态波传播理论,研究周期激励下阶梯形超声变幅杆重复撞击加工工件的瞬态动力响应,及负载对变幅杆放大特性的影响。首先,建立阶梯形变幅杆力学模型,采用瞬态波响应法分别对接触过程和分离过程动力控制方程进行求解,得到适用于任意级数的阶梯形变幅杆的特征项传递函数,和重复撞击系统的瞬态响应理论解。以工程中常用的三级阶梯形变幅杆为算例,分析了不同外载频率下变幅杆重复撞击动力特性和负载工件对变幅杆聚能效果的影响,得出考虑加工件撞击产生的瞬态响应下的变幅杆放大系数,小于自由振动空载的设计值。可为精细超声加工变幅杆的设计提供更为精确的理论依据     

饱和多孔介质动力分析的数值流形单元

基于数值流形方法中覆盖函数的基本思想,构造了适用于饱和多孔介质动力耦合分析的三节点平面流形单元,该单元满足Babuska-Brezzi稳定性准则与Zienkiewicz-Taylor分片试验条件,对于位移和孔隙压力具有不等阶的插值函数,且所有节点上具有相同自由度。用标准Galerkin法和Newmark法将饱和多孔介质动力基本方程在空间和时间上离散,得到饱和多孔介质动力分析的流形元离散的算法公式。数值结果表明,与传统有限元相比在孔隙流体不可压缩且非渗流的条件下,数值流形单元对于压力场的计算具有良好的数值稳定性。     

集中载荷作用下饱和多孔Timoshenko简支梁的动力响应

基于饱和多孔弹性Timoshenko梁的动力数学模型,研究了梁中点承受突加载荷作用两端可渗透饱和多孔弹性Timoshenko简支梁的动力响应,得到了问题的解析解,给出了梁中点无量纲挠度、固相骨架弯矩和孔隙流体压力等效力偶等随无量纲时间的响应。考察了剪切和横截面转动惯性效应等对动力响应的影响,比较了饱和多孔Timoshenko、Shear、Rayleigh和Euler-Bernoulli梁的动力响应,结果表明:剪切效应使饱和多孔Timoshenko梁动力响应的幅值和周期增大,而横截面转动惯性仅增加梁动力响应的周期;固相骨架与孔隙流体的相互作用具有粘性效应,随着相互作用系数的增加,饱和多孔梁挠度和弯矩幅值减小,流体压力等效力偶幅值增大,且振幅衰减加快。同时,随着长细比的增加,饱和多孔Timoshenko梁的挠度幅值和周期逐渐减小,并最终趋于饱和多孔Euler-Bernoulli梁的挠度幅值和周期。     

A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues

Hydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed-penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six-node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six-node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six-node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed-penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.     

A hybrid finite element formulation of the linear biphasic equations for hydrated soft tissue

A hybrid finite element method has been developed for application to the linear biphasic model of soft tissues. The biphasic model assumes that hydrated soft tissue is a mixture of two incompressible, immiscible phases, one solid and one fluid, and employs mixture theory to derive governing equations for its mechanical behaviour. These equations are time dependent, involving both fluid and solid velocities and solid displacement, and will be solved by spatial finite element and temporal finite difference approximation. The first step in the derivation of this hybrid method is application of a finite difference rule to the solid phase, thus obtaining equations with only velocities at discrete times as primary variables. A weighted residual statement of the temporally discretized governing equations, employing C° continuous interpolations of the solid and fluid phase velocities and discontinuous interpolations of the pore pressure and elastic stress, is then derived. The stress and pressure functions are chosen so that the total momentum equation of the mixture is satisfied; they are jointly referred to as an equilibrated stress and pressure field. The corresponding weighting functions are chosen to satisfy a relationship analogous to this equilibrium relation. The resulting matrix equations are symmetric. As an illustration of the hybrid biphasic formulation, six-noded triangular elements with complete linear, several incomplete quadratic, and complete quadratic stress and pressure fields in element local co-ordinates are developed for two dimensional analysis and tested against analytical solutions and a mixed-penalty finite element formulation of the same equations. The hybrid method is found to be robust and produce excellent results; preferred elements are identified on the basis of these results.     

Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling

An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid–solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non‐linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non‐linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd.     

Modeling of coupled dual-scale flow–deformation processes in composites manufacturing

The present contribution is a part of the work towards a framework for holistic modeling of composites manufacturing. Here we focus our attention onto the particular problem of coupled dual-scale deformation–flow process such as the one arising in RTM, Vacuum Assisted Resin Infusion (VARI) and Vacuum Bag Only (VBO) prepregs. The formulation considers coupling effects between macro-scale preform processes and meso-scale ply processes as well as coupling effects between the solid and fluid phases. The framework comprises a nonlinear compressible fiber network saturated with incompressible fluid phase. Internal variables are introduced in terms of solid compressibility to describe the irreversible mesoscopic infiltration and reversible preform compaction processes. As a main result a coupled displacement–pressure, geometrically nonlinear, finite element simulation tool is developed. The paper is concluded with a numerical example, where a relaxation–compression test of a planar fluid filled VBO preform at globally un-drained and partly drained conditions is considered.     

Mixed finite element method for saturated poroelastoplastic media at large strains

A mixed finite element for hydro‐dynamic analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, effective stresses, strains for the solid phase and pressure, pressure gradients, and Darcy velocities for the fluid phase are interpolated as independent variables. The weak form of the governing equations of coupled hydro‐dynamic problems in saturated porous media within the element are given on the basis of the Hu–Washizu three‐field variational principle. In light of the stabilized one point quadrature super‐convergent element developed in solid continuum, the interpolation approximation modes for the primary unknowns and their spatial derivatives of the solid and the fluid phases within the element are assumed independently. The proposed mixed finite element formulation is derived. The non‐linear version of the element formulation is further derived with particular consideration of pressure‐dependent non‐associated plasticity. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elastoplastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non‐linearity, the co‐rotational formulation approach is used. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization due to strain softening in poroelastoplastic media subjected to dynamic loading at large strain. Copyright © 2003 John Wiley & Sons, Ltd.     

A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation

The non-linear response of soft hydrated tissues under physiologically relevant levels of mechanical loading can be represented by a two-phase continuum model based on the theory of mixtures. The governing equations for a biphasic soft tissue, consisting of an incompressible solid and an incompressible, inviscid fluid, under finite deformation are presented and a finite element formulation of this highly non-linear problem is developed. The solid phase is assumed to be hyperelastic, and the stress-strain relations for the solid phase are defined in terms of the free energy function. A finite element model is formulated via the Galerkin weighted residual method coupled with a penalty treatment of the continuity equation for the mixture. Using a total Lagrangian formulation, the non-linear weighted residual statement, expressed with respect to the reference configuration, leads to a coupled non-linear system of first order differential equations. The non-linear constitutive equation for the solid phase elasticity is incrementally linearized in terms of the second Piola-Kirchhoff stress and the corresponding Lagrangian strain. A tangent stiffness matrix is defined in terms of the free energy function; this matrix definition can be applied to any free energy function, and will yield a symmetric matrix when the free energy function is convex. An unconditionally stable implicit predictor-corrector algorithm is used to obtain the temporal response histories. The confined compression mechanical test of soft tissue in stress relaxation is used as an example problem. Results are presented for moderate and rapid rates of loading, as well as small and large applied strains. Comparison of the finite element solution with an independent finite difference solution demonstrates the accuracy of the formulation.     

A new acoustic interface element for fluid-structure interaction problems

A new comprehensive acoustic 2-D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.     

Acoustic and vibrational damping in porous solids

A porous solid may be characterized as an elastic-viscoelastic and acoustic-viscoacoustic medium. For a flexible, open cell porous foam, the transport of energy is carried both through the sound pressure waves propagating through the fluid in the pores, and through the elastic stress waves carried through the solid frame of the material. For a given situation, the balance between energy dissipated through vibration of the solid frame, changes in the acoustic pressure and the coupling between the waves varies with the topological arrangement, choice of material properties, interfacial conditions, etc.Engineering of foams, i.e. designs built on systematic and continuous relationships between polymer chemistry, processing, micro-structure, is still a vision for the future. However, using state-of-the-art simulation techniques, multiple layer arrangements of foams may be tuned to provide acoustic and vibrational damping at a low-weight penalty.In this paper, Biot's modelling of porous foams is briefly reviewed from an acoustics and vibrations perspective with a focus on the energy dissipation mechanisms. Engineered foams will be discussed in terms of results from simulations performed using finite element solutions. A layered vehicle-type structure is used as an example.     

Finite element modelling—predictor of implant survival?

The cancellous bone stresses surrounding proximal femoral prostheses were investigated using the finite element method and the results correlated with clinical subsidence data for similar implant configurations. The finite element study has shown that press-fit prostheses generate significantly higher cancellous bone stresses than bonded (cemented and HA coated) prostheses. The cancellous bone stresses surrounding press-fit implants are sensitive to the coefficient of friction, with up to a 60% decrease observed when the coefficient of friction was increased from 0 to 0.4. Resecting the femoral neck generally increased the cancellous bone stresses however varying the thickness of the cement mantle had little or no effect. Good correlation was found between the finite element results and the clinically measured subsidence data. Implant configurations generating higher cancellous bone stresses were those which subsided the most. This observation suggests that it may be possible to use the initial cancellous bone stresses to predict the likelihood of migration and hence late aseptic loosening.