心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法. 在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性. 本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应. 基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比. 结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.      

聚硅氧烷硅胶的黏超弹性力学行为研究

聚硅氧烷硅胶是一类以Si——O键为主链、硅原子上直接连接有机基团的无色透明高分子聚合物, 因其具有优异的超弹性性能而广泛应用于精密减震结构、柔性电子器件等领域. 在聚硅氧烷硅胶减震结构和柔性电子器件的设计中, 材料在大变形和动态加载下的黏超弹性力学行为的精确描述至关重要. 本文针对该问题进行了系统的研究:首先, 将该硅胶的超弹性和黏弹性行为进行解耦, 确定其黏超弹性本构方程的基本框架;其次, 基于单轴拉压、平面拉伸试验确定其准静态超弹性模型的各项参数;再次, 利用霍普金森压杆冲击试验确定其黏弹性模型的各项参数;在此基础上, 将超弹性和黏弹性模型合并为适用于大应变和大应变率的黏超弹性动态本构模型;最后, 利用落锤冲击试验对该硅胶薄片的冲击变形行为进行了研究, 并利用上述建立的动态本构模型对落锤冲击过程进行了有限元模拟. 结果表明:本文建立的黏超弹性本构模型可有效预测该硅胶在冲击载荷下的力学行为, 从而为聚硅氧烷硅胶减震结构和柔性电子器件的优化设计提供了理论和应用基础.      

黏弹性本构关系构建方法及应用举例

黏弹性力学是力学重要分支之一。本文从基本的黏弹性元件出发,逐级从黏弹性变形基本单元推广到普遍的黏弹性变形模型,引入并推导本构方程。最后结合典型黏弹性材料的高温蠕变行为,介绍了黏弹性理论在工程实际中的应用。结合笔者近几年的黏弹性理论教学实践,结合学生的课堂反应,从教学内容、方法和环节等方面进行探讨。文中教学措施可为讲授力学课程的教师提供参考。     

线性黏弹性球面波的特征线分析

基于ZWT黏弹性本构方程建立了体现高应变率效应的黏弹性球面波的控制方程组,包含5个偏微分方程,解5个未知量v、r、、r和。采用特征线法,问题转化为解3族特征线上的5个常微分方程,物理上图像清晰,数学上易于求解。特征线数值分析显示,黏弹性球面波的衰减和弥散效应超过线弹性球面波。球面扩散引起的环向拉应力是导致介质拉伸破坏的主因。进一步还针对强间断黏弹性球面波得出其衰减特性的解析表达式,表明这种更强的衰减特性是几何扩散效应和本构黏性效应两者共同作用的后果。     

聚硅氧烷硅胶的黏超弹性力学行为研究

聚硅氧烷硅胶是一类以Si—O键为主链、硅原子上直接连接有机基团的无色透明高分子聚合物,因其具有优异的超弹性性能而广泛应用于精密减震结构、柔性电子器件等领域.在聚硅氧烷硅胶减震结构和柔性电子器件的设计中,材料在大变形和动态加载下的黏超弹性力学行为的精确描述至关重要.本文针对该问题进行了系统的研究:首先,将该硅胶的超弹性和黏弹性行为进行解耦,确定其黏超弹性本构方程的基本框架;其次,基于单轴拉压、平面拉伸试验确定其准静态超弹性模型的各项参数;再次,利用霍普金森压杆冲击试验确定其黏弹性模型的各项参数;在此基础上,将超弹性和黏弹性模型合并为适用于大应变和大应变率的黏超弹性动态本构模型;最后,利用落锤冲击试验对该硅胶薄片的冲击变形行为进行了研究,并利用上述建立的动态本构模型对落锤冲击过程进行了有限元模拟.结果表明:本文建立的黏超弹性本构模型可有效预测该硅胶在冲击载荷下的力学行为,从而为聚硅氧烷硅胶减震结构和柔性电子器件的优化设计提供了理论和应用基础.     

Kevlar29纱线动态拉伸力学性能与本构方程

为了能够清晰地表征芳纶纱线在不同应变率下的力学行为,进行了Kevlar29纱线的准静态和动态拉伸试验,结合分离式霍普金森拉杆理论和运动目标追踪法,获得了Kevlar29纱线在不同应变率下的应力-应变曲线,分析了纱线动态拉伸的变形与断裂过程,揭示了Kevlar29纱线力学性能的应变率效应;通过最小二乘法拟合得到了基于纱线应变率效应的黏弹性本构方程,分析了三元件和五元件本构模型的差异及适用性。结果表明：随着应变率升高,Kevlar29纱线的断裂应变减小,拉伸强度和韧性先增大后减小,拉伸模量先增大后趋于稳定;五元件黏弹性本构模型能够较好地表征纱线力学性能的应变率效应。     

数值仿真轴向运动黏弹性梁非线性参激振动

分别通过两种直接数值方法研究速度变化的经典边界条件下轴向运动黏弹性梁参数振动的稳定性。在控制方程的推导中,采用物质导数黏弹性本构关系和只对时间取偏导数的黏弹性本构关系;分别运用有限差分法和微分求积法对两种经典边界下轴向变速运动黏弹性梁的非线性控制方程求数值解,计算得到梁中点非线性参数振动的稳定稳态响应。数值结果表明,两种黏弹性本构关系对应的稳态响应存在明显差别,同时发现两种直接数值方法的仿真结果基本吻合,证明数值仿真具有较高精度。     

基于CDM的黏弹性薄板压屈失效分析

研究黏弹性薄板的压屈失效问题.基于连续介质损伤力学与Schapery对应原理,得到耦合各向异性蠕变损伤的黏弹性本构模型,构造板的分层模型以考虑损伤演化的空间特征,建立具初挠度板的非线性压屈控制方程与边界条件,并进行空间与时间域上的数值离散和迭代求解.计算结果与实验曲线的对比表明本文的分析方法是有效的,黏弹性材料的蠕变损伤将导致结构刚度不断削弱,在一定应力水平下,板发生变形快速增加的压屈失效.     

基于ZWT方程的线黏弹性球面波分析

针对时间尺度为1~100 s的爆炸冲击加载,忽略低频Maxwell体的松弛效应,同时为简化分析,忽略非线性弹簧效应项,推导了三维应力状态下的线黏弹性ZWT本构关系。基于球面波的基本动力学方程,结合ZWT线黏弹性本构关系,得到了以位移u表征的三阶波动方程。利用该方程分析固体介质中线黏弹性球面波传播过程中的吸收和弥散现象,得知:高频球面波的衰减因子趋于常数,相速趋于高频下的纵波速度;低频球面波的衰减因子和圆频率的平方成正比,其相速趋于低频下的纵波速度;低频球面波的纵波波速低于高频球面波的纵波波速,两者的比值和介质的泊松比、弹性模量及Maxwell体弹性模量相关。     

黏弹性夹层环形薄板自由振动的理论解

基于薄板小挠度理论和Kelvin-Voigt 黏弹性本构方程,建立了黏弹性夹层环形薄板振动控制方程.采用分离变量法计算了内边固支、外边自由黏弹性夹层环形薄板的固有频率和振型,并与有限元计算结果进行比较. 分别讨论了夹心层比和内外半径比对固有频率及衰减系数的影响. 研究表明:系统频率随夹心层厚度增大,先增大后减小,而衰减系数一直增大;系统频率和衰减系数随内外半径比增大而增大.     

冻土水热力耦合作用的数学模型及数值模拟

将冻土体视为空间弹性体,提出了土体在冻结过程中水分场、温度场、应力场三场耦合的一般数学模型,并给出了相应的离散方程及其解法,最后给出了数值算例,并与实测值比较,证明了该模型和算法的正确性。     

The energy release rate for hygrothermal coupling elastic materials

In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically. The project supported by the Key Project of Chinese Ministry of Education (03145) and the Science Fund of Southwest Jiaotong University. The English text was polished by Yunming Chen.     

Coupled Solvent and Heat Transport of a Mixture of Swelling Porous Particles and Fluids: Single Time-Scale Problem

A three-spatial scale, single time-scale model for both moisture and heat transport is developed for an unsaturated swelling porous media from first principles within a mixture theoretic framework. On the smallest (micro) scale, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individual phases or nonoverlapping continua occupying distinct regions of space and satisfying the classical field equations. These equations are homogenized forming overlaying continua on the intermediate (meso) scale via hybrid mixture theory (HMT). On the mesoscale the homogenized swelling particles consisting of the homogenized vicinal fluid and colloid are then mixed with two bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. On the largest (macro) scale the saturated homogenized particles, bulk liquid and vapor solvent, are again homogenized forming four overlaying continua: doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both are developed via the Coleman and Noll method of exploiting the entropy inequality coupled with linearization about equilibrium. The macroscale constitutive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscale generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, pressure gradients, external force fields, and temperature gradients.     

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.     

Non-isothermal polymer melt flow in sudden expansions

This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features.     

刚性微粒填充的高聚物非线性粘弹性本构关系的微力学分析

在应变具有可加性条件下,本文分析表明Eshelby线性微力学理论,包括其等效包含体方法和相应的平均化方法可推广应用于研究高刚度微粒填充高聚物的非线性粘弹性本构关系。     

基于实验的数值反演的滚动轮胎稳态温度场的有限元分析

根据轮胎温度场的单向解耦分析思想,形成了一个基于ABAQUS程序的轮胎稳态温度场的分析方法,单向解耦过程分为变形、损耗、热传导三个分析过程。变形分析中,采用了平衡态的超弹性材料模型;损耗分析中,依据变形分析获得的应力应变场,结合材料粘性损耗特性来获得损耗能量;热传导分析中,依据实测的轮胎胎侧温度场,提出了一种基于实验的数值反演方法来确定胎侧的对流热边界条件。由于轮胎胎侧的形状和结构细节,其对流热边界不同于旋转平圆盘的对流热边界,本文的数值反演方法避免了实测胎侧对流热交换系数的困难。     

A finite deformation thermomechanical constitutive model for triple shape polymeric composites based on dual thermal transitions

Shape memory polymers (SMPs) have gained strong research interests recently due to their mechanical action that exploits their capability to fix temporary shapes and recover their permanent shape in response to an environmental stimulus such as heat, electricity, irradiation, moisture or magnetic field, among others. Along with interests in conventional “dual-shape” SMPs that can recover from one temporary shape to the permanent shape, multi-shape SMPs that can fix more than one temporary shapes and recover sequentially from one temporary shape to another and eventually to the permanent shape, have started to attract increasing attention. Two approaches have been used to achieve multi-shape shape memory effects (m-SMEs). The first approach uses polymers with a wide thermal transition temperature whilst the second method employs multiple thermal transition temperatures, most notably, uses two distinct thermal transition temperatures to obtain triple-shape memory effects (t-SMEs). Recently, one of the authors’ group reported a triple-shape polymeric composite (TSPC), which is composed of an amorphous SMP matrix (epoxy), providing the system the rubber-glass transition to fix one temporary shape, and an interpenetrating crystallizable fiber network (PCL) providing the system the melt-crystal transition to fix the other temporary shape. A one-dimensional (1D) material model developed by the authors revealed the underlying shape memory mechanism of shape memory behaviors due to dual thermal transitions. In this paper, a three-dimension (3D) finite deformation thermomechanical constitutive model is presented to enable the simulations of t-SME under more complicated deformation conditions. Simple experiments, such as uniaxial tensions, thermal expansions and stress relaxation tests were carried out to identify parameters used in the model. Using an implemented user material subroutine (UMAT), the constitutive model successfully reproduced different types of shape memory behaviors exhibited in experiments designed for shape memory behaviors. Stress distribution analyses were performed to analyze the stress distribution during those different shape memory behaviors. The model was also able to simulate complicated applications, such as a twisted sheet and a folded stick, to demonstrate t-SME.     

多孔介质在压力梯度作用下的热质耦合数值模拟

多孔介质干燥导致热质耦合传输过程。本文基于连续介质力学的宏观尺度,对多孔介质的热、湿和气三者耦合迁移进行数值模拟,研究压力梯度对热质传输的影响。多孔介质传质机理主要为水汽和空气的对流和扩散传输、吸附水在含湿量梯度作用下的自由扩散和其在温度梯度即Soret效应驱动下的流动。采用Galerkin加权余量的有限元方法,提出了...     

温度梯度对热致型形状记忆聚合物板力学性能的影响

形状记忆聚合物作为一种新型的智能材料,由于质量轻、成本低以及变形回复率大等优势,已经在航空、医学等领域得到广泛应用。当前对于热致型形状记忆聚合物力学行为的研究,大都集中在整体变温的情况下,随着应用环境的越来越广泛,温度梯度对材料力学性能的影响效果越发重要。本文在均匀应力的假设下,给出材料在不同初始和传热条件下的温度梯度分布情况,结合传热学和热致型形状记忆聚合物相变理论本构模型,分别讨论了不同温度梯度对存储应变、弹性模量等力学性能的影响,通过理论分析和实验数据对比验证了模型正确性。本文研究可为不同导热情况下,对热致型形状记忆聚合物力学行为监测提供思路,也为形状记忆聚合物的进一步工程应用提供理论依据。