水凝胶多场耦合计算力学

作为一种具有多场耦合特性的智能柔体材料,水凝胶的制备技术、性能表征与结构应用得到迅速发展。本文在分析水凝胶本构理论和结构设计的基础上,提出了水凝胶多场耦合计算力学的基本方法和范式,包括微观粗粒化分子动力学模拟和宏观耦合有限元方法等,计算了化学-力学耦合作用下水凝胶材料与结构的变形和应力,给出了多个数值算例与结果比较。研究指出多场耦合计算力学将成为水凝胶材料和结构分析的主要手段,并推动水凝胶等这类智柔材料的性能设计与工程应用。     

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

智能软材料热-电-化-力学耦合问题的研究进展

本文重点评述了自然界中的典型智能软材料:聚合物胶体和水凝胶以及关节软骨的多场耦合力学问题的国内外研究现状。基于唯象热力学理论和哈密顿原理,建立了一般性的热-电-化-力学多场耦合理论。重点针对等温过程的化学-力学耦合本构关系和控制方程,通过哈密顿原理,建立了化力耦合系统的有限元列式。证明了化学-力学耦合理论架构的封闭性。通过数值算例分析了水凝胶和关节软骨的多场耦合作用。最后展望了智能软材料多场耦合研究的未来发展趋势。      

智能复合材料的化学-力学完全耦合理论及有限元计算

许多智能复合材料例如生物组织和聚合物胶体,都表现出多场耦合行为.目前化学-力学耦合理论属于一个比较新的领域,还不成熟.本文主要研究化学一力学耦合行为,并在ABAQUS软件中进行了数值模拟计算.应用力学平衡方程、离子扩散方程和包含力学-化学耦合因素的的本构关系椎导出了力学-化学耦合的等效积分形式,建立力学-化学耦合的有限元方程.在ABAQUS软件中开发用户单元子程序,进行数值模拟.计算结果表明:力学与化学存在着相互耦合作用,浓度变化能引起固体的变形,同样力学作用也能引起浓度重分布:由于耦合作用,固体的有效性能与扩散性质都发生了改变:力学-化学耦合作用过程实际是机械能与化学能之间能量转换过程;最终,研究体中械能与化学能达到相互平衡状态,且质量守恒.本文的理论和方法可应用于模拟生物组织、粘土等材料的力学-化学耦合行为.     

化学-力学耦合理论与数值方法

该文研究了化学场中的质量扩散与力学耦合问题,构造了化-力耦合情况下的力学本构关系与质量扩散的本构关系,并由这些本构关系和化学场、力学场的控制方程,得到化-力场耦合的有限元方程.通过数值算例,详细分析了由应力场引起的质量重分布和由化学场引起的结构变形.研究表明,力学与化学之间存在明显的相互作用,并采用有限元数值方法进行了分析.     

智能软材料热""电-化-力学耦合问题的研究进展

正智能软材料是指具有较低模量,在外场(如热、电、磁、化、光等)作用下能够产生较大力学响应的材料。本文评述了聚合物胶体、水凝胶以及关节软骨等典型智能软材料的多场耦合力学问题的国内外研究现状,重点讨论了这类智能软材料以化学扩散为特征的热-电-化-力学耦合的基本理论和研宄方法。详细介绍了具有代表性的国内外主要研究团体的研究进展。阐述了基于热力学理论和哈密顿原理所建立的一般性热-电-化-力学多场耦合理论框架。针对等温过程的化学-力学耦合的本构关系和控制方程,证明了化学-力学耦合     

多孔介质的热-电-化-力学耦合理论及应用

本文针对自然界中不同种类的多孔介质,评述了包含化学效应的多场耦合力学问题的国外内研究现状.介绍了研究多场耦合问题的理论架构,并基于唯象理论和热力学理论,建立了一般性的热-电-化-力学多场耦合理论,在此基础上简化为化学-力学耦合理论,利用相应的控制方程和本构关系, 给出了线性耦合系统的变分原理,并证明了化学-力学耦合理论架构的封闭性. 基于所提出的化-力耦合模型,通过数值算例解释了多孔介质中的化学-力学耦合现象.最后对多孔介质,特别是对活体生物软组织中的多场耦合研究中存在的问题进行了讨论,并展望了本领域的未来发展趋势.     

离子交换膜金属复合材料力－电耦合变形数值模拟

本文基于电场-化学场-机械场耦合作用机理,采用数值模拟方法,研究离子交换膜金属复合材料(Ionic Polymer Metal Composites 简称IPMCs)宏观变形的细观机理。借用大型商业有限元软件ANSYS开发平台,结合MATLAB编制用户子程序,制定了数值分析流程,给出了典型IPMC悬臂梁宏观挠曲变形结果。文章重点研究了IPMC板迭层结构的输出力效率、金属电极层的厚度最佳值和非均匀挠曲变形细观机理的宏观分析方法,计算结果与实验比较以显示数值方法的正确性。文章的研究结果对材料工作者合理的制作IPMC致动器产品,具有理论指导意义。     

连续流式电泳浓度场的三维分析

本文研究含不同微粒的缓冲液通过方形连续流式电泳室时在横向电场作用下的分离问题,首次全面考虑了三维的温度场,速度场和浓度场的相互作用,通过数值模拟揭示了微重力环境及通常重力条件下各参数的影响。文中还提出一种拟三维算法,能使数值模拟的工作量大大减小而所得结果与三维算法的结果一致。     

力场-化学场耦合作用对含裂纹固体电解质力学行为的研究

为了研究力场-化学场耦合作用下的含裂纹电解质的断裂问题,本文构造了耦合情况下力场和浓度场的本构关系,并由这些本构关系建立了力场-化学场耦合问题的有限元方程。通过具体的算例,进一步探讨了裂纹尖端应力场和氧空位浓度分布的耦合作用对GDC(氧化钆掺杂的氧化铈)力学行为的影响,发现在耦合作用下,裂尖应力场对氧空位的分布有明显的诱导作用。     

两性pH敏感凝胶瞬态溶胀问题的基本方程和数值解

聚电解质两性凝胶的侧链有可电离的酸性和碱性基团,因其能对所处溶液环境的pH值产生响应,又可称作两性pH敏感凝胶．两性pH敏感凝胶属于超弹性材料,其变形问题涉及力学-化学耦合．同时,由于凝胶的变形伴随着溶剂分子的迁移,导致变形不能瞬间完成,故应研究两性pH敏感凝胶变形发展的全过程．由于其实用价值高,研究难度大,两性pH敏感凝胶的瞬态溶胀问题近年来引起了国内外众多研究人员的关注．本文以非线性连续介质力学理论和孔隙弹性理论为基础,结合电离平衡、唐南平衡等条件,获得了能描述两性pH敏感凝胶材料在外界激励下形变发展全过程的基本方程,探究了外加载荷、溶液pH值、盐溶液浓度等因素对两性pH敏感凝胶瞬态溶胀的影响,所得结果对该材料的应用有一定参考价值．     

Computational analysis of smart soft hydrogels subjected to pH-electrical coupled stimuli: Effects of initial geometry

A chemo-electro-mechanical formulation, referred to as the multi-effect-coupling pH-stimulus (MECpH) model, is presented in this paper for the analysis of the effects of the initial geometrical size on the responsive behavior of pH-sensitive hydrogels subject to the coupled stimuli of environmental solution pH and externally applied electric voltage. The model is composed of coupled nonlinear partial differential equations, and it accounts for the diffusion of ionic species, distributive electric potential and large mechanical deformation. In addition, the correlation between the diffusive hydrogen ion within the hydrogel and charge groups fixed to the polymeric network chains is incorporated quantitatively into this MECpH model. For the simulation of the response characteristics of the smart hydrogel, we solve the one-dimensional steady-state problem using the Hermite–Cloud meshless technique. For the MECpH model, the present numerical simulations were compared with experimental data available from literature to validate the accuracy and robustness of the model, and good agreement was observed. Several parameter studies were then carried out in the analysis of the hydrogel swelling when immersed in solution, and it was observed that the initial geometrical size has significant influence on the volume variations of these pH-responsive hydrogels.     

Effective Molecular Dynamics Model of Ionic Solutions for Large-Scale Calculations

A model of ionic solutions is proposed which can be used to calculate aqueous salt solutions in different nanostructures. The interaction potential of the model includes the Lennard-Jones potential and angularly averaged dipole–dipole and ion–dipole interactions. Lennard-Jones potential parameters for different ions are obtained. Characteristics of aqueous solutions at different salt concentrations are calculated using the molecular dynamics method. It is shown that the calculated values of the hydration shells of ions parameters are in good agreement with the theoretical and experimental data at a salt concentration of 1 mol/kg. The computational scheme used in the calculations is described. It is shown that calculations using the proposed model require less computing resources compared with the standard models of ionic solutions.     

Chemically induced swelling of hydrogels

We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the model involves a supplemental interfacial equation imposing configurational force balance. We present a hybrid eXtended-Finite-Element/Level-Set Method for obtaining approximate solutions to the governing equations of the model. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued to engineer hydrogels with optimal response times.     

Analytical Solution of Compression,Free Swelling and Electrical Loading of Saturated Charged Porous Media

Analytical solutions are derived for one-dimensional consolidation, free swelling and electrical loading of a saturated charged porous medium. The governing equations describe infinitesimal deformations of linear elastic isotropic charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.     

Kinetics of smart hydrogels responding to electric field: A transient deformation analysis

A multiphysics model is presented in this paper for simulation of kinetics of the smart hydrogels subject to an externally applied electric field, especially for analysis of the transient deformation of the hydrogel. The model termed the multi-effect-coupling electric stimulus (MECe) takes account of the coupled chemo-electro-mechanical multiphysics domains and the multi-phase effect of polymeric network and interstitial liquid as well as ionic species. The MECe model is validated well by transient simulation and comparison with available experimental data. Kinetics of ionic concentration of diffusive species is simulated. Parameter studies on the hydrogel displacement are conducted in detail for influences of externally applied electric voltage, initially fixed-charge density and surrounding bath solution concentration.     

Large deformation and electrochemistry of polyelectrolyte gels

Immersed in an ionic solution, a network of polyelectrolytes imbibes the solution and swells, resulting in a polyelectrolyte gel. The swelling is reversible, and the amount of swelling is regulated by ionic concentrations, mechanical forces, and electric potentials. This paper develops a field theory to couple large deformation and electrochemistry. A specific material model is described, including the effects of stretching the network, mixing the polymers with the solvent and ions, and polarizing the gel. We show that the notion of osmotic pressure in a gel has no experimental significance in general, but acquires a physical interpretation within the specific material model. The theory is used to analyze several phenomena: a gel swells freely in an ionic solution, a gel swells under a constraint of a substrate, electric double layer at the interface between the gel and the external solution, and swelling of a gel of a small size.     

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels. At a low temperature, uncrosslinked PNIPAM can be dissolved in water and form a homogenous liquid solution. When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer. Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel. When the temperature is changed, the hydrogel undergoes a phase transition: the amount of water in the hydrogel in equilibrium changes with temperature discontinuously. While the aqueous solution is a liquid and cannot sustain any nonhydrostatic stress in equilibrium, the hydrogel is a solid and can sustain nonhydrostatic stress in equilibrium. The nonhydrostatic stress can markedly affect various aspects of the phase transition in the hydrogel. We adopt the Flory-Rehner model, and show that the interaction parameter as a function of temperature and concentration obtained from the PNIPAM-water solution can be used to analyze diverse phenomena associated with the phase transition of the PNIPAM hydrogel. We analyze free swelling, uniaxially and biaxially constrained swelling of a hydrogel, swelling of a core-shell structure, and coexistent phases in a rod. The analysis is related to available experimental observations. Also outlined is a general theory of coexistent phases undergoing inhomogeneous deformation.     

Macroscopic Behavior of Swelling Porous Media Derived from Micromechanical Analysis

A new macroscopic model for swelling porous media is derived based on a rigorous upscaling of the microstructure. Considering that at the microscale the medium is composed of a charged solid phase (e.g. clay platelets, bio-macromolecules, colloidal or polymeric particles) saturated by a binary monovalent aqueous electrolyte solution composed of cations + and anions – of an entirely dissociated salt, the homogenization procedure is applied to scale up the pore-scale model. The microscopic system of governing equations consists of the local electro-hydrodynamics governing the movement of the electrolyte solution (Poisson–Boltzmann coupled with a modified Stokes problem including an additional body force of Coulombic interaction) together with modified convection–diffusion equations governing cations and anions transport. This system is coupled with the elasticity problem which describes the deformation of the solid phase. Novel forms of Terzaghi's effective principle and Darcy's law are derived including the effects of swelling pressure and osmotically induced flows, respectively. Micromechanical representations are provided for the macroscopic physico-chemical quantities.     

Transient analysis of temperature-sensitive neutral hydrogels

A model for transient deformation of neutral hydrogels that takes into account conservation of momentum, energy and mass for the solid polymer and fluid phase is derived, nondimensionalized and analyzed. Slow- and fast-response hydrogels are studied for three cases based on the response of (i) a spherical hydrogel, (ii) a constrained hydrogel slab to a step change in temperature, and (iii) the deformation in a temperature gradient. Model predictions for case (i) are shown to agree well with experiments for swelling and shrinking. For case (ii), solvent can be seen entering at the sides and flowing into the interior and towards the corners, such that the corners undergo a faster deformation than the sides. Immersed in a temperature gradient, case (iii), the hydrogel undergoes a bending motion and reaches a curved equilibrium shape, similar to the bending motion of polyelectrolyte hydrogels subjected to an external electric field. The benefit of the scale analysis conducted here, to predict correctly, prior to numerical computations, important characteristics such as stress, osmotic pressure and deformation times, is also highlighted.