感性材料与结构化学—力学耦合行为分析模型及多尺度计算方法研究
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摘要
含羞草、向日葵和捕蝇草等高等植物根据外界不定向刺激产生明显而迅速的局部运动称为感性运动。在此运动中,植物结构内部的细胞通过细胞膜的离子传输通道将化学能转化为细胞间的膨压运动所需要的机械能,起着天然的作动器作用。利用植物的感性运动的作动机理,可仿生合成一类新型智能形状自适应材料——感性材料(nastic material)。实验表明该类智能材料可提供均衡的促动力、位置和频带宽度,且具有较高的能量密度。感性材料在研究高性能形状自适应智能作动器以及靶向药物载体等方面具有重要的应用价值。目前,国内外针对仿生植物运动的感性材料的研究正处于起步阶段。因此,相关的研究具有重要的学术意义和工程应用前景。
本文首先建立感性材料与结构化学与力学相结合的多物理场耦合分析模型。感性材料由基体材料夹杂封闭液体腔组成,液体腔壁上包含人工合成的细胞膜,该膜上嵌有负责各类物质的跨膜传输的离子传输通道,如离子泵、离子通道、离子协运机制等。本研究先从感性运动机理出发,从单个胞元的感性结构角度,研究感性材料响应过程中内部离子分布以及结构的力学响应,以验证本文所采用的膜离子传输模型结合基体结构的力学模型的多场耦合模型的有效性,并通过调节离子传输模型的模型参数以及其它初始环境参数如溶质浓度等,讨论这些参数对感性结构瞬态响应的影响。在此基础上,建立多感性胞元相互作用的耦合分析模型,并给出了计算结果。
由于感性胞元尺度小、数量多,造成感性材料与结构具有多尺度特征。这类多尺度材料在预测其性能方面往往面临着实验分析或者数值模拟上的困难。鉴于此,本文针对感性材料中作动单元周期性分布的特点,建立感性材料与结构分析的两尺度模型,求解带有液体腔膨胀特征的感性胞元等效力学参数；在此基础上,结合细胞膜生物离子传输模型,建立了感性材料与结构的耦合两尺度计算方法。
其次,本文提出含液闭合多孔材料力学分析的二维扩展多尺度有限元法。含液闭孔材料是指包括感性材料在内由闭合多孔液体腔微结构组合而成的多功能材料。研究工作发现,由于液体的不可压缩特性,采用普通四节点矩形粗网格单元的扩展多尺度有限元方法计算含液闭孔材料时,往往会出现较强的单元边界效应,从而造成计算结果误差较大。为解决此类问题,本文发展了高阶粗网格单元及其数值基函数构造方法,可有效提高扩展多尺度有限元的计算精度。为进一步提升精度,本文提出周期边界条件来构造粗网格的数值基函数,并设计一致性检测方法验证该边界条件的合理及有效性。检测结果表明,采用周期性边界条件求解数值基函数可使扩展多尺度有限元方法和常规数值均匀化方法保持良好的一致性。
进一步,本文提出感性材料与结构力学分析的三维扩展多尺度有限元法,并发展三维高阶粗网格技术及与之对应的二次周期边界条件基函数构造方法。在此基础上,结合生物离子传输模型,发展了感性材料与结构的耦合三维扩展多尺度有限元方法,以同时求解膜离子传输过程和结构瞬态变形响应。数值算例表明,本文发展的耦合扩展多尺度有限元方法具有很高的计算精度和效率,能有效地预测感性材料的各性能参数实时变化情况,且能方便进行降尺度分析,求解感性材料细观尺度上的结构瞬态响应。
此外,本文提出基于非规则多边形粗网格单元的扩展多尺度有限元法。该方法消除了传统的多尺度有限元方法中仅能采用规则单元作为粗网格单元的局限性；同时,根据材料的细观微尺度特征将非均质材料区域划成多边形粗网格单元,有利于提高多尺度有限元法模拟该类非均质问题的精度。在此方法中,首先采用线性边界条件求解多边形粗单元的数值基函数；其次,结合常规有限元中的多边形单元有理形函数技术,发展了基于有理函数的超样本边界条件技术用于提高多边形扩展多尺度有限元的计算精度。在此基础上,本文发展了混合扩展多尺度有限元方法,即将常规有限元和多边形扩展多尺度有限元方法结合到同一个计算模型中。该方法对结构内部具有多尺度特征的局域采用扩展多尺度有限元网格处理,而对于边界非规则区域以及需要额外关注点,如应力集中点等,直接采用细尺度有限元方法进行网格划分,兼顾了计算效率和精度。
最后,本文基于扩展多尺度有限元方法提出含液闭孔结构多尺度优化设计方法,以研究含液闭孔胞元尺寸、布局以及内部液体腔体积膨胀值分布对整体含液闭孔结构力学性能的影响。首先提出了含液闭孔材料的结构形状及载荷一体化多尺度优化算法。该多尺度优化算法以结构中含液胞元的细观上尺寸如液体腔半径和载荷(液腔中液体体积增量)为设计变量,以结构的宏观力学响应为目标进行优化。进一步,本文发展了含液闭孔结构的多尺度拓扑优化方法。该多尺度拓扑优化方法首先以结构最小柔顺性为优化目标,采用类似SIMP模型对结构的宏观粗网格等效刚度阵进行插值,建立含液闭孔结构柔顺性的拓扑优化列式：最后,针对含液闭孔材料能够利用胞体内部液体腔体积增量产生结果变形的特性,提出含液闭孔材料柔性机构的设计方法,以结构指定位置方向输出位移为目标,建立液体体积膨胀作用下的含液闭孔柔性机构多尺度拓扑优化数学模型。基于自主软件平台SiPESC完成了相关程序研发,并数值验证了本文发展的多尺度优化方法的有效性。
In the natural world, some plants like the Mimosa, Sunflower and venus Flytrap, can generate localized movements in response to external environmental stimuli through a biological process named nastic motion. In this motion, the biolocical ion transport makes the water to flow into or out of the motor cells imbedded in the structure, which can be regard as the muscles of the biological system. With these inspirations, a novel biomimetic smart material, i.e. a nastic material, has been developed to design advanced actuators in recent year. The nastic materials are considerd to be high energy density actuators that convert chemical energy stored in bio-fuels to generate mechanical forces. Researches indicate that the nastic materials can not be only ultisized to design high-performance shape adaptive smart actuators, but also be ideal for biomedical application such as targeted vaccine delivery. Howerver, nastic materials are still a new phenomenon, and the accessible literatures about nastic materials are still sparse. So, the related investigations will be of great importance for theoretical procgress and engineering applications.
Firstly, a coupled Chemo-mechanical model is developed to simulate the mechanical and biological response of the nastic materials and structure. The nastic material considered is composed of closed liquid cell structures and synthetic membranes. Many types of biological channels, such as the ion pumps, ion channels and ion cotransporters, are embedded within the membrane to transport the species across it. Based on the theory of the nastic movement, we firstly study the mechanical response of the matric and the whole process of the ion transporting of the membrane based on a single nastic actuator. The aim is to validate the effectiveness of the coupled multiphysical model developed. Furthermore, we studied the sensitivities of the various input parameters, such as the initial solute concentrations, which have a big influence on the deformation and response time of the nastic actuators. At last, we developed a new coupled model to perform the mechanical analysis of the nastic structures with multi-actuators, and some numerical results are given to validate the models developed.
Due to the fact that the nastic mateirals generally consist of a large number of micro actuators, it is always a difficult task to perform the multiphysical simulation of the nastic structures by the general numerical methods or the classic experiments. To overcome these difficulties, we establish a two-scale model to calculate the nastic structures with microcapsules periodically distributed inside in. The effective coefficients of the nastic unit cells with closed fluid inclusion inside, such as the effective elastic constants and the effective bending properties, is numerically calculated with the homogenization analysis. With these coefficients, we developed a coupled two-scale model (CTSM), which combining the two-scale model with the biological ion transport model mentioned above, to simulate the transient multiphical response of the nastic structures with multiscale features.
Secondly, an extended multiscale finite element method (EMsFEM) is proposed for the mechanical analysis of the closed liquid cell materials. This tpye of functional materials contained microscopic fluid filled inclusions and the nastic materials are a special case of them. Due to the fact that the fluid inside the close cells general imcompressible, the strong boundary effects will be indueced and the errors of the results will become larger when the conventional four-node quadrilateral coarse-grid elements are utlized in the EMsFEM. Thus, a type of higher order coarse-grid elements which are more reasonable and can predicate the structural deformation more accurately of the closed liquid cells are developed. Moreover, the periodic boundary conditions (PBCs), which are inspired by the PBCs used in the homogenization method (the RVE method), are proposed to constructe the numerical base functions of the coarse-grid elements. A consistency test is carried out to validate the new boundary conditions, and the numerical results indicate that a good consistency can be obtained between the macroscopic coarse element constructed by the MEsFEMs with PBCs and the element generated by the conventional homogenization method.
Furthermore, a3D extended multiscale finite element method (3D-EMsFEM), is developed to perform the mechanical analysis of nastic structures which periodically consists of the microcapsules. Accordingly, the techniques of the high order coarse-grid element and the corresponding high order PBCs, are introduced for the construction of the numerical base functions and improve the accuracy of the3D-EMsFEM.. Furthermore, a Coupled EMsFEM (CEMsFEM) which combines the ion transport model is proposed to predicate the active response of the nastic structures. The results indicate that the coupled method developed not only can track the reactions of the ion transporters of the active membrane, but also can calculate the transient mechanical response on the fine scale with the downscaling computation.
On the other hand, an EMsFEM is developed to solve the mechanical behaviours of heterogeneous materials with randomly distributed polygonal microstructure. To improve the accuracy of the method, a type of rational oversampling technique is imposed to calculate the oscillatory boundary conditions for the construction of multiscale base functions. A mixed extended multiscale finite element method, which combines the EMsFEM and the standard FEM into a same model, is developed. In the method, the regions with multiscale features are modeled by the multiscale coarse-grid, while the region without multiscale features or the domains that need a high-precision computation are directly meshed by the general finite elements.
At last, a new multiscale shape and topology optimization method is presented to design the closed liquid cell materials based on the EMsFEM. The multiscale optimization method firstly focuses on seeking the optimum geometrical parameters of the closed liquid cells at the microscale in terms of maximize the macroscale mechanical response of the structure. Moreover, based on the EMsFEM, a multiscale topology optimization method is further developed to optimize the distributions of closed liquid cells with objective on minimize system compliance. In this topology optimization method, the design domain is discretized by the multiscale coarse elements, while a SIMP-based density approach is employed to interpolate the equivalent stiffness matrix of the coarse-grid element. Ultimately, due to the fact that non-uniform volume expansions of the fluid in cells can induce the elastic action, the multiscale topology optimization method is extended to design biomimetic compliant actuators of the closed liquid cell materials. The multiscale optimization methods developed are implemented in the FE-package SiPESC, and numerical examples are carried out to validate the accuracy of these methods.
本文首先建立感性材料与结构化学与力学相结合的多物理场耦合分析模型。感性材料由基体材料夹杂封闭液体腔组成,液体腔壁上包含人工合成的细胞膜,该膜上嵌有负责各类物质的跨膜传输的离子传输通道,如离子泵、离子通道、离子协运机制等。本研究先从感性运动机理出发,从单个胞元的感性结构角度,研究感性材料响应过程中内部离子分布以及结构的力学响应,以验证本文所采用的膜离子传输模型结合基体结构的力学模型的多场耦合模型的有效性,并通过调节离子传输模型的模型参数以及其它初始环境参数如溶质浓度等,讨论这些参数对感性结构瞬态响应的影响。在此基础上,建立多感性胞元相互作用的耦合分析模型,并给出了计算结果。
由于感性胞元尺度小、数量多,造成感性材料与结构具有多尺度特征。这类多尺度材料在预测其性能方面往往面临着实验分析或者数值模拟上的困难。鉴于此,本文针对感性材料中作动单元周期性分布的特点,建立感性材料与结构分析的两尺度模型,求解带有液体腔膨胀特征的感性胞元等效力学参数；在此基础上,结合细胞膜生物离子传输模型,建立了感性材料与结构的耦合两尺度计算方法。
其次,本文提出含液闭合多孔材料力学分析的二维扩展多尺度有限元法。含液闭孔材料是指包括感性材料在内由闭合多孔液体腔微结构组合而成的多功能材料。研究工作发现,由于液体的不可压缩特性,采用普通四节点矩形粗网格单元的扩展多尺度有限元方法计算含液闭孔材料时,往往会出现较强的单元边界效应,从而造成计算结果误差较大。为解决此类问题,本文发展了高阶粗网格单元及其数值基函数构造方法,可有效提高扩展多尺度有限元的计算精度。为进一步提升精度,本文提出周期边界条件来构造粗网格的数值基函数,并设计一致性检测方法验证该边界条件的合理及有效性。检测结果表明,采用周期性边界条件求解数值基函数可使扩展多尺度有限元方法和常规数值均匀化方法保持良好的一致性。
进一步,本文提出感性材料与结构力学分析的三维扩展多尺度有限元法,并发展三维高阶粗网格技术及与之对应的二次周期边界条件基函数构造方法。在此基础上,结合生物离子传输模型,发展了感性材料与结构的耦合三维扩展多尺度有限元方法,以同时求解膜离子传输过程和结构瞬态变形响应。数值算例表明,本文发展的耦合扩展多尺度有限元方法具有很高的计算精度和效率,能有效地预测感性材料的各性能参数实时变化情况,且能方便进行降尺度分析,求解感性材料细观尺度上的结构瞬态响应。
此外,本文提出基于非规则多边形粗网格单元的扩展多尺度有限元法。该方法消除了传统的多尺度有限元方法中仅能采用规则单元作为粗网格单元的局限性；同时,根据材料的细观微尺度特征将非均质材料区域划成多边形粗网格单元,有利于提高多尺度有限元法模拟该类非均质问题的精度。在此方法中,首先采用线性边界条件求解多边形粗单元的数值基函数；其次,结合常规有限元中的多边形单元有理形函数技术,发展了基于有理函数的超样本边界条件技术用于提高多边形扩展多尺度有限元的计算精度。在此基础上,本文发展了混合扩展多尺度有限元方法,即将常规有限元和多边形扩展多尺度有限元方法结合到同一个计算模型中。该方法对结构内部具有多尺度特征的局域采用扩展多尺度有限元网格处理,而对于边界非规则区域以及需要额外关注点,如应力集中点等,直接采用细尺度有限元方法进行网格划分,兼顾了计算效率和精度。
最后,本文基于扩展多尺度有限元方法提出含液闭孔结构多尺度优化设计方法,以研究含液闭孔胞元尺寸、布局以及内部液体腔体积膨胀值分布对整体含液闭孔结构力学性能的影响。首先提出了含液闭孔材料的结构形状及载荷一体化多尺度优化算法。该多尺度优化算法以结构中含液胞元的细观上尺寸如液体腔半径和载荷(液腔中液体体积增量)为设计变量,以结构的宏观力学响应为目标进行优化。进一步,本文发展了含液闭孔结构的多尺度拓扑优化方法。该多尺度拓扑优化方法首先以结构最小柔顺性为优化目标,采用类似SIMP模型对结构的宏观粗网格等效刚度阵进行插值,建立含液闭孔结构柔顺性的拓扑优化列式：最后,针对含液闭孔材料能够利用胞体内部液体腔体积增量产生结果变形的特性,提出含液闭孔材料柔性机构的设计方法,以结构指定位置方向输出位移为目标,建立液体体积膨胀作用下的含液闭孔柔性机构多尺度拓扑优化数学模型。基于自主软件平台SiPESC完成了相关程序研发,并数值验证了本文发展的多尺度优化方法的有效性。
In the natural world, some plants like the Mimosa, Sunflower and venus Flytrap, can generate localized movements in response to external environmental stimuli through a biological process named nastic motion. In this motion, the biolocical ion transport makes the water to flow into or out of the motor cells imbedded in the structure, which can be regard as the muscles of the biological system. With these inspirations, a novel biomimetic smart material, i.e. a nastic material, has been developed to design advanced actuators in recent year. The nastic materials are considerd to be high energy density actuators that convert chemical energy stored in bio-fuels to generate mechanical forces. Researches indicate that the nastic materials can not be only ultisized to design high-performance shape adaptive smart actuators, but also be ideal for biomedical application such as targeted vaccine delivery. Howerver, nastic materials are still a new phenomenon, and the accessible literatures about nastic materials are still sparse. So, the related investigations will be of great importance for theoretical procgress and engineering applications.
Firstly, a coupled Chemo-mechanical model is developed to simulate the mechanical and biological response of the nastic materials and structure. The nastic material considered is composed of closed liquid cell structures and synthetic membranes. Many types of biological channels, such as the ion pumps, ion channels and ion cotransporters, are embedded within the membrane to transport the species across it. Based on the theory of the nastic movement, we firstly study the mechanical response of the matric and the whole process of the ion transporting of the membrane based on a single nastic actuator. The aim is to validate the effectiveness of the coupled multiphysical model developed. Furthermore, we studied the sensitivities of the various input parameters, such as the initial solute concentrations, which have a big influence on the deformation and response time of the nastic actuators. At last, we developed a new coupled model to perform the mechanical analysis of the nastic structures with multi-actuators, and some numerical results are given to validate the models developed.
Due to the fact that the nastic mateirals generally consist of a large number of micro actuators, it is always a difficult task to perform the multiphysical simulation of the nastic structures by the general numerical methods or the classic experiments. To overcome these difficulties, we establish a two-scale model to calculate the nastic structures with microcapsules periodically distributed inside in. The effective coefficients of the nastic unit cells with closed fluid inclusion inside, such as the effective elastic constants and the effective bending properties, is numerically calculated with the homogenization analysis. With these coefficients, we developed a coupled two-scale model (CTSM), which combining the two-scale model with the biological ion transport model mentioned above, to simulate the transient multiphical response of the nastic structures with multiscale features.
Secondly, an extended multiscale finite element method (EMsFEM) is proposed for the mechanical analysis of the closed liquid cell materials. This tpye of functional materials contained microscopic fluid filled inclusions and the nastic materials are a special case of them. Due to the fact that the fluid inside the close cells general imcompressible, the strong boundary effects will be indueced and the errors of the results will become larger when the conventional four-node quadrilateral coarse-grid elements are utlized in the EMsFEM. Thus, a type of higher order coarse-grid elements which are more reasonable and can predicate the structural deformation more accurately of the closed liquid cells are developed. Moreover, the periodic boundary conditions (PBCs), which are inspired by the PBCs used in the homogenization method (the RVE method), are proposed to constructe the numerical base functions of the coarse-grid elements. A consistency test is carried out to validate the new boundary conditions, and the numerical results indicate that a good consistency can be obtained between the macroscopic coarse element constructed by the MEsFEMs with PBCs and the element generated by the conventional homogenization method.
Furthermore, a3D extended multiscale finite element method (3D-EMsFEM), is developed to perform the mechanical analysis of nastic structures which periodically consists of the microcapsules. Accordingly, the techniques of the high order coarse-grid element and the corresponding high order PBCs, are introduced for the construction of the numerical base functions and improve the accuracy of the3D-EMsFEM.. Furthermore, a Coupled EMsFEM (CEMsFEM) which combines the ion transport model is proposed to predicate the active response of the nastic structures. The results indicate that the coupled method developed not only can track the reactions of the ion transporters of the active membrane, but also can calculate the transient mechanical response on the fine scale with the downscaling computation.
On the other hand, an EMsFEM is developed to solve the mechanical behaviours of heterogeneous materials with randomly distributed polygonal microstructure. To improve the accuracy of the method, a type of rational oversampling technique is imposed to calculate the oscillatory boundary conditions for the construction of multiscale base functions. A mixed extended multiscale finite element method, which combines the EMsFEM and the standard FEM into a same model, is developed. In the method, the regions with multiscale features are modeled by the multiscale coarse-grid, while the region without multiscale features or the domains that need a high-precision computation are directly meshed by the general finite elements.
At last, a new multiscale shape and topology optimization method is presented to design the closed liquid cell materials based on the EMsFEM. The multiscale optimization method firstly focuses on seeking the optimum geometrical parameters of the closed liquid cells at the microscale in terms of maximize the macroscale mechanical response of the structure. Moreover, based on the EMsFEM, a multiscale topology optimization method is further developed to optimize the distributions of closed liquid cells with objective on minimize system compliance. In this topology optimization method, the design domain is discretized by the multiscale coarse elements, while a SIMP-based density approach is employed to interpolate the equivalent stiffness matrix of the coarse-grid element. Ultimately, due to the fact that non-uniform volume expansions of the fluid in cells can induce the elastic action, the multiscale topology optimization method is extended to design biomimetic compliant actuators of the closed liquid cell materials. The multiscale optimization methods developed are implemented in the FE-package SiPESC, and numerical examples are carried out to validate the accuracy of these methods.
引文
[1]姚康德,成国祥.智能材料[M].北京：化学工业出版社.
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