Constitutive Modelling of Resins in the Stiffness Domain

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.     

粘弹性本构模型的准静力位移识别

对一类边界条件，建立粘弹性准静力位移与本构参数的显式关系，给出优化识别的叠代格式，从二阶微分模型出发，识别粘弹性本构模式，讨论了信息误差对反演结果的影响     

Constitutive model of ferroelectric composites with a viscoelastic and dielectric relaxation matrix I

Based on micromechanics and Laplace transformation, a constitutive model of ferroelectric composites with a linear elastic and linear dielectric matrix is developed and extended to the ferroelectric composites with a viscoelastic and dielectric relaxation matrix. Thus, a constitutive model for ferroelectric composites with a viscoelastic and dielectric relaxation matrix has been set up Project supported by the National Natural Science Foundation of China (Grant No. 19891180).     

非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程

通过对非饱和土非线性本构方程和场方程的线性化，推导出了非饱和土的线性本构方程和场方程，把线性方程表示为与Biot饱和多孔介质方程相似的形式；证明了Darcy定律对非饱和土的适用性；说明了Biot饱和多孔介质方程是这些线性方程的特征。所有这些都表明用混合理论处理非饱和土本构问题的正确性。     

Constitutive models of ferroelectric composites with a viscoelastic and dielectric relaxation matrix (II)

Experimental analysis of ferroelectric composites with a viscoelastic and dielectric relaxation matrix is carried out, and the electromechanical coupling behavior of the ferroelectric composites is calculated by means of the constitutive model proposed in this paper. Comparisons between the experimental results and the calculations show that the constitutive model can reflect the electromechanical coupling behavior of the ferroelectric composites. The analysis indicates that the effect of viscoelasticity and dielectric relaxation of the matrix on the electromechanical coupling behavior of ferroelectric composites cannot be neglected.     

昆虫翼拍动中受载变形的粘弹性本构模型

昆虫翼拍动受载时发生被动变形,被看作为有助于改善飞行性能的机制之一．决定这种被动变形大小的一个关键因素是昆虫翼的材料本构关系,至今缺乏研究．基于蜻蜓翼(离体)的应力松弛实验和模型翼拍动时受载变形的有限元数值分析,揭示了粘弹性本构关系是昆虫翼材料性能的合理描述,并研究了粘弹性参数对被动变形的影响．     

Modelling an anomalous stress relaxation in glassy polymers (the Kitagawa effect)

Constitutive relations are derived for the nonlinear viscoelastic response of glassy polymers. The model is based on the concept of adaptive links (a version of the theory of transient networks), where the rates of annihilation of active links are determined by the Eyring formula. Adjustable parameters in the constitutive equations are found by using experimental data for a polyester resin in standard relaxation tests. The stress-strain relations are applied to describe an anomalous stress relaxation in solid polymers observed in tensile test after strain reversal (the Kitagawa effect). Qualitative agreement is demonstrated between results of numerical simulation and observations.     

一种考虑聚醚醚酮（PEEK）不同力学状态的本构模型

聚醚醚酮（简称PEEK）以其优良的性能而广泛应用于高端机械、 核工程和航空等科技领域.为了描述其在应变、应变率和温度3种因素作用下的力学行为,依据PEEK在不同温度下呈现的3种力学状态,在著名的JC(Johnson Cook)本构模型的基础上,提出了针对高分子不同力学状态的分段JC本构模型.与传统JC模型及文献中改进JC模型相比,提出的分段JC模型能够更精确地表征PEEK在中高温下的力学行为,为PEEK在复合材料中的应用和分析奠定了理论基础.     

单轴作用下岩土材料的双重介质本构模型

基于弹塑性力学和损伤力学理论,将岩土材料视为孔隙-裂隙双重介质,假设孔隙介质不发生损伤,而裂隙介质随应变的增加发生损伤,建立了单轴作用下岩土类材料的双重介质本构模型隐式表达式,并利用Newton迭代法得出了材料的全程应力-应变曲线．分析结果表明,岩土材料中裂隙空间展布的多态性（均匀展布、集中展布和随机展布）是岩土材料本构关系千变万化的根本原因．由于双重介质本构模型将岩土材料的弹性主体（孔隙介质部分）和损伤主体（裂隙介质部分）分化开来,对于研究岩土或含损伤材料的破坏具有实用价值和理论意义．     

Constitutive modeling of void-growth-based tensile ductile failures with stress triaxiality effects

In most metals and alloys, the evolution of voids has been generally recognized as the basic failure mechanism. Furthermore, stress triaxiality has been found to influence void growth dramatically. Besides strain intensity, it is understood to be the most important factor that controls the initiation of ductile fracture. We include sensitivity of stress triaxiality in a variational porous plasticity model, which was originally derived from hydrostatic expansion. Under loading conditions rather than hydrostatic deformation, we allow the critical pressure for voids to be exceeded so that the growth due to plasticity becomes dependent on the stress triaxiality. The limitations of the spherical void growth assumption are investigated. Our improved constitutive model is validated through good agreements with experimental data. Its capacity for reproducing realistic failure patterns is also indicated by a numerical simulation of a compact tensile (CT) test.     

基于形变晶粒增殖过程的弹塑性本构模型*

本文根据多晶金属变形的细观过程特征,将形变晶粒分为三类.提出塑性形变晶粒增殖的概念,并由此导出较为简洁的弹塑性本构关系.能对若干实验结果给出合理的解释.表明材料的宏观屈服、率相关和加工硬化等现象与形变晶粒演化的动力学过程密切相关.     

基于内变量理论的电流变液本构关系

研究了电流变液的微结构本构关系.其理论框架是基于内变量理论和机理的分析.电流变液是由高介电常数的颗粒悬浮在某种液体中组成的.在电场作用下,极化的颗粒将沿着电场方向聚集在一起形成链状结构.颗粒聚集体的大小和方向将随外加电场和应变率的变化进行调整,因而可以通过建立起能量守恒方程和力平衡方程来确定颗粒聚集体的大小和方向的变化.那么,一个三维的、清晰的本构关系可以由相互作用能和系统的耗散能导出.具体考虑和讨论了在简单剪切载荷作用下的系统响应,发现电流变液的切变剪薄粘滞系数同系统Mason数之间近似于幂指数∝(Mn)-082的关系.     

散射理论中多连通域的混合边值问题

本文讨论了散射理论中的Helmholtz方程在多连通域中的Dirichlet-Neumann-第三混合边值问题.文章建立了与此边值问题对应的积分方程组,并讨论了此问题解的性质及对应的积分方程零空间的性质.     

Near-surface buckling in stability of a system consisting of a moderately rigid substrate, a viscoelastic bond layer, and an elastic covering layer

Within the frame work of the three-dimensional linearized theory of stability of deformable bodies (TLTSDB), the near-surface buckling instability of a system consisting of a half-plane (substrate), a viscoelastic bond layer, and an elastic covering layer is suggested. The equations of the TLTSDB are obtained from the three-dimensional geometrically non linear equations of viscoelasticity theory by using the boundary-form perturbation technique. By employing the Laplace transform, a method for solving the problem is developed. It is supposed that the covering layer has an insignificant initial imperfection. The stability of the system is considered lost if the imperfection starts to increase and grows indefinitely. Numerical results for the critical compressive force and the critical time are presented. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 517–530, July–August, 2006.     

幂律非线性粘弹性材料中的裂纹扩展*

对蠕变不可压幂律非线性粘弹性材料中裂纹的蠕变扩展进行了分析,为描述银纹带中的力学行为,假设在裂纹尖端邻域中断裂过程区中分布着阻抗裂纹张开的粘聚应力б_f,.通过对均匀应力参考状态平凡解的摄动,将非线性粘弹性问题化成线性问题处理.对于幂指数.n≌1的弱非线性情况得到了应力与位移表达式.提出断裂过程区局域能量判据,导出了裂纹孕育时间t*与蠕变扩展率a的预测公式.     

Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.     

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

A theorem of the Dore-Venni type for noncommuting operators

A theorem of the Dore-Venni type for the sum of two closed linear operators is proved, where the operators are noncommuting but instead satisfy a certain commutator condition. This result is then applied to obtain optimal regularity results for parabolic evolution equations and evolutionary integral equations which are nonautonomous. The domains of the involved operators may depend on , but is required to satisfy a certain smoothness property. The results are then applied to parabolic partial differential and integro-differential equations.