On the analytic expression of the free energy in linear viscoelasticity

Two definitions of free energy for a linear viscoelastic material, due to Graffi and to Coleman and Owen, are considered, and the compatibility of these definitions with some expressions of the free energy proposed in the literature is examined. For the expressions of Staverman and Schwarzl and of Breuer and Onat, the two definitions are proved to be equivalent, and the set of all relaxation functions for which the two expressions are indeed free energies is determined. Two more expressions, proposed by Volterra and Graffi and by Morro and Vianello, are taken into consideration. For them, only the classes of relaxation functions for which they are free energies according to the first definition, is completely characterized. All results are established under regularity assumptions weaker than those usually made in the literature.     

含瓦斯煤的内时本构关系及其参数的实验研究

根据含瓦斯煤的力学实验结果，采用内蕴时间塑性理论建立了含瓦斯煤的本构关系，给出了本构关系中材料参数的确定方法，并进行了实验验证。     

拉－扭复合加载下不锈钢的弹塑性本构关系——Ⅱ．理论

提出应力是塑性应变空间内蕴几何学参数的泛函．一般情况下，塑性应变空间是非欧几何空间，而其度量张量是塑性应变和其历史的函数，但在初始各向同性和不可压的情况下可取成欧氏空间．本文在Ｉｌｙｕｓｈｉｎ理论，和Ｖａｌａｎｉｓ理论的基础上，提出在拉－扭复合加载下的εｐ１－εｐ３空间中新的积分型弹塑性本构关系，所建理论预测的结果和实验［１］相当一致，表明理论是合理的     

Differentiability Properties of Rotationally Invariant Functions

Let f be a function on the set Lin of all tensors (= square matrices) on a vector space of arbitrary dimension. If f is rotationally invariant (with respect to the left and right multiplication by proper orthogonal tensors), it has a representation through a symmetric even function of the signed singular values of the tensor argument A∈Lin. It is shown that f is of class C ^r ,r=0,1,...,∞, if and only if is of class C ^r , and an inductive formula is given for the derivatives D ^r f. This revised version was published online in August 2006 with corrections to the Cover Date.     

非线性粘弹理论中的单积分型本构关系

本文综述了非线性粘弹理论中的单积分本构表达,评述了多种有代表性的单积分型非线性粘弹理论,对几种本构方程加以分析比较,以揭示它们的内涵,明了其非线性表述原理。      

A note on the Cauchy relations

The Cauchy relations originated in the context of the molecular theory of elasticity. Assuming them implies a reduction of the independent elastic constants which characterize the constitutive tensor in the linear anisotropic case. This paper brings to light a property of the elastic tensor through its decomposition into a symmetric part and into a skew part in the 2nd and 3rd indices. The skew part, which vanishes if and only if the Cauchy relations hold, is connected with a self-equilibrated stress field. The isotropic case is examined as a particular example.

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Sommario Le relazioni di Cauchy ebbero origine nell'ambito della teoria molecolare dell'elasticità; la loro assunzione implica una riduzione delle costanti elastiche indipendenti che caratterizzano il tensore costitutivo nel caso anisotropo lineare. In questa breve nota si mette in luce una proprietà del tensore elastico attraverso la sua decomposizione in una parte simmetrica ed in una antisimmetrica nel 2° e 3° indice: la parte antisimmetrica, che risulta nulla se e solo se valgono le relazioni di Cauchy, è associata ad un campo di tensioni autoequilibrate. Si analizza, come caso particolare, il caso isotropo.

     

Notes on the X-ray Theory

My aim is to better compare thermoelasticity theory with a continuum theory of X-ray observations of crystals, to be described, to make it easier to adapt ideas and techniques from one to the other. To this end, I will present some different ways of formulating the X-ray theory. Also, I will adapt symmetry considerations from the former, partly to analyze problems of a kind not considered in thermoelasticity theory. This revised version was published online in August 2006 with corrections to the Cover Date.     

材料生长与变形的连续介质模型:弹性本构方程

本文着重探讨了生长变形体连续介质理论中的本构模型。首先列出了描述生长变形体能量平衡的微分方程以及熵不等式；以此为基础，通过将密度演化的历史作为独立的本构变量扩展了理性力学的因果性公理与决定性公理，具体而详细地推导了简单材料的生长弹性本构方程，给出了这些本构方程中的相关本构变量之间的约束不等式，得到了“生长变形体的自由能与其密度成反比”的结论，并从热力学上对这一结果进行了定性的解释。最后，文中对几个尚待解决的问题进行了说明，并指出了今后的发展方向。     

拉－扭复合加载下不锈钢的弹塑性本构关系——Ⅱ．理论

提出应力是塑性应变空间内蕴几何学参数的泛函．一般情况下，塑性应变空间是非欧几何空间，而其度量张量是塑性应变和其历史的函数，但在初始各向同性和不可压的情况下可取成欧氏空间．本文在Ｉｌｙｕｓｈｉｎ理论，和Ｖａｌａｎｉｓ理论的基础上，提出在拉－扭复合加载下的εｐ１－εｐ３空间中新的积分型弹塑性本构关系，所建理论预测的结果和实验［１］相当一致，表明理论是合理的     

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。      

Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics: II. Constitutive Theory

In Part I macroscopic field equations of mass, linear and angular momentum, energy, and the quasistatic form of Maxwell's equations for a multiphase, multicomponent medium were derived. Here we exploit the entropy inequality to obtain restrictions on constitutive relations at the macroscale for a 2-phase, multiple-constituent, polarizable mixture of fluids and solids. Specific emphasis is placed on charged porous media in the presence of electrolytes. The governing equations for the stress tensors of each phase, flow of the fluid through a deforming medium, and diffusion of constituents through such a medium are derived. The results have applications in swelling clays (smectites), biopolymers, biological membranes, pulsed electrophoresis, chromotography, drug delivery, and other swelling systems.     

Mathematical modeling of magnetorheological fluids

Magnetorheological (MR) fluids are a class of smart materials whose rheological properties may be rapidly modified by the application of a magnetic field. These materials typically consist of micron-sized ferrous particles dispersed in a fluid. In the present paper, we consider the full system of equations as well as the Clausius-Duhem inequality for moving isotropic MR fluids in an electro-magnetic field. We present the material constitutive relations for a non-Newtonian incompressible MR fluid. To illustrate the validity of the constitutive relations, the flow of a MR fluid between two parallel fixed plates under the influence of a constant magnetic field perpendicular to the flow direction is considered.Received: 14 July 2003, Accepted: 18 May 2004, Published online: 22 February 2005 Correspondence to: A. Dorfmann     

A semi-analytical method for structure-internal liquid interaction problems

A composite structure-internal liquid element is proposed in this paper. Through the use of analytical functions in two orthogonal directions, the three-dimensional problem of coupled structure-internal liquid vibration is reduced to a one-dimensional one, resulting in a drastic reduction in computing efforts.Cylindrical and conical frastum composite elements are proposed to suit different problems, and examples are presented to demonstrate the accuracy of the method.     

Integral constitutive equations of elastic-plastic materials

In this paper the integral constitutive equations of elastic-plastic materials are studied. The endochronic theory can be deduced from this theory. It is shown that the endochronic should be selected compatible with the yield function of the calssical plasticity and this can be considered as a principle of selecting endochronic. Applying this principle the appropriate endochronics of the plastically compressible materials and the orthotropic materials are derived. The second approximate theory of the integral constitutive equation is also discussed in this paper.This paper was reported by the National Natural Science Foundation of China.     

The recoil of rigid PVC

Polyvinyl chloride (PVC) is widely used in industry, but it is difficult to find any extensive discussion of theological relations that describe it. The present paper discusses the behaviour of rigid PVC in extensional deformations at various temperatures. In the tests, a step elongation was applied at an initial time, then after a delay the specimen was cut, permitting recoil. Both linear and nonlinear strain regimes were studied; the linear relaxation properties (relaxation function, storage modulus) were cross-checked with eccentric-disk measurements. In the non-linear strain regime a single-integral constitutive equation of the KBKZ Wagner type was used. Separability of time and strain effects was demonstrated in our tests and so a damping function could be found which was only a function of strain. Video recordings of recoil were made, and detailed predictions of the strain-time behaviour were checked against experiments.Various constitutive equation proposals were used in the comparison, and the separated kernel integral irreversible model performed reasonably well; some other models of a differential type, and a Doi-Edwards model were not as accurate.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Some Considerations on Modeling Heat and Mass Transfer in Porous Media

In this paper some considerations are presented about the equations needed to set up a model of the process of heat and mass transfer in porous media. A clear classification is made of the various types of equations used and of their physical meaning. Special attention is paid to the thermodynamic equilibrium equations and to their derivation since they are too often taken for granted. The importance of the various transport mechanisms (of mass and energy) is analyzed and the consequences that can arise when some term is neglected are indicated.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)-NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed. Foundation items: the National Natural Science Foundation of China (59678003); Special Research Plan of the Education Department of Shaanxi Province (01JK178) Biographies: HUANG Yi (1936-) ZHANG Yin-ke (1964-)