On stress-based piecewise elasticity for limited strain extensibility materials

A one-dimensional stress-based elasticity model with limited strain extensibility is developed in this paper, based on thermodynamics arguments. Such nonlinear elastic models can be used to model certain rubber-like and biological materials with limiting chain extensibility. The derived constitutive function is a non-smooth piecewise expression, which can be regularized for numerical or physical considerations. This non-smooth constitutive expression is derived from a Gibbs potential. A three-dimensional extension of this stress-based model is also proposed in the paper. Some simple structural examples are investigated for a bar composed of this non-smooth elastic body. A homogeneous bar composed of this new class of nonlinear elastic material that is loaded is studied for different tension states, namely for concentrated or distributed axial loading. It is shown that the displacement limit extensibility can be observed at the structural scale, with finite or infinite axial load parameters.     

Model networks of end-linked polydimethylsiloxane chains

Summary Elastomeric networks of high extensibility were prepared by end-linking mixtures of vinyl-terminated polydimethylsiloxane chains having molecular weights of approximately 600 and 11,000 g mol^–1, with silanes chosen to give junction functionalities ranging from 3 to 8. The resulting bimodal networks were studied in elongation, at 25 °C, to their rupture points, and in swelling equilibrium in benzene at room temperature. The elongation moduli [f ^*] were found to be in satisfactory agreement with previous results obtained by end-linking hydroxyl-terminated polydimethylsiloxane chains. Values of [f ^*] at low and moderate deformations gave relatively low values of the ratio of elasticity constants 2C ₂/2C ₁, which is a measure of the extent to which the elongation changes from approximately affine to nonaffine as the elongation increases. The low values obtained for this ratio are presumably due to diminished interpenetration of configurational domains in the case of very short chains. In spite of its small magnitude, 2C ₂/2C ₁ does show some decrease with increase in , as predicted by the recent molecular theory of rubberlike elasticity developed by Flory. The swelling equilibrium results were also found to be in satisfactory agreement with theory. The elongation moduli increased significantly at high elongations, and the values of the elongation at which the upturn was first discernible were very nearly independent of , This is consistent with the interpretation of this anomalous behaviour in terms of limited chain extensibility. The maximum extensibility generally decreased somewhat with increase in and this caused a decrease in both the ultimate strength and the toughness of the elastomer, as measured by the energy required for rupture.     

Finite extensibility and orientational effects in rubbers. A physical interpretation of the ‘van der Waals equation’ for the elastic force

We propose a physical interpretation of the so-called van der Waals equation of state for rubbers, which gives a relation between the force and the deformation. On a phenomenological basis this equation takes the finite extensibility and a non-defined interaction into account. Here the fininte extensibility is discussed for the dilute case (no entanglements) and the highly entangled limit. The intramolecular interactions are described by orientational effects. The resulting equation of state for the force shows the same features as the van der Waals equation.Dedicated to Prof. H.-G. Kilian on the occasion of his 60th birthday.     

Analytical solution of partial differential equations for radial transport of a solute in double porous media

The mathematical model for radial transport of a solute is summed up in this paper. The action of non-equilibrium linear adsorption, the double property of porous media and the decay of solute are considered. With the first kind of boundary condition, one finds the analytical solution of these equations by Laplace transform and calculates the dimensionless solution by FORTRAN program with DJS-040. The distribution and change of solute are evaluated and the solution under various limit cases is given. By numerical analysis, one obtains some valuable conclusions.     

Hierarchical atom type definitions and extensible all‐atom force fields

The extensibility of force field is a key to solve the missing parameter problem commonly found in force field applications. The extensibility of conventional force fields is traditionally managed in the parameterization procedure, which becomes impractical as the coverage of the force field increases above a threshold. A hierarchical atom‐type definition (HAD) scheme is proposed to make extensible atom type definitions, which ensures that the force field developed based on the definitions are extensible. To demonstrate how HAD works and to prepare a foundation for future developments, two general force fields based on AMBER and DFF functional forms are parameterized for common organic molecules. The force field parameters are derived from the same set of quantum mechanical data and experimental liquid data using an automated parameterization tool, and validated by calculating molecular and liquid properties. The hydration free energies are calculated successfully by introducing a polarization scaling factor to the dispersion term between the solvent and solute molecules. © 2015 Wiley Periodicals, Inc.     

纳米复合水凝胶的力学行为与刺激响应性

纳米复合水凝胶（nanocomposite hydrogels,NC凝胶）由于其简便的制备方法、独特的组成、优异的力学性能、高光学透明度以及良好的溶胀/去溶胀性等,引起了广泛的关注.近年来,本课题组在NC凝胶的力学行为及刺激响应性NC凝胶的制备方面取得了可喜的研究成果.观察到新合成的和溶胀平衡的聚N-异丙基丙烯酰胺（PNIPAm）-锂藻土LaponiteNC凝胶的超拉伸性,发现了在大应变下的应变硬化现象;发现利用Mooney-Rivlin方程可以描述NC凝胶的压缩应力-应变,但不能描述较大的应变硬化;Creton模型能很好地描述NC凝胶在大形变下的应力-应变曲线,特别是凝胶的应变硬化;从NC凝胶小应变下的平衡剪切模量得到了有效交联密度,观察到NC凝胶形变-回复过程的迟滞现象,测定了NC凝胶的松弛指数.我们认为NC凝胶具有超拉伸性的原因是其较低的交联密度和适度的松弛速率;在响应性NC凝胶的制备方面,发现了溶胶型Laponite的水分散液的稳定窗口,避免了加入离子性单体引起的聚集沉淀;通过共聚制备了具有超拉伸性、pH响应或温度和pH双响应的透明NC凝胶.本文主要综述了我们课题组在NC凝胶力学行为及响应性NC凝胶领域的一些研究进展,并分析了NC凝胶研究领域仍然未解决的科学问题,以及今后可能的发展方向.     

Pure Axial Shear of Isotropic, Incompressible Nonlinearly Elastic Materials with Limiting Chain Extensibility

The purpose of this research is to investigate the pure axial shear problem for a circular cylindrical tube composed of isotropic hyperelastic incompressible materials with limiting chain extensibility. Two popular models that account for hardening at large deformations are examined. These involve a strain-energy density which depends only on the first invariant of the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The stress fields and axial displacements are characterized for each of these models. Explicit closed-form analytic expressions are obtained. The results are compared with one another and with the predictions of the neo-Hookean model. This revised version was published online in August 2006 with corrections to the Cover Date.     

土地资源的可拓性及优化配置系统结构模型

本文应用可拓学的理论和方法，对土地资源的特征及优化配置原理进行分析，设计了优化配置系统结构模型，为土地资源的优化配置和合理利用提供了一种新的科学方法。     

A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids

We consider an incompressible nonlinearly elastic material in which a matrix is reinforced by strong fibers, for example fibers of nylon or carbon aligned in one family of curves in a rubber matrix. Rather than adopting the constraint of fiber inextensibility as has been previously assumed in the literature, here we develop a theory of fiber-reinforced materials based on the less restrictive idea of limiting fiber extensibility. The motivation for such an approach is provided by recent research on limiting chain extensibility models for rubber. Thus the basic idea of the present paper is simple: we adapt the limiting chain extensibility concept to limiting fiber extensibility so that the usual inextensibility constraint traditionally used is replaced by a unilateral constraint. We use a strain-energy density composed with two terms, the first being associated with the isotropic matrix or base material and the second reflecting the transversely isotropic character of the material due to the uniaxial reinforcement introduced by the fibers. We consider a base neo-Hookean model plus a special term that takes into account the limiting extensibility in the fiber direction. Thus our model introduces an additional parameter, namely that associated with limiting extensibility in the fiber direction, over previously investigated models. The aim of this paper is to investigate the mathematical and mechanical feasibility of this new model and to examine the role played by the extensibility parameter. We examine the response of the proposed models in some basic homogeneous deformations and compare this response to those of standard models for fiber reinforced rubber materials. The role of the strain-stiffening of the fibers in the new models is examined. The enhanced stability of the new models is then illustrated by investigation of cavitation instabilities. One of the motivations for the work is to apply the model to the biomechanics of soft tissues and the potential merits of the proposed models for this purpose are briefly discussed.