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171.
Jeremiah G. Murphy 《Journal of Elasticity》2007,86(2):139-154
The form of the classical stress–strain relations of linear elasticity are considered here within the context of nonlinear
elasticity. For both Cauchy and symmetric Piola-Kirchhoff stresses, conditions are obtained for the associated strain fields
so that they are independent of the material constants and compatible with existence of a strain–energy function. These conditions
can be integrated in both cases to obtain the most general strain field that satisfies these conditions and the corresponding
strain–energy function is obtained. In both cases, a natural choice of form of solution is suggested by the special case of
the compatibility conditions being satisfied identically. It will be shown that some strain–energy functions previously introduced
in the literature are special cases of the results obtained here. Some recent linear stress–strain relations, proposed in
the context of Cauchy elasticity, are examined to see if they are compatible with hyperelasticity.
相似文献
172.
A note on line forces in gradient elasticity 总被引:2,自引:1,他引:2
The theory of gradient elasticity is applied to line forces. Line forces acting on a point within the body and a concentrated normal force (Flamant problem) which acts on a half plane are studied. Closed analytical solutions which have a simple form are obtained for displacement fields of these forces. The gradient elasticity solutions are free from undesirable displacement singularities predicted by classical elasticity. 相似文献
173.
A. E. Alekseev 《Journal of Applied Mechanics and Technical Physics》2005,46(2):291-298
The stability problem of a centrally compressed infinite plate is solved with allowance for the transverse normal deformation caused by uniform load for various boundary conditions at the edges. The linearized nonlinear equations of elastic deformation of thin plates taking into account transverse shear and transverse normal deformation are used. The obtained critical loads are compared with existing solutions.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 170–178, March–April, 2005. 相似文献
174.
Continuous and integrable solutions and one-to-one relationships between boundary forces and displacements are found through the direct integration of the differential equations of the plane elastic problem for a half-plane with boundary conditions for either forces or displacements or with mixed boundary conditions. The necessary equilibrium conditions for forces and the compatibility conditions for displacements that ensure the correctness of the solutions are formulated 相似文献
175.
本文就薄板后屈曲问题建立一组新型的边界元计算公式,用这组公式求解能方便处理各种边界问题,另外文中将面内应力分解成基本部份和附加部份,并利用微分算子分解理论导得了挠度的一个不同形式的基本解,由于计算公式中,实现了面内位移和挠度的解耦,从而使迭代过程得到简化,文末还对圆板后屈曲路径进行了计算,得到了满意的结果。 相似文献
176.
The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant
end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an
inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates
of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation
with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth
functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop
a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial
differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the
influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit
optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and,
in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
177.
Arturas Suchodolskis Vidmantas Feiza Arunas Stirke Ana Timonina Almira Ramanaviciene Arunas Ramanavicius 《Surface and interface analysis : SIA》2011,43(13):1636-1640
Chemical pretreatment is widely used to facilitate transformation of living cells when foreign components are introduced into a cell through the cell wall. The influence of appropriate chemicals on the wall properties and mechanism of transformation is still a matter of intensive studies. Saccharomyces cerevisiae cells (also known as baker's yeast) were investigated by atomic force microscopy (AFM). The cell walls were modified by lithium acetate and dithiothreitol. The AFM imaging was performed in liquid water‐based environment. The living cells were fixed by trapping into the holes of a polycarbonate membrane. Mechanical and morphological properties of initial intact cells and treated cells were investigated. The increased stiffness of the chemically treated cells was observed. As deduced from the applied theoretical Hertz‐Sneddon model, the treated cells show completely different response mechanism to applied mechanical pressure in comparison with the intact cells. Also, the increased roughness of the cell wall of the treated yeasts was observed. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
178.
179.
180.
The molecular basis for rubber elasticity is arguably the oldest and one of the most important questions in the field of polymer physics. The theoretical investigation of rubber elasticity began in earnest almost a century ago with the development of analytic thermodynamic models, based on simple, highly-symmetric configurations of so-called Gaussian chains, i.e. polymer chains that obey Markov statistics. Numerous theories have been proposed over the past 90 years based on the ansatz that the elastic force for individual network chains arises from the entropy change associated with the distribution of end-to-end distances of a free polymer chain. There are serious conceptual objections to this assumption and others, such as the assumption that all network nodes undergo a simple volume-preserving linear motion and that all of the network chains have the same length. Recently, a new paradigm for elasticity in rubber networks has been proposed that is based on mechanisms that originate at the molecular level. Using conventional statistical mechanics analyses, Quantum Chemistry, and Molecular Dynamics simulations, the fundamental entropic and enthalpic chain extension forces for polyisoprene (natural rubber) have been determined, along with estimates for the basic force constants. Concurrently, the complex morphology of natural rubber networks (the joint probability density distributions that relate the chain end-to-end distance to its contour length) has also been captured in a numerical model (EPnet). When molecular chain forces are merged with the network structure in this model, it is possible to study the mechanical response to tensile and compressive strains of a representative volume element of a polymer network. As strain is imposed on a network, pathways of connected taut chains, that completely span the network along strain axis, emerge. Although these chains represent only a few percent of the total, they account for nearly all of the elastic stress at high strain. Here we provide a brief review of previous elasticity theories and their deficiencies, and present a new paradigm with an emphasis on experimental comparisons. 相似文献