论文标题
非线性各向同性弹性的增量体积模量，Young的模量和泊松比：物理上合理的响应
The incremental bulk modulus, Young's modulus and Poisson's ratio in nonlinear isotropic elasticity: physically reasonable response
论文作者
论文摘要
定义了用于有限各向同性弹性的增量（或切线）大量模量，该模量定义了，将静水压力的增量与相对体积的相应增量进行比较。它的积极性为涉及应变能函数的第二个衍生物的物理响应提供了严格的标准。同样，通过将当前应力与相对体积变化进行比较，可以定义平均（或叶）的大量模量。该批量模量的积极性提供了一个物理合理的响应标准，比前者更严格。增量体积模量的概念扩展到各向异性弹性。对于单轴张力的状态，对于非线性各向同性弹性的增量泊松比和增量幼型模量的定义类似，并且具有与增量体积模量相似的性能。考虑了不可压缩性，贝尔，埃里克森和恒定面积的各向同性约束的增量泊松比。对于可压缩的新霍克固体的特定示例，对增量模量进行了评估。假定为阳性的基态拉美弹性模量的边界足以保证所有菌株的增量体积和杨氏模量的阳性。但是，尽管基态泊松比为阳性，但我们发现增量泊松比在足够大的轴向扩展中变为负。
An incremental (or tangent) bulk modulus for finite isotropic elasticity is defined which compares an increment in hydrostatic pressure with the corresponding increment in relative volume. Its positivity provides a stringent criterion for physically reasonable response involving the second derivatives of the strain energy function. Also, an average (or secant) bulk modulus is defined by comparing the current stress with the relative volume change. The positivity of this bulk modulus provides a physically reasonable response criterion less stringent than the former. The concept of incremental bulk modulus is extended to anisotropic elasticity. For states of uniaxial tension an incremental Poisson's ratio and an incremental Young's modulus are similarly defined for nonlinear isotropic elasticity and have properties similar to those of the incremental bulk modulus. The incremental Poisson's ratios for the isotropic constraints of incompressibility, Bell, Ericksen, and constant area are considered. The incremental moduli are all evaluated for a specific example of the compressible neo-Hookean solid. Bounds on the ground state Lamé elastic moduli, assumed positive, are given which are sufficient to guarantee the positivity of the incremental bulk and Young's moduli for all strains. However, although the ground state Poisson's ratio is positive we find that the incremental Poisson's ratio becomes negative for large enough axial extensions.
