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首页> 外文期刊>International Journal of Solids and Structures >A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point
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A new 3-D finite element for nonlinear elasticity using the theory of a Cosserat point

机译：基于Cosserat点理论的新型3D非线性弹性有限元

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The theory of a Cosserat point has been used to formulate a new 3-D finite element for the numerical analysis of dynamic problems in nonlinear elasticity. The kinematics of this element are consistent with the standard tri-linear approximation in an eight node brick-element. Specifically, the Cosserat point is characterized by eight director vectors which are determined by balance laws and constitutive equations. For hyperelastic response, the constitutive equations for the director couples are determined by derivatives of a strain energy function. Restrictions are imposed on the strain energy function which ensure that the element satisfies a nonlinear version of the patch test. It is shown that the Cosserat balance laws are in one-to-one correspondence with those obtained using a Bubnov-Galerkin formulation. Nevertheless, there is an essential difference between the two approaches in the procedure for obtaining the strain energy function. Specifically, the Cosserat approach determines the constitutive coefficients for inhomogeneous deformations by comparison with exact solutions or experimental data. In contrast, the Bubnov-Galerkin approach determines these constitutive coefficients by integrating the 3-D strain energy function using the kinematic approximation. It is shown that the resulting Cosserat equations eliminate unphysical locking, and hourglassing in large compression without the need for using assumed enhanced strains or special weighting functions. (C) 2003 Elsevier Ltd. All rights reserved. [References: 34]
机译：Cosserat点的理论已被用来制定一个新的3-D有限元，用于非线性弹性动力学问题的数值分析。该单元的运动学与八节点砖单元中的标准三线性近似一致。具体来说，Cosserat点的特征是八个指向矢矢量，这些矢量由平衡定律和本构方程确定。对于超弹性响应，指向矢对的本构方程由应变能函数的导数确定。对应变能函数施加了限制，以确保元素满足补丁测试的非线性版本。结果表明，Cosserat平衡定律与使用Bubnov-Galerkin公式获得的定律一一对应。尽管如此，两种方法在获得应变能函数的过程中还是有本质的区别。具体而言，Cosserat方法通过与精确解或实验数据进行比较来确定非均匀变形的本构系数。相反，Bubnov-Galerkin方法通过使用运动学近似对3-D应变能函数进行积分来确定这些本构系数。结果表明，由此产生的Cosserat方程消除了非物理性的锁定，并消除了大气压下的沙漏，而无需使用假定的增强应变或特殊的加权函数。 （C）2003 Elsevier Ltd.保留所有权利。 [参考：34]

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