The Anelastic Ericksen Problem: Universal Deformations and Universal Eigenstrains in Incompressible Nonlinear Anelasticity
The Anelastic Ericksen Problem: Universal Deformations and Universal Eigenstrains in Incompressible Nonlinear Anelasticity
复制标题
滞弹性埃里克森问题：不可压缩非线性滞弹性中的通用变形和通用特征应变
DOI：
10.1007/s10659-020-09797-2
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发表时间：
2020
影响因子：
2
通讯作者：
A. Goriely
中科院分区：
文献类型：
--
作者：
Christian Goodbrake;A. Yavari;A. Goriely
Ericksen的问题包括确定所有的平衡变形，可以维持单独的应用程序的边界牵引任意不可压缩的各向同性超弹性材料的无应力配置是几何平坦的。我们首先使用该问题的几何公式来推广这一点，以表明所有已知的通解关于特殊欧几里得群的李群对称。其次，我们将这个问题扩展到它的滞弹性版本，其中的无应力配置的身体是一个黎曼流形。物理上，这种情况对应于非平凡有限本征应变的情况。我们明确描述了共享对称性存在于经典问题的普遍本征应变，并表明，在本征应变的存在下，六个已知的经典家庭的普遍解决方案合并成三个不同的滞弹性家庭，区分其特定的对称群。这些族的某些通解对应于众所周知的滞弹性本征应变的情况。此外，我们发现，其中一些家庭拥有一个分支的异常解决方案，并证明这些解决方案的独特功能和平衡应力，他们产生。
Ericksen’s problem consists of determining all equilibrium deformations that can be sustained solely by the application of boundary tractions for an arbitrary incompressible isotropic hyperelastic material whose stress-free configuration is geometrically flat. We generalize this by first, using a geometric formulation of this problem to show that all the known universal solutions are symmetric with respect to Lie subgroups of the special Euclidean group. Second, we extend this problem to its anelastic version, where the stress-free configuration of the body is a Riemannian manifold. Physically, this situation corresponds to the case where nontrivial finite eigenstrains are present. We characterize explicitly the universal eigenstrains that share the symmetries present in the classical problem, and show that in the presence of eigenstrains, the six known classical families of universal solutions merge into three distinct anelastic families, distinguished by their particular symmetry group. Some generic solutions of these families correspond to well-known cases of anelastic eigenstrains. Additionally, we show that some of these families possess a branch of anomalous solutions, and demonstrate the unique features of these solutions and the equilibrium stress they generate.
影响因子：
2.4
作者：
RODRIGUEZ, EK;HOGER, A;MCCULLOCH, AD
通讯作者：
MCCULLOCH, AD