Construction of polyconvex energies for non-trivial anisotropy classes
Construction of polyconvex energies for non-trivial anisotropy classes
复制标题
非平凡各向异性类的多凸能量的构造
DOI：
10.1007/978-3-7091-0174-2_4
复制
发表时间：
2010
影响因子：
5.3
通讯作者：
P. Neff
中科院分区：
文献类型：
--
作者：
V. Ebbing;J. Schröder;P. Neff
超弹性材料的行为可以很好地用多凸能量来描述，因为如果满足矫顽力条件，那么就保证了极小值的存在。我们概述了描述非平凡各向异性类的多凸能量的构造，即三斜、单斜、菱形、四边形、三角形和立方对称群，以及横向各向同性。材料的各向异性分别用右柯西-格林张量和特定的二阶和四阶结构张量的不变量来描述。为了证明所提出的多凸能量模拟实际各向异性材料行为的能力，我们重点研究了参考状态附近的四阶弹性张量与不同各向异性材料的实验数据的拟合。
Hyperelastic material behavior can be preferably described by using polyconvex energies, since the existence of minimizers is then guaranteed, if, in addition, the coercivity condition is satisfied. We give an overview of the construction of polyconvex energies for the description of non-trivial anisotropy classes, namely the triclinic, monoclinic, rhombic, tetragonal, trigonal and cubic symmetry groups, as well as transverse isotropy. The anisotropy of the material is described by invariants in terms of the right Cauchy-Green tensor and a specific second-order and a fourth-order structural tensor, respectively. To show the capability of the proposed polyconvex energies to simulate real anisotropic material behavior we focus on fittings of fourth-order elasticity tensors near the reference state to experimental data of different anisotropic materials.