论文标题
拉普拉斯拉伸：欧拉和拉格朗日配方
Laplace Stretch: Eulerian and Lagrangian Formulations
论文作者
论文摘要
研究了两个变形梯度张量的三角分解。第一个称为拉格朗日配方，由旋转张量的高三角形伸展运动组成。第二个称为Eulerian配方，由一个由不同的旋转张量的下三角形拉伸组成。相应的伸展张量分别表示为拉格朗日和欧拉拉普拉斯拉伸。分析了运动学（具有物理解释）和工作共轭应力度量，并为每种配方进行比较。虽然Lagrangian公式已用于先前的工作中，用于对各向异性和超\弹性材料的组成型建模，但欧拉制剂（Eulerian Fiquaration）对于对各向同性固体的建模可能是有利的，并且没有物理上可识别的参考配置，但似乎并未在连续机械设置中使用其他位置。
Two triangular factorizations of the deformation gradient tensor are studied. The first, termed the Lagrangian formulation, consists of an upper-triangular stretch premultiplied by a rotation tensor. The second, termed the Eulerian formulation, consists of a lower-triangular stretch postmultiplied by a different rotation tensor. The corresponding stretch tensors are denoted as the Lagrangian and Eulerian Laplace stretches, respectively. Kinematics (with physical interpretations) and work conjugate stress measures are analyzed and compared for each formulation. While the Lagrangian formulation has been used in prior work for constitutive modeling of anisotropic and hyper\-elastic materials, the Eulerian formulation, which may be advantageous for modeling isotropic solids and fluids with no physically identifiable reference configuration, does not seem to have been used elsewhere in a continuum mechanical setting.
