拉普拉斯拉伸：欧拉公式和拉格朗日公式
Laplace Stretch: Eulerian and Lagrangian Formulations
摘要：
研究了变形梯度张量的两种三角分解。第一，称为拉格朗日公式，由一个上三角形拉伸premultiplied旋转张量。第二，称为欧拉制定，由一个下三角形拉伸postmultiplied由不同的旋转张量。相应的拉伸张量分别表示为拉格朗日和欧拉拉普拉斯拉伸。分析和比较了每种制剂的运动学（物理解释）和工作共轭应力测量。虽然拉格朗日公式已被用于各向异性和超弹性材料的本构建模的前期工作，欧拉公式，这可能是有利的建模各向同性固体和流体没有物理上可识别的参考配置，似乎没有被用于其他地方的连续力学设置。
英文摘要：
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.
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