欧拉共轭应力应变
Eulerian conjugate stress and strain
摘要：
新的结果，提出了共轭的应力任意欧拉应变措施。共轭应力取决于两个任意量：应变测度f（V）和由自旋Ω定义的共转速率。它表明，对于每一个选择的f有一个唯一的自旋，称为f-自旋，这使得共轭应力尽可能接近柯西应力。当应变测量为Hencky应变log（V）时，f自旋减少到对数自旋。公式和结果强调了欧拉和拉格朗日应力分别与应变f（V）和f（U）共轭形式的相似性。许多结果涉及方程AX-XA=Y的解，该解以简洁的格式呈现。
英文摘要：
New results are presented for the stress conjugate to arbitrary Eulerian strain measures. The conjugate stress depends on two arbitrary quantities: the strain measure f(V) and the corotational rate defined by the spin Ω. It is shown that for every choice of f there is a unique spin, called the f-spin, which makes the conjugate stress as close as possible to the Cauchy stress. The f-spin reduces to the logarithmic spin when the strain measure is the Hencky strain log(V). The formulation and the results emphasize the similarities in form of the Eulerian and Lagrangian stresses conjugate to the strains f(V) and f(U), respectively. Many of the results involve the solution to the equation AX-XA=Y, which is presented in a succinct format.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
