平面各向同性弹性体中可加体积-等容分裂的锐秩一凸性条件
Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split
摘要：
考虑了平面各向同性超弹性中的体积-等容分裂，并对这种情况下的秩一凸性准则进行了精确的分析，表明Legendre-Hadamard椭圆性条件在适当的意义下是分离和简化的.从Knowles和Sternberg经典的二维判别准则出发，将秩一凸性的条件化为一族一维耦合微分不等式.特别是，这使我们能够推导出一个简单的秩一凸分类的广义哈达玛能量的类型$W(F)=\fracμ{2}\frac{\lVert F\rVert^2}{\det F}+f(\det F)$ ;这样的能量是秩一凸的当且仅当函数$f$是凸的。
英文摘要：
We consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-Hadamard ellipticity condition separates and simplifies in a suitable sense. Starting from the classical two-dimensional criterion by Knowles and Sternberg, we can reduce the conditions for rank-one convexity to a family of one-dimensional coupled differential inequalities. In particular, this allows us to derive a simple rank-one convexity classification for generalized Hadamard energies of the type $W(F)=\fracμ{2}\frac{\lVert F\rVert^2}{\det F}+f(\det F)$; such an energy is rank-one convex if and only if the function $f$ is convex.
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。
