论文标题
平面各向同性弹性的尖锐排名呈添加体积分裂
Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split
论文作者
论文摘要
我们考虑平面各向同性超弹性中的体积分裂，并对这种情况进行精确分析，这表明Legendre-Hadamard椭圆度条件分离并在适当的意义上进行了简化。从Knowles和Sternberg的经典二维标准开始，我们可以将排名一的凸度的条件减少到一个一维耦合差异不平等的家庭。特别是，这使我们能够为$ w（f）= \fracμ{2} \ frac {\ lvert f \ rvert f \ rvert^2} {\ det f} {\ det f}+f（\ det f（\ det f）;当且仅当功能$ f $是凸的时，这种能量是排名一号的凸。
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.
