论文标题
在二维线性弹性中的三孔问题上，在Quasiconvex船体上
On the quasiconvex hull for a three-well problem in two dimensional linear elasticity
论文作者
论文摘要
我们为对称的Quasiconvex hull $ q^e（\ MATHCAL {U}）$提供定量的内边界和外部边界，这是由三孔集生成的线性应变上的，三孔集$ \ MATHCAL {u} $ in $ \ MATHBB {r}在我们的研究中，我们考虑了三口井的所有可能兼容配置，并证明，如果存在$ \ MATHCAL {U} $中的两个矩阵，则是排名兼容的$ q^e（\ Mathcal {u}）$，与其对称的层压层层均匀的convex hull $ l^e（\ null $ l^e（\ Mathcalcal）$相吻合。我们通过在$ \ Mathcal {u} $中提供$ l^e（\ Mathcal {u}）$的明确表征（\ Mathcal {U}）$来完成此结果。最后，我们讨论了外部结合的最佳性及其与二次多凸功能的关系。
We provide quantitative inner and outer bounds for the symmetric quasiconvex hull $Q^e(\mathcal{U})$ on linear strains generated by three-well sets $\mathcal{U}$ in $\mathbb{R}^{2\times 2}_{sym}$. In our study, we consider all possible compatible configurations for three wells and prove that if there exist two matrices in $\mathcal{U}$ that are rank-one compatible then $Q^e(\mathcal{U})$ coincides with its symmetric lamination convex hull $L^e(\mathcal{U})$. We complete this result by providing an explicit characterization of $L^e(\mathcal{U})$ in terms of the wells in $\mathcal{U}$. Finally, we discuss the optimality of our outer bound and its relationship with quadratic polyconvex functions.
