界面位错双相材料杆理论的推导
Derivation of a rod theory for biphase materials with dislocations at the interface
摘要：
从三维弹性力学出发，导出了在界面处有预定位错的双相材料的杆理论。假设存储的能量密度是非负的，并且在由SO（3）的两个副本组成的集合上为零。首先，我们严格证明了位错在界面的假设。然后，我们考虑多相材料的典型标度，我们进行了渐近研究的重新标度的能量，杆的直径为零，在$Γ$收敛的框架。
英文摘要：
Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies of SO(3). First, we rigorously justify the assumption of dislocations at the interface. Then, we consider the typical scaling of multiphase materials and we perform an asymptotic study of the rescaled energy, as the diameter of the rod goes to zero, in the framework of $Γ$-convergence.
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