动载荷下不可压缩超弹性球形薄膜的若干定性性质

对于由横观各向同性不可压缩的Rivlin-Saunders材料组成的球形薄膜,研究了薄膜的内、外表面在周期阶梯载荷作用下的轴对称变形的非线性动力学特性.通过令球形结构的厚度趋近于1,得到了近似描述薄膜径向对称运动的二阶非线性常微分方程.详细讨论了解的定性性质.特别地,给出了球形薄膜随时间的运动产生非线性周期振动的可控性条件,证明了在某些情形下周期振动的振幅会出现"∞"型同宿轨道以及周期振动的振幅会出现不连续增长现象,并给出了相应的数值模拟.

АГ-Convergence Result for Thin Curved Films Bonded to a Fixed Substrate with a Noninterpenetration Constraint

The behavior of a thin curved hyperelastic film bonded to a fixed substrate is described by an energy composed of a nonlinearly hyperelastic energy term and a debonding interracial energy term. The author computes the Г-limit of this energy under a noninterpenetration constraint that prohibits penetration of the film into the substrate without excluding contact between them.