超弹性材料的不稳定性问题

INSTABILITY PROBLEMS FOR HYPER-ELASTIC MATERIALS

超弹性材料是一类性能独特、不可替代且有广泛工程应用的高分子材料,对其独特的材料不稳定性问题的研究极大地推动了连续介质力学有限变形理论和超弹性理论的发展。综述了超弹性材料中的材料不稳定性问题的研究成果和最新进展,包括Rivlin立方块问题、薄壁球壳和薄壁圆筒的内压膨胀问题、圆柱的扭转问题、块体的表面不稳定性问题、空穴的生成、增长和闭合问题等。阐述了这类材料中各类非线性不稳定性问题的特点、问题的求解、主要结果及今后进一步的研究方向等。

Hyper-elastic materials are a kind of irreplaceable macromolecule materials with unique characteristics and wide applications. Researches on the unique instability problems of hyper-elastic materials have greatly promoted the development of finite deformation and hyper-elastic theory in the field of continuum mechanics. Various instability problems for hyper-elastic materials are reviewed in this paper, such as the Rivlin cube problem, inflation of thin-walled cylindrical tubes and thin-walled spherical shells, torsional instability of cylindrical tubes, surface instability of compressed or bent blocks, the formation of void and the sudden growth and collapse of void. The characteristics and solution methods are then analyzed for this nonlinear problem of material instability, and finally, main results and future developments are given and discussed.