Theoretical Study of Finite Deformations of Elastic Materials having Internal Constraints.

1.不可展(保长)弹性材料有限变形理论的发展。(1)建立了平面问题的分析方法，解决了一些截面突变梁的挠度问题。(2)对于不同荷载作用下的梁，明确了变形、应力和奇异应力的一些方面。此外，我们还讨论了它们的断裂模式。(3)确定了奇异应力面的结构，得到了有限变形和增量变形的平衡方程。(4)明确了弹性静力冲击的结构和产生的条件。此外，我们还从能量消耗的角度对其进行了讨论。不可膨胀(保面积)弹性材料有限变形理论的发展。(1)我们考察了生物膜的本构关系，发现其中一些可以用不可膨胀的内部约束来近似表达。(2)建立了保面积材料的运动学模型，得到了反应应力的表达式。(3)讨论了反应应力及其平衡。(4)我们证明了平面问题可以用类似于保长度材料的方法来处理。对于轴对称问题，我们提出了基本控制方程和求解方法。

1. Development of the Theory of Finite Deformations of Inextensible(Length-Preserving) Elastic Materials.(1)We established the method of analysis of plane problems and solved some problems of the deflection of beams whose cross-section changes abruptly. (2)For these beams under various loads, we made clear some aspects of deformations, stresses, and singular stresses. Furthermore, we discussed their fracture modes. (3)We determined the structure of singular stress surface; we obtained their equilibrium equations for finite deformations as well as incremental deformations. (4)We made clear the structure of elastostatic shocks and conditions for their appearance. Furthermore, we discussed it in terms of energy dissipation.2. Development of the Theory of Finite Deformations of Inexpansible(Area-Preserving) Elastic Materials.(1)We examined the constitutive relations of bio-membranes and found that some of them were approximately expressible in terms of the internal constraint to inexpansibility. (2)We developed the kinematics of area-preserving materials and obtained the expressions for reaction stresses. (3)We discussed the reaction stresses and their equilibria. (4)We showed that plane problems could be treated in the similar way as those for length-preserving materials. For axisymmetric problems, we proposed the basic governing equations and the method of solution.