Resarch on Elasto-Plastic Material with Microstructures

介绍了微孔塑性材料在有限变形范围内的方向和滑移矢量。从理论上讨论了该理论与弹性耦合应力理论及高阶应变梯度理论的关系。建立了考虑耦合应力的塑性材料的本构关系，并推导了一个速率型本构方程的实例，其中屈服条件不仅取决于通常的柯西应力，而且取决于耦合应力。为了得到实际微结构材料本构方程的进一步数学形式，我们采用孔洞材料（即多孔材料）作为微结构材料的模型，并对多孔板的弹塑性行为进行了实验研究。实验得到的具有准随机分布孔洞的穿孔板的屈服应力可以用一位研究者提出的各向异性屈服函数进行近似模拟。利用立体学方法和狄利克雷镶嵌法对孔洞分布进行评价，可以定量地分析孔洞间距对塑性变形的影响。这意味着这里提出的程序可能成为评估具有微观结构的材料的整体塑性性能的有用工具，尽管需要进一步的检查来精确描述穿孔板的各向异性行为。

Directors and slip vectors were introduced to the theory of plastic materials with microsturcutes in the rage of the finite deformation. The relation between the proposed theory and the couple stress thory of elasticity together with the higher order strain gradient theory was discussed thoretically. The constitutive relation considering couple stress for plastic materials was also developed and an example of the rate-type constitutive equation was derived, where the yeild condition depends on not only the usual Cauchy stress but also the couple stress.To obtain the further mathematical form of constitutive equations for the real material with microstructures, we adopted the material with voids (i.e.porous material) as a model of materials with microstructures and the elastic-plastic behavior of perforated sheets were investigated experimentally.The yield stresses of perforated sheets with quasi-randomly distributed holes experimentally obtained can be simulated in the first approximation by the anisotropic yield function proposed by one of investigators. Evaluating the void distribution by the stereological method together with the use of Dirichlet tessellation, the effect of void spacing during plastic deformation can be treated quantitatively. This means that the procedure proposed here may become a useful tool for evaluating the overall plastic property of the material with microstructures, though a further examination will be necessary for precise description of the resulting anisotropic behavior of perforated sheets.