Resarch on Elasto-Plastic Material with Microstructures

在有限变形范围内，将指向矢和滑移矢量引入微结构塑性材料理论。从理论上讨论了该理论与弹性偶应力理论和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本构关系，导出了一个速率型本构方程的算例，其中的屈服条件不仅取决于通常的柯西应力，还取决于偶应力。为了得到实际材料微观结构本构方程的进一步数学形式，我们采用含孔洞的材料(即多孔材料)作为微结构材料的模型，对穿孔板材的弹塑性行为进行了实验研究。实验得到的含准随机分布孔洞的穿孔板材的屈服应力可用研究者提出的各向异性屈服函数在一次近似下模拟。用体视学方法评价孔洞分布，结合Dirichlet剖分，可以定量地处理塑性变形中孔洞间距的影响。这意味着，这里提出的方法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，尽管有必要进行进一步的检验以精确地描述由此产生的穿孔薄板的各向异性行为。

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.