CAJ | 학술논문

基于细观力学，建立颗粒材料的宏观应力-应变与接触力、接触位移、枝矢量等细观量之间的关系。用改进的Voronoi-Delaunay法对颗粒材料进行几何和物理上划分，得到改进Bagi双胞元体系；以固体胞元为基础，运用牛顿第二定律和Gauss定理提出含有旋转矢量和重力的颗粒材料平均等效应力，避免了颗粒材料的准静态假设；在孔隙胞元区域内利用变形协调条件推导出含有孔隙面矢量等几何变量的颗粒材料平均等效应变。结合文献的二维颗粒材料宏观试验结果验证了双胞元平均等效应力-应变的正确性；在三维情形下，对比双胞元等效应变和最优拟合应变结果，同样验证了基于双胞元的颗粒材料应力-应变关系，因此，该颗粒材料应力-应变关系可以为数值模拟颗粒材料力学行为提供依据。
기우세관역학，건립과립재료적굉관응력-응변여접촉력、접촉위이、지시량등세관량지간적관계。용개진적Voronoi-Delaunay법대과립재료진행궤하화물리상화분，득도개진Bagi쌍포원체계；이고체포원위기출，운용우돈제이정률화Gauss정리제출함유선전시량화중력적과립재료평균등효응력，피면료과립재료적준정태가설；재공극포원구역내이용변형협조조건추도출함유공극면시량등궤하변량적과립재료평균등효응변。결합문헌적이유과립재료굉관시험결과험증료쌍포원평균등효응력-응변적정학성；재삼유정형하，대비쌍포원등효응변화최우의합응변결과，동양험증료기우쌍포원적과립재료응력-응변관계，인차，해과립재료응력-응변관계가이위수치모의과립재료역학행위제공의거。
Based on granular mesomechanics, this paper sets up the relationship between the macro stress-strain and the mesoscopic quantities including the contact force, contact displacement and branch vector in granular materials. The method of improved Voronoi-Delaunay tessellation for granular materials in geometry and physics is further modified into two cell systems of Bagi. Taking solid cell systems as the basic elements, the average stress tensor that includes particle rotation vector and acceleration of gravity is derived based on Newton’s second law of motion and Gauss theorem. It avoids a static hypothesis. The average strain tensor expression including the void surface vector is derived based on the void cell with compatibility requirement. Two cell systems average equivalent stress-strain is correct combined with the literature of experimental resulting in two dimensions. Compared with two cell systems average equivalent strain and best fitting stress results under three dimensions, granular material stress-strain relationship based on the two cell systems is also validated. Therefore, the granular material stress-strain relationship of the two cell systems provides a theoretical basis for numerical simulation of mechanical properties of granular materials.