无限大基体中双圆形夹杂的应力干涉问题研究

Researches on interacting double circular inclusions in an infinite matrix

建立了一种新型圆形夹杂单元,用于考察y向拉伸情况下无限大板中双圆形夹杂互相干涉问题,分析材质、位置关系与间距等对夹杂应力场的影响。算例考虑了两夹杂连线与x轴的夹角12分别为0°,45°和90°三种情况,计算结果表明:(1)该模型能够用较少的单元数获得令人满意的计算结果,尤其适用于多夹杂的应力分析;(2)夹杂/基体刚度比k不同时,夹杂/基体界面上的周向应力的最大值与最小值的出现位置差异可能很大;(3)两夹杂的距离越近,夹杂之间基体的正应力σy会急剧上升或下降,具体变化趋势取决于k和21;(4)特定21的情况下,夹杂/基体刚度比k使夹杂之间基体的正应力σy单调变化。

A super element with an inclusion in conjunction with conventional hybrid elements is presented for the analysis of interacting double circle inclusions in an infinite plane matrix. In numerical examples, double inclusions with inclination angle φ12 =0°, 45° and 90° are considered, and the influences of material properties, inclination positions and center distances on the local stresses of matrix are investigated. According to the numerical results, it is found that. （1） The present hybrid element method yields satisfactory results with less elements, thus it is meaningful for stress analysis of the micromechanical analysis of heterogeneous materials with randomly distributed circular inclusions; （2） Position angles where peak hoop stresses appear at change with stiffness ratios of inclusions and matrix; （3） With different values of k and φ12, the normal stresses σy in the matrix between two inclusions may increase or decrease rapidly with the shortening of center distances of the two inclusions; 4） With different values of inclination angles, normal stresses σy in the matrix between two inclusions change monotonously with stiffness ratios of inclusions and matrix.