基于应变梯度理论的假设应变有限元方法

采用基于应变梯度理论的假设应变有限元方法研究了微尺度梁弯曲的尺寸效应.在假设应变单元设计中,非局部的应变梯度项通过围绕高斯点的胞元进行数值积分得到.在本构方程中引入等效应变梯度项,在积分本构方程时就可以反映材料在微细变形时的尺寸效应.为了验证本方法的正确性,对微尺度下的悬臂梁进行了模拟计算.计算结果与已发表的实验结果比较吻合,表明可以模拟出材料微细变形的尺寸效应,具有较好的计算精度.

Assumed strain finite element method based on the theory of strain gradient

An assumed strain finite element method based on the theory of strain gradient was proposed to explore the size effect that frequently exhibited in micro-beam bending. In element design, strain gradient terms were obtained by using numerical integration of a cell constructing around a Gaussian point. An equivalent strain gradient term was incorporated into the constitutive model to reflect the effect of highly localized inhomogeneous deformation. In this way, an assumed strain finite element method program was developed. To validate the performance of the proposed method, a numerical simulation of micro-beam bending was carried out. Numerical resuits show a good agreement with the reported experimental data. It is concluded that the proposed approach is of good capability to reflect the response of microstructure.