研究在微细尺度下，有效模拟金属材料变形尺度效应的数值方法。将四边形面积坐标法与MSG应变梯度理论的本构方程相结合，通过用户子单元UEL加入到ABAQUS的数值模拟中。在有限元模拟过程中，采用传统八节点等参元时常遇到网格严重畸变的问题，而基于四边形面积坐标方法的单元却在网格严重畸变时仍然能够保持较高的精度，在非线性问题中有广阔的应用前景，而且经典理论无法解释试验中观察到的尺寸效应现象，因此采用MSG塑性应变梯度理论的本构方程解决尺度效应问题。应用文献中的数据对电抛光镍做数值模拟，以验证新的理论模型的正确性，对JX-2管线钢做试验研究，并对所得的铁素体、贝氏体、铁素体和贝氏体的双相体三种微观组织进行数值模拟，对比试验和模拟结果证明新的理论模型在工程中具有良好的可应用性，较传统塑性理论能更好地预测试验结果。

A user-defined finite element subroutine (UEL) available in ABAQUS package is developed which can be used to simulate the micron-level size effect in large elastic-plastic deformation. Compared with traditional 8-node isoparametric elements,models formulated by quadrilateral area coordinate method are less sensitive to the mesh distortion. To quantify the size effect,the mechanism-based strain gradient plasticity is employed in the elastic-plastic constitutive model and is incorporated the quadrilateral area coordinate method. A numerical simulation is performed on the electro-polished nickel to verify correction of the new method. The micro-indentation experiment is done for the JX-2 pipeline steel (microstructure a dual phase consisting of ferrite and bainite). Through the comparison of the experimental and numerical results,it is shown that the new method outperforms the classical plasticity in the accuracy of predicting experimental results.