中文摘要：

研究了材料模拟中一类新型耦合多尺度的自适应有限元方法.采用微观分子动力学耦合宏观有限元的桥尺度方法来模拟材料破坏的前期行为,其中宏观有限元计算推广到了一般非结构三角形网格.材料破坏形成后,停止微观尺度的计算,它的进一步发展和演化通过一个宏观模型来描述,采用自适应有限元方法来求解这一宏观模型.其中,后验误差估计的基础是变分多尺度理论,即自适应网格加密是基于粗尺度上残差分布和细尺度上单元Green＇s函数.计算中采用了破坏准则来模拟材料的断裂.数值实验表明了方法的有效性.

英文摘要：

A new adaptive finite element method coupling with multiscale simulation for material computation is proposed in this paper. The early behaviors of the material damage are simulated by BSM that coupling microscale MD with macroscale FE, in which the macroscale finite element computation has been generalized to irregular triangular meshes. Once material fracture is formed, its further development is only described by a macroscale model with the adaptive finite element method. A posteriori error estimator was proposed with the variational multiscale theory. Meanwhile, the adaptive meshes were based on the residual distribution of the coarse scale and the Green＇s function in the fine scale. A given failure criteria is used to determine the split of the mesh. Efficiency of the proposed method is validated by numerical experiments.