报 告 题 目：On the Cauchy-Born approximation: modeling、simulation and analysis

主 讲 人：杨 志 坚

单 位：武汉大学

时 间：11月24日15:00

腾 讯 ID: 949-439-140

摘 要：

The recent development of molecular dynamics models has dramatically improved and enriched traditional continuum mechanics models. It provides an atomistic-based constitutive model, taking into account detailed atomic interactions. At zero temperature, the Cauchy–Born (CB) rule offers an efficient constitutive model. In this talk, we will extend the CB approximation to finite temperature for systems at thermodynamic equilibrium. I will address several issues regarding the derivation and implementation of the CB approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola–Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach, both for simple and for complex lattices. The issue of the validity and accuracy of the CB rule will also be discussed.

简 介：

杨志坚教授分别于1999年和2001年在北京大学获本科与硕士学位、2006年在美国普林斯顿大学获博士学位、2006年至2008在加州理工学院航空航天系从事博士后研究、2009年至2010年在美国罗彻斯特理工学院担任助理教授、2010年6月至今担任武汉大学数学与统计学院教授、博士生导师。现为教育部科技委委员、东亚工业与应用数学学会主席、湖北省工业与应用数学学会理事长、计算科学湖北省重点实验室主任。曾获中国工业与应用数学学会第一届优秀青年学者奖。主持国家杰出青年科学基金、科技部重点研发计划、基金委重大研究计划集成项目及湖北省创新群体等科研项目。现为EAJAM、CSIAM-AM等杂志编委。主要研究领域为科学与工程计算、多尺度建模与计算及应用、人工智能的数学理论及应用。