Abstract:

It is often desirable to introduce microscopic degrees of freedom in continuum mechanics. In 1909, the Cosserat brothers introduced such a model that incorporates a pointwise rotation to elasticity. As an example of the micropolar theory, the Cosserat model describes, for instance, granular media.

In this talk, we first observe connections between generalized continuum models and Hilbert complexes and the Bernstein-Gelfand-Gelfand (BGG) construction. This connection leads to a systematic approach to understand (and potentially generalize) micropolar models. Based on this observation, we derive numerical discretization of the Cosserat models using distributional finite elements and ideas from Finite Element Exterior Calculus. The resulting scheme is robust with the physical parameters (locking-free) including the Lamé constant and a coupling parameter: when the coupling parameter goes to zero, the scheme solves standard elasticity; when the parameter is infinity, the scheme solves a high-order couple stress problem.

Bio:

胡凯博，2017年博士毕业于北京大学, 曾在挪威奥斯陆大学和美国明尼苏达大学做博士后研究, 任英国牛津大学 Hooke 研究员. 现任爱丁堡大学皇家学会大学研究员 (Royal Society University Research Fellow). 曾获SIAM计算科学与工程早期职业奖 (2023), ERC Starting Grant (2024). 文章入选 SIAM 高影响力文章合集 (SIAM High Impact Article Collection). 研究兴趣包括保结构有限元方法, 离散几何与拓扑及应用.