Monday, February 26, 2018

3:00pm - 4:00pm

Mimetic-Informed Computational Mechanics: Theory, Method Development and Applications

AbstractDue to its unique and intriguing properties, polygonal/polyhedral discretization is an emerging field of computational mechanics, which relies on the theoretical foundations of barycentric coordinates. Based on mimetic methods, which mimics fundamental properties of mathematical and physical systems (e.g. exact mathematical identities of tensor calculus); the Virtual Element Method (VEM) was recently proposed as a framework to handle unstructured polygonal and polyhedral discretizations and beyond (e.g. arbitrary non-convex shapes). Unlike the Finite Element Method (FEM), there are no explicit shape functions in the VEM, which is a feature that leads to flexible definitions of the local VEM spaces. In this talk, we introduce two novel VEM formulations for two classes of computational mechanics problems: soft materials under extremely large deformations and topology optimization. First, to study soft materials, we present a novel two-field mixed VEM framework for finite elasticity. The framework features a nonlinear stabilization scheme, which evolves with deformation; and a local mathematical displacement space, which can effectively handle any element shape, including concave elements or ones with non-planar faces. We verify convergence and accuracy of the proposed mixed virtual elements by means of examples using unique element shapes inspired by Escher (the Dutch artist famous for his so-called impossible constructions). We present a physically based application of those elements to investigate the onset and growth of cavities in elastomers. Second, from the application/design viewpoint, we present a novel and efficient topology optimization framework on general polyhedral discretizations by synergistically incorporating the VEM and its mathematical/numerical features in the underlining formulation. As a result, the tailored VEM space naturally leads to a continuous material density field interpolated from nodal design variables. This approach yields a mixed virtual element with an enhanced density field. We present examples that explore the aforementioned features of our VEM-based topology optimization framework and contrast our results with the traditional FEM-based approaches that dominate the technical literature.

BiographyMr. Heng Chi is a PhD candidate in the School of Civil and Environmental Engineering at Georgia Institute of Technology. His research interests are on developing novel computational methods for various applications (e.g. soft materials, micro-mechanics and topology optimization), as well as exploring the design and realization of multi-functional material systems using topology optimization and advanced manufacturing. He is the winner of the 2017 Robert J. Melosh Medal for the Best Student Paper on Finite Element Analysis. Mr. Heng Chi received his B.E. degree in Civil Engineering from Tianjin University in 2011, and his M.S. degree in Civil Engineering from the University of Illinois at Urbana-Champaign in 2014.