Geometrically Consistent Mixed Finite Element Methods for Nonlinear Solids via Hilbert Complexes

Abstract

The objective of the proposed research program is to develop mixed finite element methods for nonlinear elasticity and inelasticity that conform with the topological properties of the underlying bodies. Such numerical schemes will be very useful for modeling nonlinear solids with complex geometries that arise in many applications such as heterogeneous media and more generally, solids with cracks, corners, voids, inclusions, dislocations, etc. The main tool in this project is a mathematical structure called differential complex for nonlinear solids that was recently introduced by the PI and a graduate student (supported by an AFOSR grant). This structure allows one to incorporate the effects of topological properties of bodies in studying solutions of the governing partial differential equations.

Document Details

Document Type
DoD Grant Award
Publication Date
Mar 23, 2016
Source ID
FA95501610003

Entities

People

  • Arash Yavari

Organizations

  • Air Force Office of Scientific Research
  • Georgia Tech Research Corporation
  • United States Air Force

Tags

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.
  • Research Science/Academic Research