Mathematical Models and Advanced Numerical Methods for Complex Flows and Structures
Abstract
Our results pertain to two complex flow problems: Brittle fracture and turbulence. Our results are partly numerical and algorithmic and partly theoretical, in formulation of improved models, equations and physical formulation. A new mass conservative mesoscale model for the simulation of brittle fracture of solid materials has been developed. In our previous work, we represented the solids by spring networks, using an algorithm based on the energy minimization of the network of triangular springs, with critical strain and splitting of over stressed bonds and connected to them nodes ensuring the conservation of mass during the crack evolution. The applicability of the network-based brittle fracture method is limited by its compatibility with established engineering codes for solid dynamics, which are primarily based on finite element methods. In the second phase of the project, we focused on the adaptation of the brittle fracture method to the finite element framework in 2D and 3D, thus extending capabilities of finite element methods for the description of fracture dynamics. While the core of our new method is still based on energy minimization, our new code is based on a simplified version of the ALE (Arbitrary Lagrangian Eulerian) formulation to allow large displacement and arbitrary mesh motion, coupled with mesh adaptivity to improve accuracy and stability. The adoption of the finite element method allows the new software to be interoperable with standard FEM codes widely used for material studies, and the new approach also improves the accuracy of simulation of real materials. We have also developed a formulation of the contact mechanics using collision detection and the method Lagrange multipliers. The code has been parallelized for the use on multi core CPU machines. The core FEM code (with the fracture algorithms turned off) has passed several verification tests.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 25, 2016
- Accession Number
- AD1063368
Entities
People
- James Glimm
- Roman Samulyak
- Xiangmin Jiao
Organizations
- State University of New York