Register now After registration you will be able to apply for this opportunity online.
This opportunity is not published. No applications will be accepted.
A generalized meshfree approach for simulation of large-deformation mechanics
A generalized meshfree approach for simulation of large-deformation mechanics
Keywords: Meshfree, FEM, finite element analysis (FEM), computational solid mechanics, programming, C++, high performance computing
The finite element method (FEM) is one of the most popular numerical methods for simulating physical phenomena in solid mechanics. However, when tackling problems which involve large deformations, the underlying mesh may substantially limit FEM’s capabilities, as a highly distorted mesh gives rise to entangled, ill-shaped and degenerate elements. To this end, the class of meshfree methods (e.g., smoothed particle hydrodynamics (SPH), element-free Galerkin (EFG), maximum-entropy (max-ent), etc.; see [1] for detailed review) offer an attractive solution to circumvent the aforementioned mesh-related issues by eliminating the need of a mesh altogether. In contrast to FEM, meshfree methods treat a solid body as a finite set of points or particles that interact based on the governing equations and applied boundary conditions. A key challenge in the success of meshfree methods is achieving numerical stability in updated-Lagrangian simulations, which was recently addressed by Kumar et al. [2] for max-ent based methods.
This project proposes the development of an advanced computational framework for stable meshfree simulations. Specifically, the project will aim to:
(i) develop a MPI-based C++ implementation of a range of meshfree methods for massively-parallel simulations. The implementation will be built upon an existing FEM codebase (similar to the one used in the course Computational Solid Mechanics at ETH).
(ii) extend the stability enhancing techniques of Kumar~et~al.~[2] to the aforementioned methods
(iii) assess the accuracy, stability, and performance of the framework via benchmark problems.
Pre-requisites:
A background in solid mechanics and the finite element method as well as in programming in C/C++ is required.
References:
[1] Chen, J. S., Hillman, M. C., & Chi, S. W. Meshfree methods: Progress made after 20 years. Journal of Engineering Mechanics, 143(4):04017001, 2017.
[2] Kumar, S., Danas, K., & Kochmann, D. M. Enhanced local maximum-entropy approximation for stable meshfree simulations, Computer Methods in Applied Mechanics and Engineering, 344:858-886, 2019.
The finite element method (FEM) is one of the most popular numerical methods for simulating physical phenomena in solid mechanics. However, when tackling problems which involve large deformations, the underlying mesh may substantially limit FEM’s capabilities, as a highly distorted mesh gives rise to entangled, ill-shaped and degenerate elements. To this end, the class of meshfree methods (e.g., smoothed particle hydrodynamics (SPH), element-free Galerkin (EFG), maximum-entropy (max-ent), etc.; see [1] for detailed review) offer an attractive solution to circumvent the aforementioned mesh-related issues by eliminating the need of a mesh altogether. In contrast to FEM, meshfree methods treat a solid body as a finite set of points or particles that interact based on the governing equations and applied boundary conditions. A key challenge in the success of meshfree methods is achieving numerical stability in updated-Lagrangian simulations, which was recently addressed by Kumar et al. [2] for max-ent based methods.
This project proposes the development of an advanced computational framework for stable meshfree simulations. Specifically, the project will aim to:
(i) develop a MPI-based C++ implementation of a range of meshfree methods for massively-parallel simulations. The implementation will be built upon an existing FEM codebase (similar to the one used in the course Computational Solid Mechanics at ETH).
(ii) extend the stability enhancing techniques of Kumar~et~al.~[2] to the aforementioned methods
(iii) assess the accuracy, stability, and performance of the framework via benchmark problems.
Pre-requisites: A background in solid mechanics and the finite element method as well as in programming in C/C++ is required.
References:
[1] Chen, J. S., Hillman, M. C., & Chi, S. W. Meshfree methods: Progress made after 20 years. Journal of Engineering Mechanics, 143(4):04017001, 2017.
[2] Kumar, S., Danas, K., & Kochmann, D. M. Enhanced local maximum-entropy approximation for stable meshfree simulations, Computer Methods in Applied Mechanics and Engineering, 344:858-886, 2019.
Not specified
Dr. Siddhant Kumar
Mechanics & Materials, D-MAVT, ETH Zürich
Leonhardstrasse 21, LEE N225, Zürich
email: siddhant.kumar@ethz.ch