Top Qs
Timeline
Chat
Perspective

Lattice Boltzmann methods for solids

Class of computational solid dynamics methods From Wikipedia, the free encyclopedia

Lattice Boltzmann methods for solids
Remove ads

The Lattice Boltzmann methods for solids (LBMS) are a set of methods for solving partial differential equations (PDE) in solid mechanics. The methods use a discretization of the Boltzmann equation(BM), and their use is known as the lattice Boltzmann methods for solids.

LBMS methods are categorized by their reliance on:

  • Vectorial distributions[1]
  • Wave solvers[2]
  • Force tuning[3]

The LBMS subset remains highly challenging from a computational aspect as much as from a theoretical point of view. Solving solid equations within the LBM framework is still a very active area of research. If solids are solved, this shows that the Boltzmann equation is capable of describing solid motions as well as fluids and gases: thus unlocking complex physics to be solved such as fluid-structure interaction (FSI) in biomechanics.

Remove ads

Proposed insights

Summarize
Perspective

Vectorial distributions

The first attempt[1] of LBMS tried to use a Boltzmann-like equation for force (vectorial) distributions. The approach requires more computational memory but results are obtained in fracture and solid cracking.

Wave solvers

Another approach consists in using LBM as acoustic solvers to capture waves propagation in solids.[2][4][5][6]

Force tuning

Introduction

This idea consists of introducing a modified version of the forcing term:[7] (or equilibrium distribution[8]) into the LBM as a stress divergence force. This force is considered space-time dependent and contains solid properties[Note 1]

,

where denotes the Cauchy stress tensor. and are respectively the gravity vector and solid matter density. The stress tensor is usually computed across the lattice aiming finite difference schemes.

Some results

Thumb
2D displacement magnitude on a solid system using force tuning. Obtained field is in accordance with finite element methods results.

Force tuning[3] has recently proven its efficiency with a maximum error of 5% in comparison with standard finite element solvers in mechanics. Accurate validation of results can also be a tedious task since these methods are very different, common issues are:

  • Meshes or lattice discretization
  • Location of computed fields at elements or nodes
  • Hidden information in software used for finite element analysis comparison
  • Non-linear materials
  • Steady state convergence for LBMS
Remove ads

Notes

  1. Matter properties such as Young's modulus and Poisson's ratio.

See also

References

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads