Linking continuum mechanics and 3D discrete dislocation simulations

Connecting discrete and continuum dislocation mechanics: a non-singular spectral framework

In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1, 2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To this end, an analytical method to convert a discrete dislocation network to its continuous dislocation density tensor representation is first developed. From...

Discrete Modelling and Discrete Algorithms in Continuum Mechanics

Multi-physics Simulations in Continuum Mechanics

The era of commodity computing brings a profound change in the use of numerical analysis of continuum mechanics problems in science and engineering. Teraflop-rate computing facility, until recently available only to chosen few is becoming commonplace in an industrial setting. Range and complexity of problems where numerical methods are applied is also expanding. Here, massive reduction in the c...

A discrete mechanics approach to dislocation dynamics in BCC crystals

A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treat...

CARBON NANOTUBE MECHANICS: Molecular Simulations & Continuum Models for Carbon Nanotubes

To realize the incredible structural applications potential of carbon nanotubes, it is important to characterize their material response. Molecular simulations offer advantages over physical testing due to their cost effectiveness, versatility and precision. Two continuum models for single wall nanotubes (SWNT) were previously developed based on the results from molecular simulations using two ...