Simulation of Fibre Pull-out Using a Graphics Processing Unit Accelerated Discrete Element Model

Abstract

The combination of brittle material with ductile fibres can produce competent composites. The fibres transmit tensile forces across cracks that form in the brittle matrix at relatively low tensile strains. The fibre reinforcing, therefore, acts to both increase the maximum stress a structural section can support and improve the post maximum stress behaviour from brittle to ductile failure. An essential aspect of defining the effectiveness of fibre reinforcing is resolving the behaviour of the interface between the fibre and the matrix as the load being transmitted between the matrix and fibre increases. The interface behaviour for simple fibres is understood analytically, and several models exist that can predict the stresses in the interface. Numerical models using finite element methods (FEM) have been used to investigate this problem in a more general way. FEM, being inherently a description of a continuum, does not elegantly describe the debonding process that occurs during the debonding of fibres from the surrounding matrix. Discrete Element Methods (DEM) describe continuous and discontinuous materials as the interaction between multiple independent particles and are well suited for modelling fracture and evolving contacts. For this study two different DEM contact models are compared to investigate the model complexity that is required to describe fibre/matrix interface stresses and debonding accurately. A simple model (a linear spring model that only transmits normal and tangential forces) and a more complex model (parallel bonds which transmit normal and tangential forces, moments, and torsion) were used. Two stages of fibre pull-out were modelled independently using a GPU accelerated DEM simulator developed by the author: a fully bonded stage and the de-bonding stage. It was found that both models were able to simulate all stages when compared to analytical solutions. No improvement to the model behaviour was evident from using a complex contact model; for this reason, a simpler, faster contact model should be used to analyse this problem. The DEM code is written relying heavily on the Numba module which allows the compilation of Python syntax for execution on a GPU. Non-reversible bond damage is simulated, and each bond must, therefore, be stored and bond damage updated at each time step. The implementation of collision detection, particle force determination and equation of motion integration written for execution on GPU are discussed. The data structure and memory use are described. The method used to apply boundary conditions is described. The performance of the developed code is investigated by comparison with similar codes, using Numpy and Numba Python modules, written for serial execution on CPU only. It was found that the developed code was 1000 times faster than the Numpy+Python implementation and 4 times faster than the Numba+Python implementation for force determination and equation of motion integration. Collision detection was 900 times faster compared to Numpy+Python but performed slower compared to Numba+Python.