Non-reflecting boundary conditions and tensile instability in smooth particle hydrodynamics

This thesis aimed at the understanding and further development of smoothed particle hydrodynamics (SPH). The first part described the implementations of non-reflecting boundary conditions for elastic- waves in SPH. The second part contains a stability analysis of the semi-discrete SPH equations and a new method for stabilising basic SPH in tension

Globally time-reversible fluid simulations with smoothed particle hydrodynamics

This paper describes an energy-preserving and globally time-reversible code for weakly compressible smoothed particle hydrodynamics (SPH). We do not add any additional dynamics to the Monaghan's original SPH scheme at the level of ordinary differential equation, but we show how to discretize the equations by using a corrected expression for density and by invoking a symplectic integrator. Moreover, to achieve the global-in-time reversibility, we have to correct the initial state, implement a conservative fluid-wall interaction, and use the fixed-point arithmetic. Although the numerical scheme is reversible globally in time (solvable backwards in time while recovering the initial conditions), we observe thermalization of the particle velocities and growth of the Boltzmann entropy. In other words, when we do not see all the possible details, as in the Boltzmann entropy, which depends only on the one-particle distribution function, we observe the emergence of the second law of thermodynamics (irreversible behavior) from purely reversible dynamics.Comment: Submitted to a journa

Modelling elastic dynamics and fracture with coupled mixed correction Eulerian Total Lagrangian SPH

In this thesis, the Smoothed Particle Hydrodynamics (SPH) method is applied to elastic dynamics and fracture. More specifically, two coupling methods are presented which make use of both the Eulerian and Total Lagrangian formulations. These coupling methods are intended for problems whereby SPH particles, which constitute the domain, are required to convert from a Total Lagrangian kernel to an Eulerian kernel once a damage criterion is activated. The conservation equations are derived for the Eulerian and Total Lagrangian formulations, in a consistent manner which naturally presents the conditions required for the conservation of momentum and energy. These derivations are written such that they make no use of the symmetrical nature of the kernel function or the anti-symmetrical nature of the kernel function gradient. The conservation of momentum and energy is then enforced, along with improving the consistency of the formulations, by implementing the mixed kernel-and-gradient correction. This mixed correction can be applied to both the Eulerian and Total Lagrangian formulations without detracting from the energy and momentum preserving properties provided that the kernel gradient anti-symmetry property is not exploited. The symmetry terms, which are often found in SPH, are included in the derivation of the conservation equations. This is done both to reduce the number of calculations required and to simplify the first coupling procedure. Both coupled formulations are further expanded by highlighting how artificial viscosity can be introduced. A disadvantage of the first coupling method, this being the incompatibility with artificial stress, is also detailed. The equations of state and the plasticity and damage models used in this work are outlined. Additionally, a number of practical details concerning numerical implementation are given. These include the coupled implementations of ghost particle boundary conditions, memory storage, OpenMP implementation, and the Predict, Evaluate, Correct (PEC) form of leapfrog time integration used. Lastly, the proposed formulations and models are verified and validated. This is done by modelling progressively more complex simulations that verify individual aspects of the formulations. Either analytical or experimental results are used for validation where possible. The final simulations highlight how high velocity impacts can be modelled using the proposed coupled mixed correction Eulerian Total Lagrangian SPH method

Mesh-free methods for liquid crystal simulation.

The key aim of this Thesis is the development and implementation of a set of simulation techniques for LCs capable of tackling mesoscopic phenomena. In this, we concentrate only on mesh-free particle numerical techniques. Two broad approaches are used, namely bottom-up and top-down.While adopting the bottom-up approach, we employ the DPD method as a foundation for devising a novel LC simulation technique. In this, we associate a traceless symmetric order tensor, Q, with each DPD particle. We then further extend the DPD forces to directly incorporate the Q tensor description so as to recover a more complete representation of LC behaviour. The devised model is verified against a number of qualitative examples and applied to the simulation of colloidal particles immersed in a nematic LC. We also discuss advantages of the developed model for simulation of dynamic mesoscopic LC phenomena.In the top-down approach, we utilise recently emergent numerical mesh-free methods. Specifically, we use the SPH method and its variants. The developed method includes hydrodynamics, variable order parameter and external electric and magnetic fields. The developed technique is validated against a number of analytical and numerical solutions.Subsequently, we apply our top-down methods to the simulation of the complex 3D post-aligned bistable nematic (PABN) device. This includes a smooth geometry representation in order to fully exploit the developed mesh-free numerical techniques. We study both the static and dynamic behaviours of the PABN device for a number of distinct post shapes

Discontinuous Fiber Composites, Volume II

Discontinuous fiber-reinforced polymers have gained importance in transportation industries due to their outstanding material properties, lower manufacturing costs and superior lightweight characteristics. One of the most attractive attributes of discontinuous fiber-reinforced composites is the ease with which they can be manufactured in large numbers, using injection and compression molding processes. The main aim of this Special Issue is to collect various investigations focused on the processing of discontinuous fiber-reinforced composites and the effect that processing has on fiber orientation, fiber length and fiber density distributions throughout the final product. Papers presenting investigations on the effect that fiber configurations have on the mechanical properties of the final composite products and materials were welcome in the Special Issue. Researchers who model and simulate processes involving discontinuous fiber composites as well as those performing experimental studies involving these composites were welcomed to submit papers. The authors were encouraged to present new models, constitutive laws, and measuring and monitoring techniques to provide a complete framework on these groundbreaking materials and to facilitate their use in different engineering applications