Numerical Modelling of 3G Artificial Turf Under Vertical Loading By David Christopher Cole A doctoral thesis submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University Wolfson School of Mechanical, Electrical and Manufacturing Engineering Loughborough University United Kingdom © David Christopher Cole 2020 Abstract The research into artificial turf sport surfaces has seen significant growth over the last decade, linked to the proliferation of artificial turf surfaces in Europe for use in high participation sports. The latest third generation (3G) surfaces are typically comprised of multi-components exhibiting behaviours that are non-linear and rate dependant. Of particular importance is the vertical loading response, i.e. hardness or shock absorption, as it has been linked to both player performance and injury risk. Modelling sports surfaces can be of benefit to predict the loading response and allow for optimisation of geometry and materials in a virtual environment prior to changes in manufacture or construction. Thus, the work presented in this thesis is focussed upon the development of a numerical model to describe the behaviour of 3G artificial turf systems under vertical loading. The development of the numerical model required material stress-strain data to characterise the response to vertical loading. Material characterisation required the development of a novel methodology due to the limited loading rates of standard test devices. This methodology was based on the Advanced Artificial Athlete (AAA) vertical impact test with a specification developed to ensure valid stress-strain data was captured. Testing using this method, allowed for stress-strain data for the shockpad and carpet-infill layer to be collected at representative loading rates. This data, along with supporting stress relaxation data, provided the basis for material model calibration for each of these components. Material model calibration was a multi-stage process with the first calibration conducted by optimisation equations in a specialised material modelling software. A second manual optimisation, based upon initial results from a finite element (FE) simulation of the AAA FIFA test, allowed for refinement of the material model until a predefined set of accuracy criteria was met. Further simulations of AAA impacts from different drop heights were performed to validate the material models. i Finite element models of two shockpads produced root mean square differences (RMSD) of <5% from the experimental across AAA impacts at 25, 55 and 85 mm. The carpet-infill system modelled as a single part produced RMSD differences of ~8% however with the addition of a stiffer carpet backing added to the model, this was reduced to ~3% at the 55 mm drop height. Despite continued good agreement at the 25 and 85 mm drop heights (~5% RMSD), the energy absorption of the model was excessive (>8%). Combining the models of shockpads with the carpet-infill system created a surface system model which was used to assess the predictive capability of a AAA impact. Results at 25 and 55 mm were good (<6%) but produced weaker agreement from 85 mm (<10%). The work presented in this thesis supports the theory that FE modelling of 3G turf can assist in the design and optimisation of surfaces before physical construction. The methodology for experimental material characterisation and model calibration could be applied to different shockpads and carpet-infill systems. Further work should focus on the addition of the sand infill and the response to loading from successive AAA impacts. Keywords: 3G, Artificial turf, Mechanical testing, Material modelling, Finite element modelling. ii Acknowledgements There are a number of people I would like to thank for their support throughout the PhD, without whom none of this would have been possible. First and foremost, I’d like to thank my supervisors Dr Steph Forrester and Dr Paul Fleming. I have been fortunate to be able to call on their knowledge, advice and support throughout, guiding me in the right direction and allowing me to fulfil my ambitions. An extended thanks to all the staff at the Sports Technology Institute who have taught me throughout my time in Loughborough and helped me develop as a researcher. A special thanks also to Steve Carr and Max Farrand, whose skills and expertise have been vital to the success of this and many of my other projects. To all my friends, in Loughborough and elsewhere, thanks for providing a distraction from work and offering support when I needed it most. My time here would not have been the same without you. Finally, and most importantly, thanks to my family. To my brothers Mike and Rich for their support throughout and helping me push myself further than I ever thought I could. To my parents, who believed in me even when I doubted myself and provided me with an environment to thrive. I will never be able to express my gratitude to you fully, thank you. iii Publications Arising From This Research Journal Articles Cole D, Forrester S, Fleming P. Mechanical characterisation and modelling of elastomeric shockpads. Appl Sci. 2018;8:1–11. Cole DC, Fleming PR, Morrison KM, Forrester SE. Evaluation of the Advanced Artificial Athlete and Hall Effect Sensors for Measuring Strain in Multi-Layer Sports Surfaces. SN Appl Sci. 2020; tbc Conference Proceedings Cole D, Forrester S, Fleming P. Mechanical Characterization and Numerical Modelling of Rubber Shockpads in 3G Artificial Turf. In: International Sports Engineering Association. 2018. p. 283. doi:10.3390/proceedings2060283. iv Table of Contents Abstract ............................................................................................................. i Acknowledgements ........................................................................................ iii Publications Arising From This Research .................................................... iv Table of Contents ............................................................................................. v List of Figures ................................................................................................. ix List of Tables ................................................................................................. xiv Abbreviations ................................................................................................ xvi Chapter 1 - Introduction ................................................................................... 1 1.1 Background .............................................................................................. 1 1.2 Aims and Objectives ................................................................................. 2 1.3 Thesis Structure ....................................................................................... 3 Chapter 2 - Literature Review .......................................................................... 6 2.1 Introduction ............................................................................................... 6 2.2 Background knowledge ............................................................................ 6 2.2.1 Surface history, use and development ............................................... 6 2.2.2 Surface construction .......................................................................... 8 2.2.3 Shockpad design ............................................................................. 10 2.2.4 Carpet design ................................................................................... 11 2.2.5 Infill design ....................................................................................... 13 2.2.6 FIFA quality testing .......................................................................... 14 2.2.7 Inter-surface measurement .............................................................. 17 2.2.8 Player loading mechanics ................................................................ 19 2.2.9 Modelling of 3G turf .......................................................................... 22 2.3 Material characterisation ......................................................................... 24 2.3.1 Basic theory of elasticity ................................................................... 24 2.3.2 Hyperelasticity .................................................................................. 25 2.3.3 Viscoelasticity .................................................................................. 26 2.3.4 Granular behaviour .......................................................................... 28 2.3.5 Material test methods ....................................................................... 29 2.4 Material modelling .................................................................................. 32 2.4.1 Approaches to constitutive modelling ............................................... 33 2.4.2 Hyperelastic modelling ..................................................................... 34 v 2.4.3 Viscoelastic modelling ...................................................................... 35 2.4.4 Viscoplastic modelling ...................................................................... 36 2.5 Finite element modelling ......................................................................... 38 2.5.1 Finite element method ...................................................................... 38 2.5.2 Surface modelling ...........................................................................