# Measurement of Strain and Strain Rate during the Impact of Tennis Ball Cores
## 1 Introduction  
Previous research assessing ball tracking data from professional tennis matches has established typical inbound impact conditions that the ball experiences, particularly when impacting court surfaces [1; 2]. Knowledge of the impact conditions enables replication of typical impact conditions in the laboratory. Previous efforts to understand the behaviour of the ball core in isolation has focused, almost exclusively, on normal impacts with a rigid surface as a means of validating finite element (FE) simulations [3; 4; 5; 6; 7]. These simulations require characterisation of the mechanical behaviour of the rubber compound to predict the behaviour of the modelled ball core. Characterisation of ball core materials has so far been limited to quasi-static tensile, compressive, and stress relaxation testing. The issue with current test methods are the speeds and consequent achievable strain rates for testing. Typically, tensile tests have been conducted with a crosshead speed in the range of 50-999 mm-min\({}^{-1}\)[5]. Elastomeric materials are known to exhibit strain-rate-dependent behaviour, whereby stiffness increases as strain rate increases, particularly at high strain rates [8; 9; 10]. When defining material behaviour for FE simulations, it is desirable to match the properties of the material when it is subjected to the strains and strain rates observed during use, especially if significant increases in stiffness are observed as strain rate increases.  
Previous modelling techniques have utilised an iterative process, comparing artificial stiffening of stress-strain data and alterations to damping factors with high-speed video footage and force trace data of impacts to establish a material model providing a realistic representation of the ball during impact [3; 5]. In part, the use of artificial stiffening is a result of the limitations of available material testing equipment. Only through simulation have maximum strains and strain rates during impactbeen estimated. [PERSON] [3] estimated maximum strains in the region of 0.5 with maximum strain rates in the region of 300 s\({}^{-1}\). [PERSON] [6] recorded maximum strains in the region of 0.3 for an impact against a rigid surface at 30 m\(\cdot\)s\({}^{-1}\).  
Traditional strain measurement devices such as strain gauges and extensometers do not lend themselves to high velocity ball impacts due to the associated connected electronics and possible alterations in deformation caused by the sensor being in contact with the surface. Optical strain measurement techniques utilising digital image correlation (DIC), such as GOM Correlate Professional (GOM GmbH, Braunschweig, Germany), provides a means of three-dimensional surface strain measurement utilising multiple cameras. GOM Correlate identifies stochastic image information, referred to as facets, by evaluating the grey values present within the facet. Optimal facets have a distinct and equally distributed pattern, with maximum possible contrast in grey values within the facet [11]. DIC could be employed to measure the strains and strain rates present during ball impacts and used to inform material characterisation testing, in turn enabling FE modelling to utilise, rather than techniques involving the artificial stiffening of quasi-static behaviour, material modelling techniques based on experimental data. Although not used to measure strain, GOM has been successfully implemented in a sporting context to measure golf ball and clubhead velocity [12].  
The aim of this investigation was to establish the strains and strain rates experienced by tennis ball cores during impact, whereby the impact conditions are representative of professional play, in turn establishing the effectiveness of non-contact DIC for strain measurement during high-velocity, high-deformation sports ball impacts. A further aim was to define the range of strains and strain rates that material characterisation tests should incorporate to understand the material behaviour during use.