## 1 Introduction  
In the United States alone, sport accounts for an estimated 3.8 million traumatic brain injuries (TBIs) annually [1]. TBIs, which include mild traumatic brain injuries (mTBIs) such as concussions, occur frequently and are severely underreported [2]. Symptoms include headaches and fatigue, which can lead to an increased risk of clinical depression, decreased satisfaction with life, and increased levels of disability [3,4]. [PERSON] and [PERSON] [1] state that preventative measures against TBI most commonly take two forms: rule changes and innovations in impact protection in the form of helmets. [PERSON] et al. [5] examined two American football helmet designs over the course of 1.28 million impacts in games and practice, and found that helmet choice could reduce the number of concussions athletes endure. The helmet modulates energy transferred to the head, and the amount of energy transferred can differ by design. Helmet and head injury studies tend to explore the helmets' ability to reduce the risk of TBIs and mTBIs in sport [5, 6, 7]. Personal protective equipment (PPE), or other safety devices designed to prevent injuries arising from impact scenarios (short duration, high loading), aim to limit peak accelerations/forces, increase contact times, distribute loading, and perform energy attenuation. The performance of these safety devices is typically assessed by simulating an impact and measuring the ability to limit peak linear acceleration or force [8,9]. Helmet testing typically involves placing the helmet on the headform of an anthropomorphic test device (ATD) or a rigid headform, and using a drop-rig to transfer a known amount of impact energy. Accelerometers within the headform are used to record temporal accelerations and obtain impact characteristics including peak acceleration and impact duration [9,10]. Injury risk is typically quantified by assessing linear acceleration in combination with impact time, and relating to a severity index, such as the Head Impact Criterion (HIC) [11] and the Gadd Severity Index (GSI) [12]. GSI has been adopted in the protective equipment testing standards of the National Operating Committee on Standards for Athletic Equipment (NOCSAE) in the United States [10]. The GSI index is defined in Equation (1),  
\[GSI=\int_{t_{0}}^{t_{f}}A^{2.5}dt \tag{1}\]  
where \(A\) is the instantaneous resultant acceleration expressed as a multiple of gravity (g), \(dt\) is the time increment in seconds, and the integration bounds are from \(t_{0}\) to \(t_{f}\), the impact duration (determined by threshold value >0 g) [10,11]. New helmets are subjected to 16 impacts (44 to 60 J) onto a fixed rigid surface in six orientations. To pass the NOCSAE criterion, the GSI value for each impact must be below 1200, which signifies a non-injurious impact. Helmets are a form of PPE used to protect the head and brain from injury. Impacts that contribute to head injury typically cause linear and rotational accelerations. The emphasis of attenuating rotational acceleration caused by oblique impacts has recently increased [13,14]. Oblique impacts increase the likelihood of brain injury [15] through mechanisms including: (i) rupturing arteries and bridging veins (causing subdural hematomas, SDH); and (ii) tearing neuro-connective tissue (causing diffuse axonal injuries, DAI) [16,17]. Mixed impacts (including rotational and linear accelerations) further increase the likelihood of fatal or coma inducing DAI and SDH [18, 19, 20]. Neither HIC nor GSI assess oblique or mixed impact testing, nor do they measure rotational acceleration, and historically helmet standards have been based on these indices [13,14]. Emphasis on linear (rather than rotational) acceleration has led to criticism of certifications and helmets alike [1]. To best attenuate linear acceleration, helmet materials are often viscoelastic, such as plastic based foams [21].