Description of MADYMO MB pedestrian models

The MADYMO user manual (TNO 2004) describes that the MADYMO MB model consists of 64 ellipsoids that represent the outer surface of an average Western European human being according to the anthropometry data of RAMSIS software (Speyer and Seidl 1997).

The different body regions of the model are assigned with the inertia values calculated based on the ones from UMTRI (Schneider 1983) for the different percentiles, 50% male, 95% male and 5% female.

Figure 4-1: Structure of the MADYMO multibody model (Van Rooij, 2003)

The skeletal structure of the human body is modelled with 52 rigid bodies, which geometry is defined through ellipsoids representing most of the bony parts of the skeleton. They are interconnected by kinematic joints, representing the articulations, as seen in the Figure 4-1. MADYMO MB human models output the acceleration, velocity and displacement, both lineal and angular, for any of the ellipsoids conforming the body as well as force and torque (in any direction) in any of the joints.

Moreover, it is equipped with the injury parameters typically used in crashworthiness scenarios as HIC, peak 3ms acceleration or Viscous Criteria although not all of them are applicable for pedestrian scenarios.

• The spine and the neck of the models are modelled by 4 kinematic joints: (1 free joint at lower lumbar location, 1 spherical joint between the lumbar and thoracic spine (L1-T12), 1 free joint at the lower neck (T1-C7) and1 free joint at the upper neck (C1-Head OC). These free joints allow elongation and the stiffness in the different directions was modelled by six-DOF (Degree of Freedom) restraints at the joint locations. The rotational stiffnesses in the spine were based on Yang (2000).

The translational stiffness in z-direction was based on the resultant elongation stiffness of the MADYMO occupant model (Happee et al., 2000), while the translational stiffnesses in x- and y-direction were chosen higher than in z-direction to prevent lateral translation. In the head, MADYMO models output the HIC as the head injury criteria for pedestrian scenarios, correlated with head injuries by Prasad-Mertz (1998) as shown in the figure.

Figure 4-2: Correlation Head Injury Criterion - MAIS injuries in the head.

• Thorax and abdomen are represented by a number of ellipsoids (pelvis, abdomen,

Section II: Multibody analyses of pedestrian scenarios

ribs, shoulders and chest) superimposed in order to avoid discontinuities in the outer surface of the model. Their contact characteristics (stiffness, hysteresis, and damping) from the lateral load on pelvis, abdomen, ribs and shoulders have been taken from the biofidelity requirements for the EuroSID-1 dummy (ISO-N455, 1996) and validated with lateral impact against Post Mortem Human Subject (PMHS) tests (Kajzer 1990, Yang 1995, Kajzer 1993, Roberts 1991).

• The hip joint was modelled by a spherical joint with joint stiffness characteristics taken from Frankel & Nordin (1980). These joint stiffnesses were found to agree well with ranges of motion of the RAMSIS human model (Speyer and Seidl, 1997).

• The knee is modelled with a kinematic free joint. Linear and nonlinear joint resistance functions have been implemented based on data available from literature, optimized for an approximately extended position, as this position is most relevant for pedestrian loading. The linear lateral bending stiffness in the knee joint was based on the dynamic data of Kajzer (1997). This dynamic stiffness is significantly larger than the quasi-static values reported by Piziali & Rastegar (1997) but comparable to EEVC requirements (EEVC, 1994). For knee lateral shear, the EEVC (1994, 1998a) has defined an injury tolerance level of 4 kN force and 6 mm displacement. This results in a linear stiffness of 6.7E5 N/m, which has been applied in the pedestrian model. For pedestrian applications, forward/rearward shear is considered of minor importance and, therefore, the stiffness selected for lateral shear has also been applied for forward/rearward shear. Results from Piziali & Rastegar (1997) indicate that this is acceptable for conditions with an extended knee. The knee flexion/extension stiffness has been implemented using volunteer data (Engin, 1979a; Ma et al. 1995) and the axial compression stiffness based on PMHS data from Walker & Hajek (1972).

• The legs are implemented with bending and fracture properties at several locations in the femur and tibia using bending/fracture joints. The location of the middle bending joint in the femur corresponds with the location of the femur load cell in the Hybrid III dummy. The positions of the upper and lower bending joints in the tibia correspond with the positions of the tibia load cells in the Hybrid III dummy.

• Cardan restraints have been implemented at the bending joints to model the bending stiffness of femur and tibia. Angular stiffness functions were derived from simulations of the quasi-static bending tests in anterior-posterior and lateral-medial directions by Yamada (1970). The angular stiffness was assumed to be equal throughout one long bone. Therefore, the same characteristics have been used for all three Cardan restraints within one segment.

• A spherical joint is used for the ankle, which rotational stiffness for dorsiflexion and inversion/eversion was derived from volunteer data (Crandall et al., 1996). Since

both volunteer and PMHS experiments have shown that the ankle dorsiflexion stiffness depends on the knee flexion angle, inward rotation of the foot has been implemented as a combination of knee and ankle rotation using data from Engin (1979b).

AA- Knee medial rotation

BB- Knee lateral rotation CC- Ankle dorsiflexion DD-Ankle plantar flexion EE- Ankle inversion FF-Ankle eversion

Figure 4-3: Knee and ankle range of motions.

Fracture of the femur and tibia has been implemented through fracture joints, which are spherical joints that are initially locked until a pre-defined fracture trigger signal exceeds the fracture tolerance level. Bending moments and shear forces were used as fracture trigger signals in these models, so when any of the trigger signal exceeds its threshold, the joint is unlocked.

Once the fracture tolerance is exceeded, the angular resistance in the fracture joint is set to zero and both parts of the fractured bone are free to rotate relative to each other.

The fracture limits selected for an average male are:

Part Shear Force Reference Bending Reference

Femur 6,3 kN EEVC (2002) 430 Nm EEVC (2002)

Tibia 4,0 kN Yang (1997) 285 Nm Nyquist (1985) Table 4-1: Summary of injury thresholds in the male average MADYMO pedestrian model.

The robustness of these fracture tolerances for the MADYMO pedestrian model were analysed thoroughly in Van Hoof (2003). In this analysis, 3 different sets of thresholds were selected covering the whole range of femur and tibia fracture tolerances found in the literature in terms of shear force and bending moment.

For each of them, its capacity to predict the severity and the timing of the injuries reported in 4 full pedestrian PMHS test (INRETS, 1997) is analysed modelling this set of tests with MADYMO. These PMHS tests were conducted at impact velocity range from 32 km/h to 40 km/h with PMHS subjects ranging from 75 to 94 years old and positioned laterally with

Section II: Multibody analyses of pedestrian scenarios

respect to the vehicle. The three sets of injury thresholds selected are shown in the Table 4-2 and the results of the analysis in terms of injuries reported and injuries predicted is shown in Table 4-3.

Table 4-2: Injury threshold sets analysed in Van Hoof (2003).

It can be seen that the original set and the one based on the high fracture tolerance only diverge in the tibia fracture threshold while the set based on the low fracture limits has thresholds 50-60% lower than the other two sets.

Injuries reported Set 1 (Original) Set 2 (Low) Set 3 (High)