3.5.1 Introduction to MADYMO
With increasing computing power becoming available at decreasing cost, mathematical modelling of vehicle and vehicle-pedestrian impacts is becoming increasingly practical and affordable. The use of commercial modelling software permits users to simulate numerous scenarios at a fraction of the cost and time associated with experimental testing.
There are two techniques commonly used to model human bodies mathematically in the field of crash analysis, namely multibody systems (MBS) and finite element analysis (FEA). The software program MADYMO (MAthematical DYnamic Modelling) (TNO Automotive) is a mathematical solver commonly used in the automotive and crash-safety sectors. It supports the use of both MBS and FEA.
The kinematics, accelerations and contact forces of a dynamic system can be quickly determined using an MBS model. However, given that MBS are constructed out of fairly simple geometric shapes and surfaces (ellipsoids, cylinders, planes etc) connected by a range of joint types then there are limitations as to how accurately they can be used to model many situations. For example, whilst MBS modelling may quite accurately describe the motion of a leg following an impact by a car bumper, any resultant soft-tissue damage is poorly quantified. Areas where deformation, damage or injury is of interest therefore need to be modelled using MADYMO’s FEA capability. Combining FEA models of areas of interest with multibody systems results in efficient computation.
3.5.2 Multibody Analysis in MADYMO
The simplest MBS is, in fact, a single body system. It would consist of a single body in a single system. If the body was connected to another body with a kinematic joint, then there would be two bodies within one system. If there was no joint, however, then there would be two systems, each containing one body. Bodies may be joined to one another within the same system so that they may form tree structures or closed chains. Closed chains are reduced to tree structures with the removal of one kinematic joint and the subsequent insertion of a closing joint.
Simple bodies can be modelled using predefined objects such as ellipsoids, cylinders and planes. More complicated bodies can be modelled using facets: a mesh of 2-D mass-less elements.
Multibody human and dummy models available in MADYMO fall into two categories: ellipsoid and facet.
Ellipsoid models are the simpler of the two and are highly computationally efficient.
A human body may be modelled via an ellipsoid model using a tree structure consisting of a parent body (for example, the torso) with a number of attached child bodies. For a very simplified model this may consist of only five child bodies organized into five branches – the head, two arms and two legs. The pedestrian model used in this study had a total of 52 bodies organized in seven branches (See MADYMO Version 6.0 Human Models Manual). The MADYMO ellipsoid model was originally designed for vehicle occupant analysis but is now primarily a pedestrian model.
Facet models allow for greater biofidelity. A typical human facet model in MADYMO has 92 bodies. The facet model is skinned with 2000 triangular elements.
Internal structures include neck, spine, pelvis and shoulders. The MADYMO facet model was designed primarily for occupant analysis.
Figure 3.1 Multibody Pedestrian Models: From Left to Right - 3-yr old Child, 6-yr old Child, 5th Percentile Female, 50th Percentile Male and the 95th Percentile Male (Source: MADYMO Human Models Manual Version 6.3, TNO Automotive)
Figure 3.2 Facet Occupant Models: From Left to Right - 95th Percentile Male, 50th Percentile Male and 5th Percentile Female (Source: MADYMO Human Models Manual Version 6.3, TNO Automotive)
3.5.3 Finite Element Analysis in MADYMO
In contrast to multibody models, FEA methods use a mesh of inter-connected nodes allowing accurate geometric representation. FEA models may include well defined and context dependant material properties, as well as allowing the inclusion of complex contact and interaction expressions.
As discussed in section 3.3.3 FEA analysis in MADYMO can be conducted using either explicit Runge-Kutta or implicit/explicit Euler integration. MADYMO uses Langrangian description i.e. nodes and elements are fixed to the material and displace with the material.
Human and dummy finite element models in MADYMO are actually multibody/FEA hybrid models. A rigid body chain, the same as used in the multibody models, is used to allow consistent positioning of the FEA and multibody models. Inertial properties
of the model are determined using a combination of the inertial properties of the underlying rigid bodies and the FEA elements.
The MADYMO FEA human and dummy models provide a higher degree of biofidelity than the purely multibody models due to the ability to accurately reproduce deformation and damage of body components. The trade-off is a considerable penalty in computation time in comparison with the much simpler multibody models.
3.5.4 Combined Multibody/FEA Simulation in MADYMO
One of the most popular features of MADYMO is the ability to mix and match multibody and finite element analysis. As mentioned previously, the MADYMO FEA human model is actually a multibody/FEA hybrid.
Because of the significant computational requirements associated with FEA analysis it is recommended that as much as possible of the system under investigation is modelled using multibody representations. Conducting entirely multibody simulations in order to determine the best approach for subsequent FEA analysis is recommended.
3.5.5 Limitations of MADYMO
Aside from the general limitations applicable to any form of mathematical modelling (see Section 3.5.2) there are some limitations of MADYMO worthy of note.
Versions of MADYMO prior to Version 6 (this research project used Version 5.4 for the majority of the simulation conducted, prior to the introduction of Version 6) contained issues regarding FEA analysis including poor contact calculation and long computational time.
Other researchers appear to have had similar difficulties with pre-Version 6 MADYMO FEA implementation. Troutbeck et al (2001) noted the following:
“In summary, the use of the finite element capabilities of MADYMO was of limited practical application. This was due to the limited material types included within MADYMO, excessive computation times, and a lack of physical testing data with which to compare the output of the simulations.”
Indeed, many of the problems Troutbeck et al experienced, such as non-SI mass units and unlocateable ‘noise’ in some parts of FEA models were also encountered by this author. Despite the issues they encountered, Troutbeck et al concluded that
“MADYMO is extremely well suited to the assessment of human injury risk”, an assessment that this author agrees with.
With MADYMO Version 6 now in widespread use it is apparent that many of the issues regarding MADYMO’s implementation of finite element analysis have been addressed. Nonetheless, very long computation times are still required for models with a large number of FEA elements and this remains as a large limitation to MADYMO’s usefulness. MADYMO’s usefulness is also reduced by the time required to gain familiarity with the software but this is by no means unique to MADYMO when compared with other FEA and accident reconstruction software packages.