Table 1 Comparison between the modeling methods used for the train collision models

Track

1. Hexahedral elements are applied.

2. #MAT 20 material is assigned.

3. All degrees of freedom are restricted.

1. Hexahedral elements are applied.

2. #MAT 20 material is assigned.

3. All degrees of freedom are restricted.

4. The actual rail profile is considered.

Carbody

1. Hexahedral elements are applied.

2. #MAT 20 material is assigned.

3. The translational freedom along with the train movement is retained and other degrees of freedom are restricted.

4. The material density is adjusted to achieve the weight change.

1. Mainly quadrilateral shell elements and triangular elements in local irregular locations are applied.

2. Hexahedral elements for structures with a thickness above 20 mm are defined.

3. The element size is controlled within 15–20 mm.

4. #MAT 24 elastoplastic material is assigned.

Bogie

1. The bogie is not modeled.

2. The equivalent weight is added to the carbody.

1. Quadrilateral shell elements are used.

2. The bogie-frame, wheel-set, axle box, gearbox, anti-rolling torsion bar, and traction rod seat are modeled separately.

3. #MAT 20 material is assigned;

4. Joint elements are added to simulate the relative motion among different parts;

5. Discrete beams are applied with #MAT 67 material to simulate the primary and secondary suspensions, considering the actual stiffness and damping.

Anti-climbing energy-absorbing device, semi-automatic and semi-permanent couplers

1. Discrete beams are applied with #MAT S08 material.

2. The corresponding curves in Figure 2 are considered as the input curves.

1. Quadrilateral shell elements are used for the structures and the #MAT 20 material is assigned.

2. Joint elements are added to simulate the relative motion between different parts.

3. Discrete beam elements are used with #MAT S08 material to simulate the mechanical characteristics, the corresponding curves in Figure 2 are considered as the input curves.

Wheel-rail contact

1. Discrete beam elements are applied with #MAT S03 material.

2. The equivalent friction force is input; the friction coefficient is considered as 0.008 [19].

1. Surface to surface contact between the wheel and rail is defined.

2. The friction coefficient is considered as 0.008 [19].

Vehicle contact

1, Contact between the vehicles is not considered.

1. Self-contact between the vehicles is defined.

2. The friction coefficient is considered as 0.15 [32].