# Selective mass scaling (SMS)

• conventional mass scaling (CMS): The mass of small or stiff elements is increased to prevent a very small timestep. Thus, artificial inertia forces are added which influence all eigenfrequencies including rigid body modes. This means, this additional mass must be used very carefully so that the resulting non-physical inertia effects do not dominate the global solution.

• selective mass scaling (SMS): Using selective mass scaling only the high frequencies are affected, whereas the low frequencies (rigid body modes) are not influenced. Thereby, a lot of artificial mass can be added to the system without adulterate the global solution. This method is very effective, if it is applied to limited regions with very small critical timesteps.

[Olovsson et al. (2005), Selective mass scaling for explicit finite element analysis, IJNME 63, 1436-1445.]

## Theory

• Explicit time integration method: diagonal (lumped) mass matrix, critical timestep

• Idea: Decreasing the highest eigenfrequencies of the system (), while affecting the lower frequencies as little as possible.
• Modification of element mass matrix in the following way:

• Therein,  is the original element mass matrix, normally lumped and  contains the artificially added mass terms. The basic philosophy is to define  to lower the non-zero eigenfrequencies of the element, while at the same time not affecting the translational rigid body behavior at all, i. e.,

.

• The resulting modified mass matrix  is a sparse matrix but no longer a diagonal matrix. Thus, the inversion of the modified mass matrix is no more as simple as without using selective mass scaling. Due to the fact that the inversion of the mass matrix would be computationally very expansive, the momentum balance

is solved using an iterative solver (conjugate gradient method).

## Example 1

• Crashing of a foam structure, 250 000 tetrahedron elements, MPP with 16 CPUs

• Performance:

timesteps CPU time speedup
no mass scaling 220911 9227 s 1.0
CMS 15874 647 s 14.3
SMS 15874 997 s 9.3
• simulation results: kinetic energy, deformation at t = 17 ms

## Example 2

• impact of a "bodyblock" on a steering wheel: Failure of a fine meshed subdomain

• volume elements with a critical timestep of dt < 0.1 ms
• simulation time till 50 ms:
• CMS with dt=1.0e-7: 5.5 Stunden
• SMS with dt=1.0e-6: 0.7 Stunden

## Example 3

• Example consists of four files. One master file (Example_SMS.key) and three include files (mass_scaling_{1-3}.inc), that may be interchanged to study the effects of no mass scaling, conventional mass scaling (CMS) or selective mass scaling (SMS), respectively.

• Only one part is using SMS (lower or blue part of sphere, while CMS is still active for the yellow part).

• Run the example with all three include files separately.

• Study the effect of the different mass scaling techniques by checking the internal energy, kinetic energy and energy ratio of the example.

• Time: 0ms

• Simulation:

• Time: 1ms

• It can be seen that at the beginning all three different models show a different level kinetic energy. The most amount of kinetic energy is being introduced by CMS due to the fact, that additional mass works on the yellow and on the blue part.

• The blue line in the diagram represents SMS for the blue part while CMS is still active for the yellow part. Hence the kinetic energy is significantly lower but not as low as for the run that was started without any mass scaling (red line)

• Of course the opposite picture is being received for the internal energy:

• The energy ratio is 1 for SMS and the run without mass scaling, but delivers additional energy for CMS.

## Current limitations

• SMS should be activated using LS-DYNA V971 R4.2.1 or higher.
• SMS is at the moment not available in combination with other contraint definitations, e. g., CONTACT_TIED_xxx, *CONSTRAINED_SPOTWELD, ... .

• SMS should be working in combination with the keywords *MAT_RIGID and *NODAL_RIGID_BODIES, if current LS-DYNA-versions are used.

• *CONTACT_SPOTWELD (7) is automatically switched to a "_OFFSET" (o7) contact formulation, as soon as for a respective part SMS is activated or SMS is activated globally. Remark: The material model *MAT_SPOTWELD_DA requires informations from *CONTACT_SPOTWELD, i. e., *MAT_SPOTWELD_DA can not be used in combination with parts, for which SMS is activated.

• The artificial mass added via selective mass scaling is stored together with the conventional added mass is the variable "added mass". It would be preferable, if there exits an additional variable for the artificial mass added via SMS, because the positive effects (low influence on kinetic energy and inertia effects) of using SMS is not directly obvious. Instead, a closer look has to be taken on the kinetic energy.

ah 04/2010

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