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News & Insights (/news-insights) / Engineering Advantage Blog (/blog) / What is Mass Scaling and When is it Appropriate in Explicit Dynamics Analysis?
Engineering Advantage
What is Mass Scaling and When is it
Appropriate in Explicit Dynamics
Analysis?
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Have you ever painstakingly worked to develop an explicit dynamics model only to find out
that it takes days to run? Wouldn’t you like to be able to speed up your runs without
sacrificing solution accuracy? Mass scaling may provide a solution.
Run time for a transient dynamics model is not only a function of the model size, but also the
time step size. In explicit dynamics, the time step is internally calculated to provide a stable
solution and to accurately predict the propagation of the highest frequency waves in the
model; the stress and shock waves. This condition limits the time step such that the stress
wave cannot travel more than the smallest element dimension in a single step. This is known
as the Courant condition which is shown in Equation 1.
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Equation 1:
July 11, 2017
by: Christina Capasso Jamerson
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Where
= Stable time step
h = Smallest element dimension in the model
c = Acoustic wave speed (speed of stress wave)
f = Scale factor to improve stability (typically 0.9)
The equation for the acoustic wave speed is different for each element type but its simplest
form is listed in Equation 2.
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Equation 2:
July 4, 2017
by: Christina Capasso Jamerson
Where E = Young’s modulus
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= density
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Request a free Explicit Dynamics Consulting Consultation today! (/contact-us)
There are three parameters that can be adjusted to increase the time step and bring down
the run time: element size, Young’s modulus, and density. While the mesh can be adjusted to
increase the element sizes, this is often impractical when geometries are complex with small
features. Young’s modulus is a material stiffness property and artificially lowering it will
adversely affect accuracy. Artificially increasing density can also adversely affect accuracy
(think force = mass times acceleration). But what if the density could be increased only in the
smallest elements that control the time step? This idea is the basis for mass scaling.
Mass scaling is an automated procedure whereby the code increases the time step by
scaling up the density in the specific elements that are controlling the time step. The user
specifies a minimum time step size and the density in those elements that have time steps
smaller than this value are increased to the point where the time step is equal to this value.
While this is a very effective tool, it’s not without its drawbacks.
Mass scaling is a tried and proven method for reducing run times in quasi-static analyses
where the velocity is low and the kinetic energy is very small relative to the internal energy
(please refer to my previous blog post,“How Can Explicit Solvers Help with Stubborn
Nonlinear Statics Model (/blog/how-can-explicit-solvers-help-stubborn-nonlinear-statics-models) ” for more
information on quasi-static analyses). But what about truly dynamic analyses where an
accurate mass distribution is critical to the solution?
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by: James Kosloski
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It is still possible to use mass scaling effectively for such models, but it should be done
judiciously. As a rule of thumb, mass can be added to non-critical regions of the model as
long as it doesn’t significantly increase the overall mass of a part.
Validation requires
READ MORE (/BLOG/SPEEDING-YOUR-ANALYSIS%E2%80%93-PART-3)
checking both the relative increase in mass as well as the location of the added mass. Only
very small amounts of mass should be added in locations where critical results are being
TAGS: Hardware (/blog?tid_1=Hardware) / FEA
evaluated.
Consulting (/blog?tid=66) / CFD (/blog?tid=80) / CFD
To demonstrate the effects of mass scaling, a model of a Polycarbonate ball with through
holes impacting a rigid plate at 20 m/s was developed in ANSYS Workbench/LS-Dyna. The
critical result used to predict damage in the ball is the maximum plastic strain in the through
holes. Two different meshes were evaluated, as shown in Figure 1. The image on the left
shows the model with a default mesh and the image on the right shows the model with a fine
mesh at the top.
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June 20, 2017
by: Eric Stamper
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tid=65)
Figure 1: Meshes – Polycarbonate Ball Impact Model
The two meshes were run with different levels of mass-scaling. The plastic strain distribution
for the default mesh without any mass scaling is shown in Figure 2. All of the plastic strain
occurs in the through holes. We can safely assume, then, that scaling the mass in the small
elements at the top of the ball in the second mesh should not affect the critical results
because these elements are relatively far from the critical regions.
Figure 2: Plastic Strain Distribution – Default Mesh
A comparison of solutions for the two different meshes and different mass scaling values is
provided in Table 1. Notice that a small amount of mass scaling (dt = 3.e-7) assigned to the
default mesh has a minimal impact on the plastic strain, while a larger amount of mass scaling
(dt = 6.e-7) has a significant effect, even though it only causes in increase of 0.19% in the
mass of the ball. However, for the model with the fine mesh at the top, a significant increase
in mass scaling (dt = 3.e-7 s up from 1.e-7 s) causes only a minor change in plastic strain
while resulting in nearly a 60% drop in run time! In this case, all of the mass scaling was
applied to the smallest elements at the top of the ball, far from the through holes, as shown in
Figure 3.
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Table 1: Model Comparison Showing the Effects of Mass Scaling
Figure 3: Added Mass (non-blue elements at top of ball)
In conclusion, mass scaling is a proven and effective tool for reducing run times in explicit
dynamics analysis (/fea-services/explicit-dynamics-analysis) , especially in models that have complex
geometry and small features that make mesh coarsening difficult. While mass scaling is
simple to apply, it needs to be done judiciously in models that are not quasi-static. Analysts
(https://caeai.com) should check both the amount of mass scaling as a percentage of part mass
and the location of the mass scaling to make sure that artificial mass is not being added to
critical regions. Small percentage increases in mass applied to critical locations can
significantly impact the accuracy of critical results. What good are results obtained quickly if
they aren’t accurate? It is always wise to run your model once without mass scaling and
compare critical results to quantify the effects of mass scaling.
I am most interested in feedback from those of you that have used mass scaling in explicit
dynamics analysis. Have you found mass scaling to be a valuable tool for speeding up your
runs without sacrificing accuracy?
Request a free Explicit Dynamics Consulting Consultation today! (/contact-us)
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Steven Hale • a year ago
As I discussed in the article, if you are simulating a quasi-static process, mass scaling is
generally acceptable because inertia effects should be small relative to static effects. On
the other hand, if inertia/dynamic effects are important, you can still use mass-scaling but
you need to make sure that the overall percentage increase in mass is very small in
regions where accuracy is critical.
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Christina_Capasso
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> Steven Hale • a year ago
approved
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Ankit Varma • a year ago
hello Steven, I found the article quite informative and useful for begineers like me. I would
like to request you to provide me some information about using mass scaling judiciously
in the case of an dynamic/explicit analysis for an welding process. thank you.
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Claudiu Feanalysis • 2 years ago
Superb article and very useful against long solving times, thank you!
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Steven Hale > Claudiu Feanalysis • 2 years ago
You're welcome - I think mass scaling can be very useful if used properly. I'm glad
you found this helpful.
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