Tips and Tricks for Explicit Simulations

Alexandre Amorim Carvalho [EN-MME]25/03/2019

Outline

• Explicit vs. Implicit

• Explicit:

• When to use it

• Typical features

• First order elements

• Tricks and tips

Implicit approach Vs. Explicit approach

Static analysis is done using the simple linear

equation [K]{x}={F}.

Time does not play any role.

A dynamic analysis follows a more complex

governing equation which is like:

[M]{x''}+[C]{x'}+[K]{x}={F}

To solve {x}, [K] must be inverted: not easy.

[K] is unknown due to displacement of

adjacent nodes:

convergence must be sought via iterations

(e.g. Newton-Raphson)

solution stable longer time steps (Δt)

Instead of solving for {x}, we solve for {x"}.

[M]{x‘’} = {F} Thus we bypass the inversion

of the complex stiffness matrix, and we just

have to invert the mass matrix [M]

If lower order elements are used the mass

matrix is a lumped matrix (diagonal),

inversion is easy.

Disadvantage is that the Euler Time

integration scheme is not used,

hence it is conditionally stable.

(no converge issues!).

We need to use very small time steps.

Calculation wave propagation

See: https://www.quora.com/What-is-time-step-in-LS-DYNA-How-are-they-calculated

F t=0: FN25 = m1/4*E16*a

t=0+δt: dN25, εE16, σE16

Imposes a force on N20

t=0+2*δt: dN20, εE16, σE16

Must be done before wave propagates

through material at the speed of sound

Minimum time-step is dependent on

smallest element!Δt = L/c

Courant condition!

Explicit

• No convergence issues

• Short time for solution of time step

• Conditionally stable: time step needs to respect

the Courant condition, can mean many time

steps

When to use explicit

• Short timed events

• Non-Linearities

• Large deformations

• Non-linear material properties

• Contact intensive events

Applications of Explicit

• Forming

• Crash and other accidents

• Explosions

• Energy deposition

Jorge

Applications at CERN

• Rutherford cables

• Forming processes

• Beam intersecting devices

• Material characterization(reverse engineering)

• Softwares: LS-DYNA (infinite licenses) & ANSYS Autodyn (Ansys license scheme)

Marco Garlaschè

& Jaime Cabanes

Tobias Polzin

Explicit typical features: material models

• Material models: plastic curves, strain rate,

anisotropic materials, cyclic plasticity, failure,

phase changing

• plastic curves equation or point interpolation

Explicit typical features: material models

Dependencies:

Strain rate and temperature

Explicit typical features: contacts

• Detection methods;

• Penalty formulation

F = stiffness*penetration;

Attention to your mesh size and

penetration detection method!

Explicit: first order elements

• Shear locking is a problem for full integrated elements: overly stiff

behaviour results from energy going into shearing the element rather

than bending it.

• Hourglassing is a problem for reduced integration elements (on

Gauss point): a fake deformation mode resulting from the excitation

of zero-energy degrees of freedom → hourglass control (SRI, ..)

Tricking an explicit simulation

• Mass scaling;

• Time scaling;

• Increase mesh size;

• Reduce the export frequency;

• Symmetry

• Reduce integration points through the thickness of shell elements;

• Single precision vs. double precision (t = +30%)

• (7 digits vs. 16 digits);

• For many time-steps, double precision is recommended;

Watch out for

springback!

Watch out for

dynamic events!

Tricking an explicit simulation

• Mass scaling – increasing mass of some elements to increase

smallest time step → reduced number of steps.

• Rule of thumb: mass scaling beyond 5% of total mass is not

recommended – may introduce unrealistic inertial effects;

• In reality, it depends where the mass is added;

Δt = L/c

Mass scaling – mass of all

elements is changed to have an

equivalent pre-defined time-step.

Selective mass scaling – mass of

smallest elements is increased to

a minimum pre-defined time-step.

Tricking an explicit simulation

• Time scaling – do we need it?

Lmin = 1.7 mm

c = sqrt(E/ρ) = 5182.1 mm/ms

Δtmin = 3.2903E-04 ms

Event period = 60000 ms

Number of steps = 182.4 million steps

1 step = 0.0046 seconds

Total = 233h

Event period = 60 ms

Number of steps = 182400 steps

Total = 13.9 minutes

Tricking an explicit simulation

• Time scaling – reducing the time of events by

a factor of 1000 is possible → reduced

number of steps.

ATTENTION: May introduce unrealistic

dynamic effects!

60 ms 6 ms 0.6 ms

BONUS TOPIC: Considère’s criterion

Necking begins when the increase in stress due

to decrease of cross-section area is greater than

the increase in load bearing capacity of the

specimen due to work hardening;

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Effe

ctive

Str

ess [M

Pa

]

Effective Plastic Strain [mm/mm]

Material Model *MAT_024

Material Model *MAT_036 0deg

Material Model *MAT_125

𝑑𝜎

𝑑𝜀< 𝜎

Benchmark boundary conditions Study 2 S2

Imposed displacement

The nodes on the top are strained up to 60%

over 60 ms.

Using the same .k file and varying only the

material model.

60% with MAT’s: 024, 036 and 125

MAT_024

t = 60ms

MAT_036

t = 60ms

MAT_125

t = 60ms

Plotting the effective stress of each element over time

Increasing the time scaling reduces

only slightly the effective plastic strains!

Similar element behavior has been

observed in forming simulations.

At very large deformations,

precision is hard to obtain.

Thank you!

Implicit Vs. Explicit

A static analysis, like a stress analysis in

FEA, is done using the simple linear

equation [A]{x}={B}. In such analysis time

does not play any role.

On the other hand, a dynamic analysis (or

transient or modal analysis also) follows a

more complex governing equation which is

like: [M]{x''}+[C]{x'}+[K]{x}={F} - Such

analysis are dependent on time.

Implicit solution is one in which the

calculation of current quantities in one time

step are based on the quantities calculated

in the previous time step. This is called

Euler Time Integration Scheme.

In an explicit analysis, instead of solving

for {x}, we solve for {x"}.

Thus we bypass the inversion of the

complex stiffness matrix, and we just have

to invert the mass matrix [M].

In case lower order elements are used,

which an explicit analysis always prefers,

the mass matrix is also a lumped matrix, or

a diagonal matrix, whose inversion is a

single step process of just making the

diagonal elements reciprocal. Hence this is

very easily done. But disadvantage is that

the Euler Time integration scheme is not

used in this, and hence it is not

unconditionally stable. So we need to use

very small time steps.

Hourglass control: Selective Reduced

Integration

• http://web.iitd.ac.in/~achawla/public_html/736/

9-Finite_Element_analytical_tecniques.pdf