The fluid-structure interaction and the fluid flow are studied in cases of a fuel tank sloshing and overturning. A
bi-phase liquid-gas material with an ALE formulation is used to define the interaction between water and air in the
fuel tank.
The purpose of this example is to study the energy propagation and the momentum transfer through several bodies, initially
in contact with each other, subjected to multiple impact. The process of collision and the energetic behavior upon
impact are described using a 3-dimensional mode.
The impact and rebound between balls on a small billiard table is studied. This example deals with the problem of
defining interfaces and transmitting momentum between the balls.
The purpose of this example is to introduce a method for characterizing and validation of the most commonly used Radioss material laws for modeling elasto-plastic materials.
After a quasi-static pre-loading using gravity, a dummy cyclist rides along a plane, then jumps down onto a lower
plane. Sensors are used to simulate the scenario in terms of time.
The purpose of this study is to demonstrate the use of quadratic interface contact using two gears in contact with
identical pitch diameter and straight teeth. Two different contact interfaces are compared.
The problem of a dummy positioning on the seat before a crash analysis is the quasi-static loading which can be resolved
by either Radioss explicit or Radioss implicit solvers.
The crashing of a box beam against a rigid wall is a typical and famous example of simulation in dynamic transient
problems. The purpose for this example is to study the mesh influence on simulation results when several kinds of
shell elements are used.
A square plane subjected to in-plane and out-of-plane static loading is a simple element test. It allows you to highlight
element formulation for elastic and elasto-plastic cases. The under-integrated quadrilateral shells are compared with
the fully-integrated BATOZ shells. The triangles are also studied.
The modeling of a camshaft, which takes the engine's rotary motion and translates it into linear motion for operating
the intake and exhaust valves, is studied.
The ditching of an object into a pool of water is studied using ALE and SPH approaches. The simulation results are
compared to the experimental data and to the analytical results.
A rubber ring resting on a flat rigid surface is pushed down by a circular roller to produce self-contact on the inside
surface of the ring. Then the roller is simultaneously rolled and translated so that crushed ring rolls along the
flat surface.
Separate the whole model into main domain and sub-domain and solve each one with its own timestep. The new Multi-Domain
Single Input Format makes the sub-domain part definition with the /SUBDOMAIN keyword.
The aim of this example is to introduce /INIVOL for initial volume fractions of different materials in multi-material ALE elements, /SURF/PLANE for infinite plane, and fluid structure interaction (FSI) with a Lagrange container.
A heat source moved on one plate. Heat exchanged between a heatsource and a plate through contact, also between a
plate and theatmosphere (water) through convective flux.
Impacts of rotating structures usually happen while the structure is rotating at a steady state. When the structure is
rotating at very high speeds, it is necessary to include the centrifugal force field acting on the structure to correctly
account for the initial stresses in the structure due to rotation.
The purpose of this example is to introduce a method for characterizing and validation of the most commonly used Radioss material laws for modeling elasto-plastic materials.
RD-E: 1101 Elasto-plastic Material Law Characterization
The purpose of this example is to introduce a method for characterizing and
validation of the most commonly used Radioss material laws for
modeling elasto-plastic materials.
The use of "engineering” and "true” stress-strain curves is pointed out. Failure
models are also introduced to better fit the experimental response.
Tension is applied to an object. The standardized “dogbone" object contains a defined
cross-sectional area . The material to be characterized is DP600 Steel.
1 A velocity is imposed at the right-end.
Units: mm, ms, kg, N, GPa.
The material undergoes isotropic elasto-plastic behavior which can be reproduced by a
Johnson-Cook (/MAT/LAW2). The tabulated material law
(/MAT/LAW36) is also studied.
The model is meshed with 4-node shells and 3-node shells as shown in Figure 2. The average element size is about 2 mm.
The shell properties use recommended best practice settings, except for the thickness
which matches the test.
5 integration points over the thickness.
QEPH shell formulation (Ishell = 24).
Iterative plasticity for plane stress (Newton-Raphson method; Iplas = 1).
Thickness changes are considered in stress computation (Ithick = 1).
Initial thickness is uniform, equal to 2.5 mm
Boundary Condition
The left side of the object is fixed in all six degrees of freedom (all three
translational and all three rotational DOFs). On the right side only translation in
X-direction is free, all other five DOFs are fixed. An imposed velocity of -1.0 m/s
in the X-direction is applied to the main node of the rigid body, shown Figure 2, whereby the elongation is increased uniformly
at low speed.
Two measurement nodes with a distance of 80 mm are chosen (Figure 3) to continuously measure the change in length in the measurement section of the sample during the
simulation and to obtain the strain on the sample.
The engineering (nominal) stress is calculated as:(1)Where,
Measure force
Cross-sectional area of the undeformed sample
The total engineering strain is calculated as:(2)Where,
Change in length between the two measurement points
Initial length of the measurement section
The true strain is computed with the relationship:(3)
Engineering strain and true strain; therefore, are linked together
by:(4)
True stresses are measured by dividing the force with the true deformed
section:(5)
Thus, to compute true stresses, the area variation must be considered. If Poisson’s
coefficient is 0.5 during plastic deformation, the true area in mono-axial traction
is:(6)
Thus, the relationship between true and engineering stresses is:(7)
Characterization of the Material Law
There are two steps to characterize the material law.
Transform the engineering stress versus engineering strain curve into a true stress
versus true strain curve (this step applies to any elasto-plastic material law).
Extract the main parameters from the true stress versus true strain curve, to define
the material law (Johnson-Cook law and material coefficients for
/MAT/LAW2 or the yield curve definition for
/MAT/LAW36).
When there is no material test data available (for example, in an early design
stage), values of Yield stress, Ultimate tensile strength (engineering stress value)
and Engineering strain at UTS must be provided to characterize
/MAT/LAW2 using Iflag = 1.
The characterization will be made for /MAT/LAW2 (Johnson-Cook
elasto-plastic), and /MAT/LAW36 (tabulated elasto-plastic). For
each of the material laws, the yield stress and Young's modulus are determined from
the curve.
The plastic strain can be defined as:(8)
An important point to be characterized on the curve is the necking point, where the
slope of the force versus the displacement curve is equal to 0, and where the
following relationships apply:(9)
Table 1. Equations Used for Analysis
Material
Property
Generic
Equation
Engineering
stress
Engineering
strain
True
stress
True
strain
True strain
rate
Results
/MAT/LAW2: Elasto-plastic Material Law using the Johnson-Cook Model
The stress versus plastic strain law is:(10)Where,
Yield stress and is read from the experimental curve
and
Material paraemters
If the material parameters and are not available, then Radioss
can use /MAT/LAW2, Iflag =
1. In this case, the UTS (Ultimate tensile strength, engineering value)
and engineering strain at UTS are entered. These values can often be found online, in
literature or from a material supplier. Radioss will then
calculate the and parameters used in Equation 10.
Normally if a real test stress-strain curve exists, the test data should be used in
/MAT/LAW36 (PLAS_TAB). However, in this example, you will assume that
the test curve is not available and use /MAT/LAW2 with Iflag =
1 to see how well using the simplified data input compares to the actual
test curve.
Data
Value
Yield stress
0.3 GPa
UTS
0.686 GPa
Strain at UTS (E_UTS)
0.129 (12.9%)
Since the simulation calculates true stress and true strain for the elements, the
engineering stress-strain curve from the simulation must be calculated. Similar to the test,
the engineering stress can be calculated by using Equation 1 and the rigid body force and original area. The engineering strain
can be calculated by using Equation 2 and the displacement between the two measurement nodes and the
original distance. In the model, the displacement of node 616 is measure with respect to the
displacement of node 102 by using a local moving system placed at node 102. This allows the
displacement between the two nodes to be output as the displacement of node 616.
Comparing the simulation results of the stress-strain curve show a perfect agreement with
respect to the maximum stress value of the tested curve. The initial behavior of the
simulation curve before the necking point shows differences to the test curve (Figure 6) and the stress value is slightly higher. This can be
improved by using /MAT/LAW36 and inputting the stress-strain curve test
data.
/MAT/LAW36: Elasto-plastic Material Law using a Tabulated Input Function
Since tensile test data is available, a more accurate method is to use that data in
material LAW36. The first step is to take the test data and calculate the true stress versus
true plastic strain curve by using Equation 4 and Equation 7.
The necking point is where the slope of the engineering stress-strain curve becomes zero.
All values after the necking point can not be used for creating the material curve for
/MAT/LAW36 and can be removed from the data and disregarded. Values
after the necking point must be extrapolated to a strain larger than failure for the
material. The necking point occurs at the engineering strain at the ultimate tensile stress
= 0.129. After this point, the curve was linearly extrapolated to 100% plastic strain as
shown in Figure 8.
Next, the true stress versus true plastic strain is calculated using Equation 8.
Using the curve in Figure 8 as input in LAW36, the simulation results perfectly
match the test curve between yield point and the necking point, as shown in Figure 9. The post necking behavior depends on the method used to
extrapolate the true stress versus true plastic strain data after necking.
/FAIL/BIQUAD: Simplified Nonlinear Strain-based Failure Criteria with Linear Damage
Accumulation
In some elasto-plastic material models, a single plastic strain at failure can be input to
model material failure. The element is deleted when the plastic strain reaches a
user-defined value .
The main disadvantage of using this approach is the element is deleted when the plastic
strain is reached no matter the stress state. There is no difference between failure in
tension or compression. Metals usually show different strains at failure for the different
states of stress. Especially in the case of compression, the failure strain is usually much
higher than for tension. To overcome this limitation, /FAIL/BIQUAD is
used instead of the simple maximum equivalent plastic strain that can be defined in the
material input. With a few simple inputs, /FAIL/BIQUAD creates a
nonlinear plastic strain at failure as a function of stress triaxality.
/MAT/LAW2 with /FAIL/BIQUAD
When the default
high strength steel (HSS) values (M_flag =2)
included in /FAIL/BIQUAD are used, the simulation shows failure
before the test. To better match the test, the /FAIL/BIQUAD
uniaxial tension plastic strain at failure value (c3) is increased from 0.5 to 0.75.
Figure 10 shows the results for both simulation
cases.
/MAT/LAW36 with /FAIL/BIQUAD
Similar to the
LAW2 simulation, the /FAIL/BIQUAD uniaxial tension plastic strain
at failure value (c3) is increased from 0.5 to 0.9 so that the failure point in the
simulation matches the test.
Conclusion
In the first part of the example, a method was introduced to
characterize and validate the most commonly used Radioss
material laws. The /MAT/LAW2 (PLAS_JOHNS) material was used with a few
material parameters to represent the material. The /MAT/LAW36 (PLAS_TAB)
material was used with experimental data of a tensile test for a more accurate simulation.
The use of "engineering” and "true” stress-strain curves was pointed out.
To describe
the failure behavior in tension and compression a simplified nonlinear strain-based failure
criterion with linear damage accumulation (/FAIL/BIQUAD) was used to
better fit the experimental response.