reflection and transmission coefficients in long bars with different cross-sectional areas exposed to pulse loading

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reflection and transmission coefficients in long bars with different cross-sectional areas exposed to pulse loading

Abaqus Users mailing list




Dear Community,


I'd like to ask for advice on modelling reflection and transmission coefficients when two bars with different cross-sectional areas contact each other and are exposed to pulse loading.


I have modelled this process in Abaqus/Explicit as a two-dimensional simulation. The investigation was conveniently done as a parametric study, defining the lateral dimension as parameter. Both bars are slim (length 2 m, diameter 2 cm) and elastic.


Two material combinations are defined:
identical materials: 2 steel bars
and different materials: first bar is steel, second bar is aluminum


Theory gives a negative reflection coefficient R and a positive transmission coefficient T.


Elements:
CAX4R is the only axisymmetric solid element available in Abaqus/Explicit with four nodes
CPE4R is the only plane strain solid element available in Abaqus/Explicit with four nodes
CPS4R is the only plane stress solid element available in Abaqus/Explicit with four nodes


Contact is defined as CONTACT PAIR with the penalty constraint. Surfaces are element-based. Abaqus was run in double precision.


The reflection and transmission coefficients from FEM data are computed as the maximum of the signal with respect to the maximum of the incident wave.


Observation:
the FEM data for identical materials and the ones for the reflection coefficient in case of different materials match the theoretical result.


A discrepancy arises for the transmission coefficient in case of different materials: the FEM data are far too big.


The result is alike for axisymmetric, plain strain and plane stress elements.


The different formulas for computing the area ratio for axisymmetric and rectangular elements is properly accounted for.


Could someone please advise me ? Is someone aware of
1) an effect not taken into account in the theoretical formulas ?
2) a compilation of measured data ?
3) FEM data published elsewhere ?


Thank you for generously sharing your expertise,


Frank Richter
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RE: reflection and transmission coefficients inlong bars withdifferent cross-sectional areas exposed to pulse loading

Abaqus Users mailing list
Frank:

I’ve never run a simulation of this type of test, but I’m wondering:  During the simulation, does the contact interface ever open?  If so, does the theory allow for this, or does it assume the surfaces are always in contact?  Perhaps a “no separation” contact interface would improve the correlation.

It’s an interesting problem.

Regards,

Dave Lindeman
Lead Research Specialist
SEMS Research Laboratory
3M Center 235-3G-08
St. Paul, MN 55144
651-733-6383

From: [hidden email] [mailto:[hidden email]]
Sent: Monday, April 24, 2017 6:36 AM
To: [hidden email]
Subject: [EXTERNAL] [Abaqus] reflection and transmission coefficients in long bars withdifferent cross-sectional areas exposed to pulse loading




Dear Community,

I'd like to ask for advice on modelling reflection and transmission coefficients when two bars with different cross-sectional areas contact each other and are exposed to pulse loading.

I have modelled this process in Abaqus/Explicit as a two-dimensional simulation. The investigation was conveniently done as a parametric study, defining the lateral dimension as parameter. Both bars are slim (length 2 m, diameter 2 cm) and elastic.

Two material combinations are defined:
identical materials: 2 steel bars
and different materials: first bar is steel, second bar is aluminum

Theory gives a negative reflection coefficient R and a positive transmission coefficient T.

Elements:
CAX4R is the only axisymmetric solid element available in Abaqus/Explicit with four nodes
CPE4R is the only plane strain solid element available in Abaqus/Explicit with four nodes
CPS4R is the only plane stress solid element available in Abaqus/Explicit with four nodes

Contact is defined as CONTACT PAIR with the penalty constraint. Surfaces are element-based. Abaqus was run in double precision.

The reflection and transmission coefficients from FEM data are computed as the maximum of the signal with respect to the maximum of the incident wave.

Observation:
the FEM data for identical materials and the ones for the reflection coefficient in case of different materials match the theoretical result.

A discrepancy arises for the transmission coefficient in case of different materials: the FEM data are far too big.

The result is alike for axisymmetric, plain strain and plane stress elements.

The different formulas for computing the area ratio for axisymmetric and rectangular elements is properly accounted for.

Could someone please advise me ? Is someone aware of
1) an effect not taken into account in the theoretical formulas ?
2) a compilation of measured data ?
3) FEM data published elsewhere ?

Thank you for generously sharing your expertise,

Frank Richter





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