Introduction

ElmerFEM is an open source multiphysics code, capable of coupling several different phenomena in a single run. It can couple the physics in both a loosly/iterative system or in a monolithic/strong form.

MFront does not have a specialised interface for ElmerFEM’s advanced material behaviours. ElmerFEM added support for Abaqus/Standar’s UMAT interface in the last couple of releases. Using this same interface, which is also supported by MFront, we can add MFront capabilities to ElmerFEM’s finite strain solver. This solver lacks any advanced material laws beyond finite elasticity. This is where the value of MFront comes into place: it brings a large amount of easy and complete material laws and behaviours to ElmerFEM.

• Isotropic and orthotropic materials are supported.
• Only finite strain behaviours are supported.
  • This means that only the Elastic Solver (Procedure = "ElasticSolve" "ElasticSolver") is supported.
• 3D and 2D elements are supported.
• The further testing is required to have a greater level of assurance, but initial tests have given valid results.

Usage

As indicated above, ElmerFEM reuses the same interface as Abaqus/Standard. In order to use MFront with ElmerFEM, the Abaqus/Standard interface has to be built as indicated here.

In the ElmerFEM side, for the input file (ElmerFEM uses the .sif extension for its simulation input) the following material declaration has to be done (as documented in the official ElmerFEM documentation.

Material 1
  ! UMAT Law
  
  Number of State Variables = Integer 1 ! Internal state variables to be saved (one for damage)
  
  Number of Material Constants = Integer 5 ! Number of constants to be read by the behaviour
  ! List material constants as {Young, Poisson, Bt, e0, a}: required by FichantLaBorderieDamage
  Material Constants(5) = Real 210000.0 0.30 50 0.0017 2 
  Density = 0.0 ! Reference density used by ElmerFEM
  Reference Temperature = 270.0 ! Reference temperature used by ElmerFEM
  
  ! Indicate where the compiled behaviour lives and which Element type is going to be used
  UMAT Subroutine = File "./src/libABAQUSBEHAVIOUR" "FICHANTLABORDERIEDAMAGEBEHAVIOUR_PSTRAIN"
  Name = "FICHANTLABORDERIEDAMAGEBEHAVIOUR_PSTRAIN"  ! This specifies the CMNAME argument of UMAT!

  ! We can then have any other extra material parameters as needed in ElmerFEM
  ! for other physical phenomena, such as heat transfer, electromagnetism...
End

Solver 1
  element="p:2"
  Equation = Linear elasticity
  Procedure = "ElasticSolve" "ElasticSolver"
  ...
  Displace Mesh = True
End

As can be seen in the example above, in ElmerFEM we need to set up the following variables:

• The number of state variables for the law that we are using.
• The number of material constants that are needed by the law.
• The actual values of the constants. Their order is the same as that in the MFront file.
• Reference density and temperature. These values are for ElmerFEM only.
• Finally we need to pass on the PATH for the compiled behaviour.
  • Then we need to specify the exact subroutine that is going to be used. If our elements are 3D, we will need to specify the 3D behaviour. In this example, our elements are planar, and therefore, we use the *_PSTRAIN subroutine generated by MFront.
• Then we can specify a CMNAME as needed by UMAT. This value is generally inconsequential unless we are compiling several laws in the same file.
  • In ElmerFEM we can create several materials, such as Material 2 and have a completely different MFront behaviour or any other as needed.

Example of compilation of a behaviour

As previously indicated, the Abaqus/Standard interface is used. This interface can be built by passing the --interface=abaqus option to MFront:

$ mfront --interface=abaqus --obuild SaintVenantKirchhoffElasticityTotalLagrangian.mfront

Treating target : all
The following library has been built :
- libABAQUSBEHAVIOUR.so :  SAINTVENANTKIRCHHOFFELASTICITYTOTALLAGRANGIAN_AXIS SAINTVENANTKIRCHHOFFELASTICITYTOTALLAGRANGIAN_PSTRAIN SAINTVENANTKIRCHHOFFELASTICITYTOTALLAGRANGIAN_3D

Here we are using the SaintVenantKirchhoffElasticityTotalLagrangian.mfront example file. As we can see, MFront then indicates the name of the library/binary that it has built and all the different element options (_AXIS, _PSTRAIN and _3D) for which the behaviour has been created. It is up to the user to then use the right element routine for the corresponding geometry that is being simulated.

Further information

The use of this interface has been documented in the following Github discussion and in the following ElmerFEM blogs: Advanced material behaviours, Fracture Mechanics application. The code example and image have been taken from Notch-Plasticity-Damage example repository.