A nonlinear elastic spring does not exist in Code-Aster. Johannes Ackva, Ingenieurbüro für Mechanik (www.code-aster.de) suggested the following approach for an implementation: Several line elements are superposed
connecting the same couple of nodes. Each line element is a linear spring in series with a gap. Such an element with a spring stiffness and a gap is realized using these Code-Aster commands:

MatElm1 = DEFI_MATERIAU(DIS_CONTACT=_F( RIGI_NOR=stiffn1, DIST_1=gap1,),)

MatElm2 = DEFI_MATERIAU(DIS_CONTACT=_F( RIGI_NOR=stiffn2, DIST_1=gap2,),)

etc.

Model=AFFE_MODELE(.. AFFE=(_F(GROUP_MA='AllSpringElms', PHENOMENE='MECANIQUE', MODELISATION='DIS_T',),),)

Res=STAT_NON_LINE(.. COMPORTEMENT=_F(GROUP_MA='AllSpringElms', RELATION='DIS_CHOC',),)

The spring stiffnesses and gap widths are adapted such that a force-displacement curve is approximated (as a polygon) which shows a progressing stiffness in compression. The practical point of this approach: no additional meshing in a PreProcessor is necessary for doubling the line elements because this can be done automatically with the Code-Aster command CREA_MAILLAGE(CREA_GROUP_MA...) So everything is codable in the command-file and runs automatically. This idea was refined using Python to represent all 3 translational and 3 angular spring directions. The figure above shows the comparision of a Code-Aster analysis using this element and results of Abaqus, both representing the same spring characteristics of a rubber element.

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