2. Assignment of discrete properties#

2.1. Discreet support meshes#

The support meshes for the discrete elements are « POI1 » (single-node mesh) or « SEG2 » (two-node segment).

2.2. Spatial discretization and modeling assignment#

In this part, we describe the choice and assignment of one of the discrete models as well as the degrees of freedom and the associated meshes. Most of the information described is taken from the documentation for using the models:

  • [U3.11.02]: « DIS_T » and « DIS_TR » models.

  • [U3.13.09]: « 2D_DIS_T » and « 2D_DIS_TR » models.

2.3. Degrees of freedom#

The degrees of freedom of discretization are defined at each node of the support mesh. The components, depending on the model chosen, are given in the following table.

Modeling

Degrees of freedom (at each node)

2D_DIS_T

DX, DY

2D_DIS_TR

DX, DY, « DRZ »

DIS_T

DX, DY, DZ

DIS_TR

DX, DY, DY, DZ, DZ, « DRX », « DRY », ``, « DRZ »

2.3.1. Matrix support meshes#

Note:

In a mesh, to transform a node into a POI1 mesh, you can use the CREA_MAILLAGE command with the CREA_POI1 keyword (see [U4.23.02]).

2.3.2. Model: AFFE_MODELE#

The modeling assignment is done through the operator AFFE_MODELE [U4.41.01].

2.4. Basic characteristics, operator AFFE_CARA_ELEM#

In this part, operands that are characteristic of discrete elements are described. The documentation for using the AFFE_CARA_ELEM operator is [U4.42.01]. These keywords make it possible to assign rigidity, mass or dampening matrices directly to entities (meshes or nodes), which support elements such as « DIS_T », « DIS_TR » (DISCRET 3D) or « 2D_DIS_T », « 2D_DIS_TR » (DISCRET_2D), rigidity (). Characteristics can be defined by any of the following four key words and govern linear elastic behavior.

2.4.1. Keyword: DISCRET or DISCRET_2D#

The characteristics of discretes are described by the following nomenclature:

\[\huge \left[~M~|~K~|~A~\right] \underline{} \left[~T~|~TR~\right]( \underline{} D) \underline{} \left[~N~|~L~\right]\]
with

\(\begin{cases}M & Masse\\K & Rigidité\\A & Amortissement\end{cases}\)

\(\begin{cases}T & Translations\\TR & Translations~et~rotations\end{cases}\)

\(D\) if present, the matrix is diagonal

\(\begin{cases}N & support~nœud~ou~POI1\\L & support~SEG2\end{cases}\)

The possibilities for assigning matrices are:

  • Stiffness matrices: K_T_D_N, K_TR_D_N, K_T_D_L, K_TR_D_L,, K_T_N, K_TR_N, K_T_L, K_TR_L

  • Mass matrices: M_T_D_N, M_TR_D_N, M_T_D_L, M_TR_D_L,, M_T_N, M_TR_N, M_T_L, M_TR_L

  • Damping matrices: A_T_D_N, A_TR_D_N, A_T_D_L, A_TR_D_L,, A_T_N, A_TR_N, A_T_L, A_TR_L

The number of values needed to define the matrices depends on the characteristic chosen in [U4.42.01].

By default, the characteristics are given in the global coordinate system. The local coordinate system can be defined for a node, a POI1 mesh or a SEG2 mesh using the ORIENTATION of AFFE_CARA_ELEM keyword and by specifying REPERE =” LOCAL “.

notes

  • Index \(T\) or \(\mathit{TR}\) must be compatible with the definition of models in AFFE_MODELE, DIS_T, or DIS_TR

  • Mass and stiffness characteristics can be applied to the same mesh. If we only assign a mass to a discrete, we get alarm DISCRETS_27 to indicate that zero stiffness is considered. Alarm DISCRETS_26 is issued in the event that only stiffness is affected. To remove these alarms it is necessary to fill in the various matrices.

  • The keyword AMOR_HYST = \({\mathit{amor}}_{h}\) makes it possible to build a complex stiffness matrix (modeling of hysteretic damping), the constructed matrix is: \(\left(1+\mathrm{i}\mathrm{.}{\mathit{amor}}_{h}\right)\mathrm{.}\mathrm{K}\) where \(\mathrm{K}\) is the K_* matrix whose values are provided in the same occurrence of the keyword DISCRET. The complex stiffness matrix will be built during a call to CALC_MATR_ELEM [U4.61.01] with option AMOR_HYST (see test SDLD313 and [R5.05.04]).

  • The complete definition of stiffness, mass or damping matrices makes it possible to define eccentric elements. Test case SDNL113 gives the example of eccentric masses (V5.02.113).

2.4.2. Tag: RIGI_PARASOL#

This functionality corresponds to a methodology used to determine the characteristics of discrete elements (translation and/or rotation springs) to be applied to the nodes of a slab based on global stiffness. This option is available in 3Det in 2D. In the case 3Dle radier will be modeled by a surface, in the case 2Dil will be modeled by a line (test SSNL130 [V6.02.130]). In the 2D case, the discretes are 2D_DIS_TR or 2D_DIS_T. The keyword factor RIGI_PARASOL distributes 6 global stiffness in proportion to the surfaces of the elements surrounding its nodes.

Test cases:

  • SSLS118 C and D [V2.03.118]

  • SSNL130 A and B [V6.02.130]

2.4.3. Tag: RIGI_MISS_3D#

This keyword will affect the exact terms of an impedance matrix calculated by MISS3D for all interface degrees of freedom (3 times the number of nodes) and for a given extraction frequency. The assignment of these terms (modeling DIS_T) is then done to the point cells POI1 of the nodes of the surface foundation.

Test case:

  • SDNX101A [V5.05.101].

2.4.4. Tag: MASS_AJOU#

In this new option MASS_AJOU, we distribute to the nodes of the fluid-structure interface via characteristics” M_T_N “, elementary values of directional mass obtained by integrating the normal pressure to each element (from distribution functions of this normal pressure depending on coordinates, in particular on altitude) are distributed to the nodes of the fluid-structure interface via characteristics” “in order to express Westergaard relationships for example or more simply the expression of hydrostatic pressure. The assignment of these terms (modeling DIS_T to be declared in AFFE_MODELE) is then done to the point cells POI1 of the nodes of the fluid-structure interface using the keyword GROUP_MA_POI1 of the keyword factor MASS_AJOU.

Test case:

  • FDLV112C [V8.01.112].

2.4.5. Tag: MASS_REP#

The objective is to simply take into account a mass and to distribute it over a surface. Option MASS_REP allows to distribute to the nodes discretes of characteristic “M_T_D_N” of the mass values obtained in proportion to the area of the surface cells or the length of the line cells. The assignment (modeling “DIS_T” to be declared in AFFE_MODELE) is done on point cells of type POI1.

Test case:

2.5. Materials: DEFI_MATERIAU#

The definition of the parameters describing the non-linear behavior of a material is carried out using the operator DEFI_MATERIAU [U4.43.01] and the choice of behavior in the keyword COMPORTEMENT of STAT_NON_LINE or DYNA_NON_LINE. The details of the laws of behavior of discretes are given in the documentation [R5.03.17] Behavioral relationships of discrete elements, except for law ASSE_CORN [R5.03.32].

  • ELAS. In the general case, it is not necessary to assign elastic behavior to the discrete. The STAT_NON_LINE operator does this assignment by default on all the cells in the model. This assignment is then overloaded when the COMPORTEMENT keyword is processed.

    On the other hand, if a discrete is affected by a temperature and we want to take into account thermal expansion (only for a « DIS_TR_L »), it is necessary to define the expansion coefficient \(\alpha\) and this is done by the definition of an elastic material. It is therefore necessary to define \(ALPHA=\alpha\), the keyword E is mandatory but its value will not be taken into account, see [R5.03.17].

  • ARME [R5.03.17]. The law of behavior ARME makes it possible to model the behavior of an airline weapon. It is a tri-linear non-linear law of behavior (with discharge) that can represent the breakage of an airline weapon.

    Test case:

    • SSNL101 [V6.02.101].

  • ASSE_CORN [R5.03.32]. The law of behavior ASSE_CORN makes it possible to model the non-linear behavior of tower angles « DIS_TR ``.The law represents both the tensile behavior of the assembly and the time-rotation relationship around the axis of the bolts, perpendicular to the assembly. The other loading directions have linear elastic behavior described by classical stiffness characteristics.

    Test case:

    • SSNL102A

  • DIS_BILI_ELAS [R5.03.17]. The law of behavior DIS_BILI_ELAS makes it possible to model bilinear elastic behavior in translation, in each direction. The coefficients of the bi-linear law may depend on the temperature.

    Test case:

    • SSND103A /B/C

  • DIS_CHOC [R5.03.17]. The law of behavior DIS_CHOC makes it possible to model contact with shock and friction between two structures, via two types of relationships:

    • the unilateral contact relationship which expresses the non-inter-penetrability between solid bodies,

    • the Coulomb friction relationship, which governs the variation of tangential forces in contact.

    This behavior is explicit and is treated by penalization. The stiffness that occurs in behavior is therefore not « physical ». It is not recommended to use this behavior to model elements whose stiffness has a « physical » meaning. In this case, it is desirable to use behavior DIS_CONTACT, which has the same material parameters and with a formalism similar to a law of plasticity.

    Test cases:

    • SDLS119A /B Taking detachment into account

    • SSND116A Contact with friction (static study)

    • SDND100C Contact with friction (dynamic study)

    • SDND102B /C Clash between masses in dynamics

    • SSNL130A /B Static study with RIGI_PARASOL

  • DIS_CONTACT [R5.03.17]. The law of behavior DIS_CONTACT makes it possible to model contact with shock and friction between two structures, via two types of relationships:

    • the unilateral contact relationship which expresses the non-inter-penetrability between solid bodies,

    • the Coulomb friction relationship, which governs the variation of tangential forces in contact.

    This behavior is implicit and is written as a classical law of behavior. The stiffness that occurs in this behavior is therefore physical. It is not recommended to use this behavior to model penalization contact. In this case, it is desirable to use behavior DIS_CHOC, which has the same material parameters, which is explicitly integrated and which treats contact and friction by penalization.

    Test cases:

    • [V5.01.100]: Releasing a friction pad with Coulomb friction

    • [V5.01.102]: Seismic response of a multi-supported nonlinear mass-spring system

    • [V5.01.108]: DIS_CONTACT law of behavior in dynamics

    • [V5.02.104]: Transient non-linear substructuration: impact of a beam on 1 support

    • [V5.03.105]: Swing a block on a table

    • [V6.02.130]: Non-deformable plate on a spring mat

    • [V6.08.116]: DIS_CONTACT law of behavior in statics

    • [V6.08.118]: Law of behavior DIS_CONTACT, management of initial contact

  • DIS_ECRO_CINE [R5.03.17]. The law of behavior DIS_ECRO_CINE is a law of elasto-plastic behavior with non-linear kinematic work hardening.

    Test cases:

    • SSND102A /B [V6.08.102] (static study)

  • DIS_ECRO_TRAC [R5.03.17]. Behavior DIS_ECRO_TRAC is a non-linear behavior that applies to either:

    • to the DXlocal degree of freedom of discrete elements with two knots (on mesh SEG2) or and discrete elements with one node (mesh POI1). The behavior is of the « isotropic work hardening » type.

    • in the local tangential plane \(\mathit{YZ}\) discrete elements with two nodes (on mesh SEG2) or and discrete elements with one node (mesh POI1). The behavior is of the « isotropic work hardening » or « kinematic work hardening » type.

    • the non-linear behavior is given by a \(F=\mathit{fonction}(\mathrm{\Delta }U)\) curve:

      • for a SEG2, \(\mathrm{\Delta }U\) represents the relative displacement of the 2 nodes in the local coordinate system of the element.

      • for a POI1, \(\mathrm{\Delta }U\) represents the absolute movement of the node in the local coordinate system of the element.

      • for a SEG2 or a POI1, \(F\) represents the effort expressed in the local coordinate system of the element.

    Test cases:

    • [V6.08.117]: Validating behavior DIS_ECRO_TRAC

    • [V5.01.124]: Seismic excitation of a discrete affected by DIS_ECRO_TRAC behavior

  • DIS_GOUJ2E_ELAS or DIS_GOUJ2E_PLAS [R5.03.17]. These laws of behavior make it possible to model a behavioral relationship of the elasto-plastic type with isotropic work hardening, linking the forces in the discrete element to the difference in displacement of the two nodes in the local \(y\) direction. The equations are derived from 3D behavior VMIS_ISOT_TRAC [R5.03.02].

    Test cases:

    • ZZZZ120 [V1.01.120]

  • DIS_GRICRA [R5.03.17]. Behavior DIS_GRICRA makes it possible to model the translational and rotational behavior of the grid-pencil connection springs of fuel assemblies. This behavior is available for SEG2 meshes.

    Test cases:

    • SSNL131 [V6.02.131]

  • DIS_VISC [R5.03.17]. The law of behavior DIS_VISC makes it possible to model a non-linear visco-elastic rheological behavior, of the extended Zener type, making it possible to schematize the behavior of a uniaxial shock absorber.

    Test cases:

  • DIS_CHOC_ENDO [R5.03.17]. This material makes it possible to define the characteristics, which will be assigned to discretes with two nodes on a SEG2: K_T_D_L mesh. The particularities of the 2 associated behaviors:

    • shock modeling,

    • the shock force is limited during loading by a threshold function dependent on the displacement,

    • damage to shock stiffness during loading,

    • taking into account the evolution of the « gap », due to repeated shocks,

    • variable depreciation during the calculation.

    The choice of behavior is usually made under the keyword RELATION of STAT_NON_LINE or DYNA_NON_LINE. Either it’s CHOC_ENDO or it’s CHOC_ENDO_PENA.

    Test cases:

    • [V5.01.109] SDND109 - Behavioral law CHOC_ENDO, in non-linear dynamics.

    • [V6.08.120] SSND120 - Law of behavior CHOC_ENDO, in nonlinear statics.

    • [V5.01.105] SDND105 - Impact of a material point against a wall, plastic buckling.

      • SDND105E: no damping, analytical reference + no regression.

      • SDND105F: with damping, not regression.

  • JONC_ENDO_PLAS [R5.03.17] and [U2.03.10]. This material makes it possible to define the characteristics of elasto-plastic behavior that is damaging during bending, which makes it possible to model a flexural junction between a veil and a floor or a slab, which will be assigned to discrete two-node nodes on a SEG2 mesh. This behavioral relationship links the MZ moments (in local coordinate system) and the rotation differential DRZ (in local coordinate system). Internal variables describe the history of irreversible evolution. On the other degrees of freedom, the relationship will be linear elastic (characteristics provided in AFFE_CARA_ELEM [U4.42.01]). The choice of behavior is usually made under the keyword RELATION of STAT_NON_LINE or DYNA_NON_LINE.

    Test cases:

    • [V6.08.114] SSND114 - Behavioral law for elasto-plastic junctions that are damaged when flexed with discrete elements. Analytical reference + non-regression.

Behavioral laws are available for the nonlinear operators STAT_NON_LINE and DYNA_NON_LINE. Some models can also be taken into account for linear transient analyses via the operator DYNA_VIBRA: DIS_VISC, CHOC,…

Behavior in STAT_NON_LINE, DYNA_NON_LINE

Item type (modeling) in AFFE_MODELE

Keywords in DEFI_MATERIAU

AFFE_CARA_ELEM keywords under DISCRET/CARA

ARME

DIS_T, DIS_TR

ARME

“K_T_D_L”, “”, “K_TR_D_L”, “K_T_D_N”, “K_TR_D_N”

ASSE_CORN

DIS_T, DIS_TR

ASSE_CORN

“K_T_D_L”, “”, “K_TR_D_L”, “K_T_D_N”, “K_TR_D_N”

DIS_BILI_ELAS

DIS_T, 2D_DIS_T, DIS_TR, 2D_DIS_TR 2D or 3D discrete elements with one or two translation/rotation nodes

DIS_BILI_ELAS

“K_T_D_L”, “K_TR_D_L”, “”, “K_T_D_N”, “”, “K_TR_D_N”

DIS_CHOC, DIS_CHOC_FROT contact and shock with Coulomb friction

DIS_T, 2D_DIS_T 2D or 3D discrete elements with two translational nodes.

DIS_CONTACT

“K_T_D_N”, “K_T_D_L” For the calculation of elastic stiffness and natural modes.

DIS_ECRO_CINE

DIS_T, D_DIS_T, DIS_TR, 2D_DIS_TR 2D or 3D discrete elements with one or two translation/rotation nodes

DIS_ECRO_CINE

“K_T_D_L”, “K_TR_D_L”, “”, “K_T_D_N”, “”, “K_TR_D_N”

DIS_ECRO_TRAC

DIS_T, D_DIS_T, DIS_TR, 2D_DIS_TR 2D or 3D discrete elements with one or two translation/rotation nodes

DIS_ECRO_TRAC

“K_T_D_L”, “K_TR_D_L”, “”, “K_T_D_N”, “”, “K_TR_D_N”

DIS_GOUJ2E_ELAS, DIS_GOUJ2E_PLAS

2D_DIS_T 2D discrete element with two translational nodes

TRACTION

“K_T_D_L”

DIS_GRICRA

DIS_TR 2D discrete element with two translational nodes

TRACTION

“K_T_D_L”

DIS_VISC

DIS_T, 2D_DIS_T, DIS_TR, 2D_DIS_TR 2D or 3D discrete elements with one or two translation/rotation nodes

DIS_VISC

“K_T_D_L”, “K_TR_D_L”, “”, “K_T_D_N”, “”, “K_TR_D_N”

JONC_ENDO_PLAS

DIS_TR 3D discrete elements with two translation/rotation nodes

JONC_ENDO_PLAS

“K_TR_D_L”

2.6. Loads and limit conditions: AFFE_CHAR_MECA and AFFE_CHAR_MECA_F#

The documentation for using AFFE_CHAR_MECA and AFFE_CHAR_MECA_F is [U4.44.01].

Supported loads are as follows:

  • PESANTEUR. This loading makes it possible to apply a loading of the gravity type. Supported models: 2D_DIS_T, 2D_DIS_TR, DIS_T, DIS_TR

    Test cases:

    • SDLD04A [V2.01.004]

  • LIAISON_ELEM. Discrete elements can be used to connect pieces of structure from different models. Possible options are 3D_POU, 2D_POU, COQ_POU, and PLAQ_POUT_ORTH. Option 3D_POU allows you to connect a massive part with a node with 6 degrees of freedom.

    Test case:

    • SDLV122A /B [V2.04,122].

    • The 2D_POU option allows you to connect the meshes of a 2D surface part with a discrete element. Test case SSLX100F /G [V3.05.100].

    • Option COQ_POU allows you to connect a mesh part into a shell with a node of a discrete element. Test case SDLL135F [V2.02.135].

    • The PLAQ_POUT_ORTH option allows you to connect a meshed part with elements TRIA3 and QUA4 with a part modeled by a discrete element.

  • DDL_IMPO/LIAISON_DDL/LIAISON_UNIF/LIAISON_SOLIDE. The boundary conditions on the nodes of 2-node discrete elements (mesh SEG2) can be defined with these operators.