Operands RELATION = GLRC_DAMAGE ================================ The documentation for model GLRC_DAMAGE [:ref:`R7.01.31 `] will be consulted. Keyword BETON ------------- The keyword factor BETON defines the geometric and material characteristics of concrete. Operand MATER ~~~~~~~~~~~~~~~ .. code-block:: text MATER = mat_concrete Define the name of the material produced by DEFI_MATERIAU used for concrete. This operand makes it possible to verify that the parameters associated with the behaviors chosen under the keywords ECOULEMENT, ECRO_ISOT, ECRO_CINE and ELAS exist in the material. Operand EPAIS ~~~~~~~~~~~~~~~ EPAIS = ep Define the thickness of the concrete plate. We check that :math:`\mathit{ep}\mathrm{\ge }0`. Note: The value of this thickness should be the same as that given in AFFE_CARA_ELEM for shell elements using the mat_beton material (defined by DEFI_GLRC). Operand GAMMA ~~~~~~~~~~~~~~~ GAMMA = gamma Defines the damage parameter that characterizes the slope of the moment — curvature curve during concrete cracking (Figure 2). :math:`\mathit{gamma}` can be considered to be the ratio between the slope during cracking on the elastic slope. If :math:`\mathit{gamma}>0`, the slope is positive. If :math:`\mathit{gamma}<0`, the slope decreases and stability is no longer guaranteed. In any case, we need to have :math:`\mathit{gamma}<\mathit{QP1}` and :math:`\mathit{gamma}<\mathit{QP2}`. The value by default is 0. This parameter is used only for damage calculation: :math:`\gamma =\frac{{p}_{f}}{{p}_{\mathrm{élas}}}` with: * :math:`\gamma`: GAMMA * :math:`{p}_{\mathrm{élas}}`: elastic slope * :math:`{p}_{f}`: slope during cracking .. image:: images/Object_23.svg :width: 250 :height: 137 .. _RefImage_Object_23.svg: **Figure** 5.1.3-a **: Moment—curvature curve of the behavior of a reinforced concrete plate under bending.** Operands QP1 and QP2 ~~~~~~~~~~~~~~~~~~~~~~ QP1 = qp1 QP2 = qp2 Define slope ratios for positive or negative bending. The ratio is assumed to be the ratio of the slope of the curvature curve — moment after cracking to the elastic slope. They are only used for damage calculation: :math:`{Q}_{P}=\frac{{p}_{2}}{{p}_{\mathrm{élas}}}` With: * :math:`{Q}_{p}`: slope ratio * :math:`{p}_{\mathrm{élas}}`: elastic slope * :math:`{p}_{2}`: slope after cracking We check that :math:`0<\mathit{QPi}<1`. C1N1/C1N2/C1N2/C1N3/C2N3/C2N1/C2N2/C2N3 Operands ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C1N1 = c1n1 C1N2 = c1n2 C1N3 = c1n3 C2N1 = c2n1 C2N2 = c2n2 C2N3 = c2n3 Define the components of the Prager kinematic work hardening tensor linking the tensors of membrane plastic deformations with the kinematic return membrane forces. :math:`N={\mathrm{CN}}_{1}{\epsilon }_{1}^{p}+{\mathrm{CN}}_{2}{\epsilon }_{2}^{p}` With: * :math:`{\mathrm{CN}}_{1}=(\begin{array}{ccc}\mathrm{C1N1}& 0& 0\\ 0& \mathrm{C1N2}& 0\\ 0& 0& \mathrm{C1N3}\end{array})` * :math:`{\mathrm{CN}}_{2}=(\begin{array}{ccc}\mathrm{C2N1}& 0& 0\\ 0& \mathrm{C2N2}& 0\\ 0& 0& \mathrm{C2N3}\end{array})` * :math:`{\epsilon }_{1}^{p}` and :math:`{\epsilon }_{2}^{p}` are the membrane plastic deformation tensors for plasticity criterion 1 and 2. We check that :math:`\mathit{CiNj}\mathrm{\ge }0`. C1M1/C1M2/C1M2/C1M3/C2M3/C2M1/C2M2/C2M3 Operands ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C1M1 = c1m1 C1M2 = c1m2 C1M3 = c1m3 C2M1 = c2m1 C2M2 = c2m2 C2M3 = c2m3 Define the components of the Prager kinematic work hardening tensor linking the plastic curvature tensors with the kinematic recall moments. :math:`M={\mathrm{CM}}_{1}{\kappa }_{1}^{p}+{\mathrm{CM}}_{2}{\kappa }_{2}^{p}` With: * :math:`{\mathrm{CM}}_{1}=(\begin{array}{ccc}\mathrm{C1M1}& 0& 0\\ 0& \mathrm{C1M2}& 0\\ 0& 0& \mathrm{C1M3}\end{array})` * :math:`{\mathrm{CM}}_{2}=(\begin{array}{ccc}\mathrm{C2M1}& 0& 0\\ 0& \mathrm{C2M2}& 0\\ 0& 0& \mathrm{C2M3}\end{array})` * :math:`{\kappa }_{1}^{p}` and :math:`{\kappa }_{2}^{p}` are the plastic curvature tensors for plasticity criteria 1 and 2. The :math:`{C}_{i}{M}_{j}` calculation is done using MOCO. :math:`{C}_{i}{M}_{j}=\frac{{p}_{\mathrm{élas}}{p}_{p}}{{p}_{\mathrm{élas}}-{p}_{p}}` with: * :math:`{p}_{\mathrm{élas}}`: elastic slope * :math:`{p}_{p}`: plastic slope We check that :math:`{C}_{i}{M}_{j}\mathrm{\ge }0`. Operands BT1/BT2et EAT/OMT ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ BT1 = bt1 BT2 = bt2 EAT = eat OMT = word In the case where finite elements support the calculation of shear forces, these operands are used to define the elastic transverse shear stiffness matrix. The :math:`V` shear forces are linked to the distortions :math:`\gamma` by: :math:`V\mathrm{=}\left[\begin{array}{cc}\mathit{BT1}& 0\\ 0& \mathit{BT2}\end{array}\right]\mathrm{:}\gamma` If the user enters the Young's modulus of transverse steels EAT as well as the transverse steel section per linear meter OMTalors, the coefficients of the stiffness matrix are deduced by the following relationship: :math:`{\mathit{bt}}_{i}\mathrm{=}\frac{5}{6}\frac{\mathit{ep}}{2}(\frac{\mathit{eb}}{1+\mathit{nub}}+\mathit{eat}\mathrm{\times }\mathit{omt})` The user cannot enter both BT1, BT2et and the parameters EAT, OMT at the same time. It is verified that these operands are strictly positive real numbers. Operands MP1X/MP1Y/MP2X/MP2Y and MP1X_FO/MP1Y_FO/MP2X_FO/MP2Y_FO ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ MP1X = mp1x MP1Y = mp1y MP2X = mp2x MP2Y = mp2y MP1X_FO = mp1x_fo MP1Y_FO = mp1y_fo MP2X_FO = mp2x_fo MP2Y_FO = mp2y_fo Define the limiting plastic moments of the generalized Johansen criterion used in behavior model GLRC_DAMA. They can be defined either by constant values or by functions. It is not possible to mix functions and constants. In addition, as soon as one of the operands is filled in, it is mandatory to fill in all of them. When these steps are not specified, they are automatically calculated. Keyword ARMA ------------ The keyword factor ARMA defines the geometric and material characteristics of passive reinforcements. Operand MATER ~~~~~~~~~~~~~~~ .. code-block:: text MATER = mat_steel Defines the name of the material produced by DEFI_MATERIAU used for passive reinforcements. This operand makes it possible to recover the material parameters used for passive reinforcements (Young's modulus :math:`{E}_{a}`, Poisson's ratio :math:`{\nu }_{a}` and elastic limit :math:`{\sigma }_{\mathrm{ya}}`). Operands OMX and OMY ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text OMX = Wxa OMY = Way Define the steel sections of a given reinforcement bed in the directions :math:`x` and :math:`y` (in linear :math:`{m}^{2}/m`, the thickness then being given in :math:`m`). We check that :math:`\mathit{Wxa}\mathrm{\ge }0` and :math:`\mathit{Wya}\mathrm{\ge }0`. RX and RY operands ~~~~~~~~~~~~~~~~~~~ .. code-block:: text RX = rxa RY = rya Define the dimensioned position of a reinforcement bed in relation to the thickness of the concrete shell, given in the directions :math:`x` and :math:`y` (:math:`\mathrm{-}1\mathrm{\le }\mathit{rxa}\mathrm{\le }1`, :math:`\mathrm{-}1\mathrm{\le }\mathit{rya}\mathrm{\le }1`, FIG. 3). .. image:: images/100000000000040200000230502141F1A2172DB0.jpg :width: 4.1772in :height: 2.2874in .. _RefImage_100000000000040200000230502141F1A2172DB0.jpg: **Figure** 5.2.3-a **: D**: D** definition of the dimensioned position of the reinforcement beds. Keyword CABLE_PREC ------------------ The keyword factor CABLE_PREC defines the geometric and material characteristics of prestressed cables as well as the prestress force used. Operand MATER ~~~~~~~~~~~~~~~ .. code-block:: text MATER = mat_cable Defines the name of the material produced by DEFI_MATERIAU used for pretension cables. This operand makes it possible to recover the material parameters used for prestress cables (Young's modulus :math:`{E}_{p}`, Poisson's ratio :math:`{\nu }_{p}` and elastic limit :math:`{\sigma }_{\mathrm{yp}}`). Operands OMX and OMY ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text OMX = WXP OMY = Wyp Define the steel sections of a given prestress cable bed in the directions :math:`x` and :math:`y` (in linear :math:`{m}^{2}\mathrm{/}m`, the thickness then being given in :math:`m`). We check that :math:`\mathit{Wxp}\mathrm{\ge }0` and :math:`\mathit{Wyp}\mathrm{\ge }0`. RX and RY operands ~~~~~~~~~~~~~~~~~~~ .. code-block:: text RX = rxp RY=ryp Define the dimensionless position of a prestress cable bed in relation to the thickness of the concrete shell, given in directions :math:`x` and :math:`y` (:math:`\mathrm{-}1\mathrm{\le }\mathit{rxp}\mathrm{\le }1`, :math:`\mathrm{-}1\mathrm{\le }\mathit{ryp}\mathrm{\le }1`). Operands PREX and PREY ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text PREX = price, PREY = accurate, Define the prestress forces (in Newton) in the :math:`x` and :math:`y` directions (they must normally be negative because a compression force is applied). Keyword LINER ------------- The keyword factor LINER defines the geometric and material characteristics of the metallic liner. Operand MATER ~~~~~~~~~~~~~~~ .. code-block:: text MATER = mat_liner Define the name of the material produced by DEFI_MATERIAU used for the metallic liner. This operand makes it possible to recover the material parameters used for the metallic liner (Young's modulus :math:`{E}_{l}`, Poisson's ratio :math:`{\nu }_{l}` and elastic limit :math:`{\sigma }_{\mathrm{yl}}`). Operand OML ~~~~~~~~~~~~ .. code-block:: text OML = Wl Define the thickness of the liner (in meters depending on the choice made for the other dimensioned parameters). We check that :math:`\mathit{Wl}\mathrm{\ge }0`. Operand RLR ~~~~~~~~~~~~ .. code-block:: text RLR = rlr, Define the dimensionless position of the liner in relation to the thickness of the concrete shell (in practice, :math:`\mathit{rlr}\mathrm{=}\mathrm{-}1` or :math:`\mathit{rlr}\mathrm{=}1`, because the metal liner is arranged on the lower or upper side of the concrete shell). Keyword ALPHA ------------- This keyword defines an "average" (and isotropic) thermal expansion coefficient for the shell element. Keyword INFO ------------ Print in RESULTAT format of the list of homogenized parameters used as input to the GLRC_DAMAGE behavior model.