Behaviour FONDATION#

Definition#

This document describes the nonlinear elasto-plastic behavior of a rectangular surface foundation subjected to static or seismic three-dimensional stress. This law of behavior is affected on 3D discrete elements composed of a single translation and rotation node (DIS_TR) affected by a diagonal stiffness matrix (K_TR_D_N) by means of the relationship FONDATION called by the nonlinear problem solving operators STAT_NON_LINE [R5.03.01] or DYNA_NON_LINE [R5.05.05]. The key word used to define characteristics in DEFI_MATERIAU is FONDA_SUPERFI.

The law represents both the sliding mechanism, the mechanism of loss of bearing capacity as well as the mechanism of detachment from the foundation. Before using one of the mechanisms mentioned above, all loading directions have linear elastic behavior described by classical stiffness characteristics.

In the law of behavior, there are three mechanisms that can be combined:

  • the first representing the slip between the underside of the foundation and the ground (treated as a plastic mechanism with work hardening);

  • the second representing the phenomenon of loss of load-bearing capacity under the effect of an excessive vertical load (treated, again, as a plastic mechanism with work hardening);

  • the third representing the phenomenon of detach-gluing of the foundation under the effect of an important moment (treated as a non-linear elastic mechanism).

For more details on the law of behavior, see the associated reference material [R5.03.31].

Internal variables#

There are 21 of them.

5 internal variables that describe the plastic displacement associated with the sliding criterion:

  • \(V1\) DASLX: translation \({U}_{x,s}^{\mathit{pl}}\) according to \(x\)

  • \(V2\) DASLY: translation \({U}_{y,s}^{\mathit{pl}}\) according to \(y\)

  • \(V3\) DASLZ: translation \({U}_{z,s}^{\mathit{pl}}\) according to \(z\)

  • \(V4\) DASLRX: rotation \({\theta }_{x,s}^{\mathit{pl}}\) according to \(x\)

  • \(V5\) DASLRY: rotation \({\theta }_{y,s}^{\mathit{pl}}\) according to \(y\)

5 internal variables that describe the plastic displacement associated with the load-bearing capacity criterion:

  • \(V6\) DACPX: translation \({U}_{x,\mathit{CP}}^{\mathit{pl}}\) according to \(x\)

  • \(V7\) DACPY: translation \({U}_{y,\mathit{CP}}^{\mathit{pl}}\) according to \(y\)

  • \(V8\) DACPZ: translation \({U}_{z,\mathit{CP}}^{\mathit{pl}}\) according to \(z\)

  • \(V9\) DACPRX: rotation \({\theta }_{x,\mathit{CP}}^{\mathit{pl}}\) according to \(x\)

  • \(V10\) DACPRY: the rotation \({\theta }_{y,\mathit{CP}}^{\mathit{pl}}\) according to \(y\)

2 internal variables that describe the work hardening associated with the sliding criterion:

  • \(V11\) DAQSLX: translation \({q}_{h,x}\) according to \(x\)

  • \(V12\) DAQSLY: translation \({q}_{h,y}\) according to \(y\)

5 internal variables that describe the work hardening associated with the load-bearing capacity criterion:

  • \(V13\) DAQCPX: kinematic work-hardening of the \({R}_{h,x}\) translation according to \(x\)

  • \(V14\) DAQCPY: kinematic work-hardening of the \({R}_{h,y}\) translation according to \(y\)

  • \(V15\) DARCP: isotropic work hardening \(R\)

  • \(V16\) DAQCPRX: kinematic work-hardening of the rotation \({R}_{r,x}\) according to \(x\)

  • \(V17\) DAQCPRY: kinematic work-hardening of the rotation \({R}_{r,y}\) according to \(y\)

1 internal variable

  • \(V18\) DAUTRE: plasticity state of the element \({d}_{\mathit{état}}\).

3 intermediate variables of work-hardening and failure criteria:

  • \(V19\) DABSSLX: kinematic work-hardening of the \({v}_{x,s}^{pl}\) translation according to \(x\)

  • \(V20\) DABSSLY: kinematic work-hardening of the \({v}_{y,s}^{pl}\) translation according to \(y\)

  • \(V21\) DABSCPZ: work-hardening of the load-bearing capacity criterion \({v}_{z,\mathit{CP}}^{pl}\)