15. M modeling#

Validation of joint \(\mathrm{2D}\) in quadratic with the JOINT_MECA_RUPT law

15.1. Characteristics of modeling#

Modeling in plane deformations D_ PLAN for the elastic element.

Plane modeling for the joint element (keyword PLAN_JOINT).

15.2. Characteristics of the mesh#

Number of knots: 13

The elastic element is a QUAD8.

The joint element is a degenerate QUAD8 (knots combined).

15.3. Tested sizes and results#

Fashion \(I\)

The joint is opened up to partial damage [7] _ . \(U\mathrm{=}\beta \mathrm{\times }{U}_{\mathit{el}}+(1\mathrm{-}\beta )\mathrm{\times }{U}_{\mathit{max}}\) Where \(\beta \mathrm{=}0.2\). Then it goes into compression zone \(U\mathrm{=}\mathrm{-}{U}_{\mathit{el}}\). Finally, the joint is put into tension until complete damage \(U\mathrm{=}{U}_{\mathit{max}}\). We test the global response (the resultant of the nodal force, FN) of the system (joint and cube) in the local coordinate system. The reference values are analytical (see page 6).

Fashion \(\mathrm{II}\)

The joint is opened in \(I\) mode until partial damage occurs, then it is stressed in \(\mathit{II}\) mode. Tangential stiffness slopes are tested at two values of normal apertures. The incremental nature of the tangential evolution causes the tangential stress to change during the partial discharge in \(I\) mode, which makes its analytical estimation complex. So we test it after the discharge by regression.

We note by:

\({\sigma }_{\mathit{pena}}\mathrm{=}{\sigma }_{\mathit{max}}{P}_{\mathit{cont}}\mathrm{\times }(E+{L}_{\mathit{cube}}\mathrm{\times }{K}_{N})\mathrm{/}(E+{L}_{\mathit{cube}}\mathrm{\times }{K}_{N}\mathrm{\times }{P}_{\mathit{cont}})\)

\({\sigma }_{t}({\delta }_{n})\mathrm{=}{K}_{T}\mathrm{\times }(1\mathrm{-}{\delta }_{n}\mathrm{/}{L}_{\mathit{CT}}){U}_{t}\)

Size tested

Reference

Tolerance ( \(\text{\%}\) )

fashion \(I\)

FN, peak value

\({\sigma }_{\mathit{max}}\), which is \(\mathrm{1.D05}\)

0.10

FN, value damaged

\(\beta {\sigma }_{\mathit{max}}\), which is \(\mathrm{2.D04}\)

0.10

FN, compression value

\({\sigma }_{\mathrm{pena}}\), which is \(\mathrm{-}\mathrm{2.D05}\)

0.10

fashion \(\mathit{II}\)

FT, for two values of \({\delta }_{n}\)

\({\sigma }_{t}({\delta }_{n})\)

0.10