5. C modeling: 2D theoretical sawing#

5.1. Characteristics of modeling#

The simulation is done with modeling PLAN_JOINT. The elements are of type TRIA3 for the studs and QUAD4 for the joint elements. We test the two laws of behavior JOINT_MECA_FROT and JOINT_MECA_RUPT, the associated material has the same name. Surface elements are elastic.

5.2. Characteristics of the mesh#

A linear mesh of two studs and the crack is produced.

Volume elements (pads): 548 TRIA3

Joint elements: 20 QUAD4

5.3. Tested sizes and results#

The first tests are carried out just before sawing in a condition where the joint and the studs are compressed homogeneously. Then the same series of tests are carried out after sawing. The values tested are the joint thickness profiles, as well as its opening and the stress. We note \({\delta }_{n}\) (\(\mathit{V7}\)) the normal joint opening, joint thickness \({\delta }_{\mathit{offset}}\) (\(\mathit{V10}\)), as well as the normal stresses \({\sigma }_{n}\). The imposed degree of freedom is equal to \({\delta }_{\mathit{impo}}=-3e-6\), the saw thickness is equal to \({\delta }_{\mathit{scie}}={\delta }_{\mathit{impo}}/3\)

5.3.1. Before sawing, law JOINT_MECA_RUPT#

The solution is given by solving problem \(\mathrm{1D}\):

Size tested	“ ANALYTIQUE “	tolerance
\({\sigma }_{n}\) at height: \(5m\)	\({\delta }_{\mathit{impo}}/(\frac{1}{2LE}+\frac{1}{\text{pena\_contact}{K}_{N}})=-6.5454545e5\)	0.1%
\({\delta }_{n}\) at height: \(2m\)	\(\frac{{\sigma }_{n}}{\text{pena\_contact}{K}_{N}}=-8.181818181e-7\)	0.1%

5.3.2. After sawing, law JOINT_MECA_RUPT#

The solution is given by solving problem \(\mathrm{1D}\):

Size tested	“ ANALYTIQUE “	tolerance
\({\sigma }_{n}\) at height: \(5m\)	\(({\delta }_{\mathit{impo}}+{\delta }_{\mathit{scie}})/(\frac{1}{2LE}+\frac{1}{\text{pena\_contact}{K}_{N}})=-4.36364e5\)	0.1%
\({\delta }_{\mathit{offset}}\) at height: \(8m\)	\(-{\delta }_{\mathit{scie}}=-1e-6\)	0.1%
\({\delta }_{n}\) at height: \(2m\)	\(\frac{{\sigma }_{n}}{\text{pena\_contact}{K}_{N}}-{\delta }_{\mathit{offset}}=-1.5454545e-6\)	0.1%

5.3.3. Before sawing, law JOINT_MECA_FROT#

The solution is given by solving problem \(\mathrm{1D}\):

Size tested	“ ANALYTIQUE “	tolerance
\({\sigma }_{n}\) at height: \(5m\)	\({\delta }_{\mathit{impo}}/(\frac{1}{2LE}+\frac{1}{{K}_{N}})=-6.923076923e5\)	0.1%
\({\delta }_{n}\) at height: \(2m\)	\(\frac{{\sigma }_{n}}{{K}_{N}}=-6.923076923e-7\)	0.1%

5.3.4. After sawing, law JOINT_MECA_FROT#

The solution is given by solving problem \(\mathrm{1D}\):

Size tested	“ ANALYTIQUE “	tolerance
\({\sigma }_{n}\) at height: \(5m\)	\(({\delta }_{\mathit{impo}}+{\delta }_{\mathit{scie}})/(\frac{1}{2LE}+\frac{1}{{K}_{N}})=-4.6153846e5\)	0.1%
\({\delta }_{\mathit{offset}}\) at height: \(8m\)	\(-{\delta }_{\mathit{scie}}=-1e-6\)	0.1%
\({\delta }_{n}\) at height: \(2m\)	\(\frac{{\sigma }_{n}}{{K}_{N}}-{\delta }_{\mathit{offset}}=-1.46153846e-6\)	0.1%