3. Modeling A

3.1. Characteristics of modeling

A single element based on a QUAD4 mesh, in D_ PLAN.

Loading and boundary conditions are modelled by:

DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)

DDL_IMPO: (NOEUD: N03, DX: 0.)

FORCE_NODALE: (NOEUD; (N01 N02), FX: \(-\frac{1}{2}{\sigma }_{d}(t)\), FY: \(-\frac{1}{2}{\tau }_{d}(t)\))

FORCE_NODALE: (NOEUD; (N01 N04), FX: \(-\frac{1}{2}{\tau }_{d}(t)\))

FORCE_NODALE: (NOEUD; (N03 N04), FY: \(\frac{1}{2}{\tau }_{d}(t)\))

FORCE_NODALE: (NOEUD; (N02 N03), FX: \(\frac{1}{2}{\tau }_{d}(t)\))

where \({\sigma }_{d}(t)\) and \({\tau }_{d}(t)\) are the positive functions defined above [§1.3].

3.2. Tested sizes and results

Behavior LEMAITRE (THETA =0.5)

Variables	Moment (s)	Reference	Tolerance
\({\varepsilon }_{{\nu }_{\mathrm{xx}}}\)	30	1.7620 10—4	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xy}}}\)	30	1.81585 10—4	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xx}}}\)	3630	1.9030 10—3	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xy}}}\)	3630	2.0789 10—3	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xx}}}\)	3660	1.9130 10—3	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xy}}}\)	3660	2.1906 10—3	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xx}}}\)	3720	1.8740 10—3	0.5%
\({\varepsilon }_{{\nu }_{\mathrm{xy}}}\)	3720	3.1813 10—3	0.5%

Behavior VISC_ENDO_LEMA (with 10 times finer temporal discretization)

Variables	Moment (s)	Reference	Tolerance
\({\varepsilon }_{{\nu }_{\mathrm{xx}}}\)	30	1.762 10—4	0.7%
\({\varepsilon }_{{\nu }_{\mathrm{xy}}}\)	30	1.816 10—4	0.7%