1. Reference problem

1.1. Geometry

Figure 1.1.a: geometry.

3D Model 2D Model GROUP_MA

Knit \(\mathrm{M1}\): Knot \(\mathrm{N1}\) to \(\mathrm{N2}\) DIS_T 2D_ DIS_T DL_T

Knit \(\mathrm{M2}\): Knot \(\mathrm{N1}\) to \(\mathrm{N3}\) DIS_TR 2D_ DIS_TR DL_TR

Knit \(\mathrm{M3}\): Knot \(\mathrm{N4}\) DIS_T 2D_ DIS_T DN_T

Knit \(\mathrm{M4}\): Knot \(\mathrm{N5}\) DIS_TR 2D_ DIS_TR DN_TR

Knit \(\mathrm{M10}\): Knot \(\mathrm{N1}\) to \(\mathrm{N20}\) DIS_T DL_T0

Knit \(\mathrm{M30}\): Knot \(\mathrm{N40}\) DIS_T DN_T0

1.2. Material properties

The law of behavior is written in the following generic form (for each degree of freedom):

the elastoplastic relationship:

the boundary surface:

the kinematic work hardening part: \(X=\frac{{k}_{x}\mathrm{.}\alpha }{{\left[1+{\left[\frac{{k}_{x}\mathrm{.}\alpha }{{F}_{u}}\right]}^{n}\right]}^{1/n}}\)

It therefore requires 5 characteristics. Their units must be in agreement with those of the study.

: elastic stiffness

: elastic limit

: kinematic stiffness

: kinematic limit force

: power

1.3. Boundary conditions and loads

Node \(\mathrm{N1}\): embedding

Nodes \(\mathrm{N2}\), \(\mathrm{N3}\), \(\mathrm{N4}\), \(\mathrm{N5}\),, \(\mathrm{N20}\), \(\mathrm{N40}\): for all degrees of freedom the signal is cyclic with imposed displacement.