1. Reference problem#

1.1. Geometry#

1.2. Material properties#

Isotropic elasticity \(E\mathrm{=}2.{E}^{11}\mathit{Pa}\) \(\nu =0.3\)

Viscoplasticity model VISCOCHAB (modeling A), without kinematic work hardening:

\(k\)	\(626.423911{E}^{6}\mathit{Pa}\)	\(\text{Q\_M}\)		\(3.982809551{E}^{8}\mathit{Pa}\)	\(\text{C2}\)	0
\(\text{A\_K}\)	\(0.215443469\)	\(\text{Q\_0}\)		\(3.982809551{E}^{8}\mathit{Pa}\)	\(\text{C1}\)	0
\(\text{B}\)	\(11.53016\)	\(\text{K\_0}\)		\(k\mathrm{\times }0.21544\mathit{Pa}{S}^{1\mathrm{/}N}\)	\(\text{G1\_0}\)	0
		\(\text{N}\)	12	\(\text{G2\_0}\)	0

Elasto-plasticity with isotropic work hardening (B modeling): model VMIS_ISOT_TRAC

Isotropic work hardening
\(\text{R\_0}\mathrm{=}\mathit{Sy}\)	\(750\mathit{E⁶}\mathit{Pa}\)
Traction curve
\({\epsilon }_{0}\)	\(\mathit{Sy}\mathrm{/}E\)	\(\sigma\)	\(\mathit{Sy}\)
\(\epsilon\)		\(\sigma\)	\(1500\mathit{E⁶}\mathit{Pa}\)

Viscoplasticity (C modeling): model VISC_ISOT_TRAC

Isotropic work hardening
\(\text{R\_0}\mathrm{=}\mathit{Sy}\)	\(750\mathit{E⁶}\mathit{Pa}\)
VISC_SINH
\(\text{SIGM\_0}\)	\(6167\mathrm{E⁶}\mathrm{Pa}\)	EPSI_0	\(3.31131121483{E}^{13}\mathit{Pa}\)
\(\text{M}\)	\(6.76\)
Traction curve
\({\epsilon }_{0}\)	\(\mathit{Sy}\mathrm{/}E\)	\(\sigma\)	\(\mathit{Sy}\)
\(\epsilon\)		\(\sigma\)	\(1500\mathrm{E⁶}\mathrm{Pa}\)

Material settings under CRIT_RUPT:

Critical constraint: \(\text{SIGMA\_C}\mathrm{=}7.8{E}^{8}\mathit{Pa}\), \(\mathit{COEF}\mathrm{=}10000.\) [4]

1.3. Boundary conditions and loads#

+———————————-+—————————-+———————————————————————————–+——————————————–++ |Imposed deformation: || +———————————-+—————————-+———————————————————————————–+——————————————–++ |:math:`{\epsilon }_{\mathrm{max}}`|\(0.05\) |speed |:math:`{1.E}^{-4}` || +———————————-+—————————-+———————————————————————————–+——————————————–++ |Time-dependent charging: || +———————————-+—————————-+———————————————————————————–+——————————————–++ |:math:`{t}_{0}\mathrm{=}0.` |:math:`\epsilon \mathrm{=}0`|\(\mathit{tmax}\mathrm{=}\) \({\epsilon }_{\mathrm{max}}/\mathrm{vitesse}`|:math:\)epsilon ={epsilon }_{mathrm{max}}`|| +———————————-+—————————-+———————————————————————————–+——————————————–++

Traction:

\(\mathit{FACEYZ}\)

\(\mathrm{Dz}=1\)

Blocking:	\(\mathit{FACEXZ}\) \(\mathrm{Dy}=0\)	\(\mathrm{FACEXY}\)	\(\mathrm{Dz}=0\)
		\(\mathrm{FACEYZ}\)	\(\mathrm{Dx}=0\)