Legacy · Mechanical validation · §8.1

Thick cylinder in a rigid shell (Zocher Ex. 2)

Internal pressure $p_0 H(t)$ , boundary $u_r(b)=0$ (rigid shell). Without aging — §8.1.

Article: Part I · DOI 10.70271/rirc.v1n2a007

Schematic

Data sheet

Item	Value
Geometry	$a=2\,\mathrm{m}$ , $b=4\,\mathrm{m}$ ; readout at $r=(a+b)/2$
Boundary	$u_r(b)=0$ ; internal pressure $p_0=100\,\mathrm{Pa}$
Regime	Plane strain (long cylinder)
Material	SLS Zocher
Analytical response	$u_r(r,t)=p_0\dfrac{a^{2}b(1+\nu)(1-2\nu)}{a^{2}+(1-2\nu)b^{2}}\bigl(\dfrac{b}{r}-\dfrac{r}{b}\bigr)J(t)$
Quantity in CSV	$u_r$ at $r=(a+b)/2$ : analytical × incremental

Material (shared — Zocher / SLS)

Material A of Zocher, Groves and Allen (1997): $E_0=0.5\,\mathrm{MPa}$ , $E_\infty=0.1\,\mathrm{MPa}$ , $\tau_\sigma=1$ t.u., $\tau_\varepsilon=\tau_\sigma E_0/E_\infty$ , $\nu=0.3$ .

ref_zocher_params.csv
ref_zocher_J_R.csv — analytical $J(t)$ and $R(t)$

The $\eta_n$ , $q_n$ algorithm under unit stress must recover $J(t)$ independently of the mesh.

Input / output files

ref_zocher_cilindro_engastado_params.csv
ref_zocher_cilindro_engastado.csv — analytical × incremental $u_r(r,t)$