Legacy · Mechanical validation · §8.3 / Fig. 6d

Spherical inclusion (Fig. 6d)

At z0z_0 the elastic stress of ΔT\Delta T in the sphere is frozen and σ\sigma is held (stress control); εθ\varepsilon_\theta grows with J(t,z0)J(t,z_0).

Article: Part I · DOI rirc.v1n2a007 · §8.3 / Fig. 6(d)

Mechanical material: Itumbiaraν=0.20\nu=0.20; αT=10×106C1\alpha_T=10\times10^{-6}\,^{\circ}\mathrm{C}^{-1}. Diffusivity: h2=0.10m2/dh^{2}=0.10\,\mathrm{m}^{2}/\mathrm{d} (do not confuse with aTa_T). Idea: T=θ(t)h(𝐱)T=\theta(t)\,h(\mathbf{x})σij=gij(𝐱)S(t)\sigma_{ij}=g_{ij}(\mathbf{x})\,S(t).

Control points (all Fig. 6 cases): ref_fig6_pontos_controle.csv.

Schematic

Spherical inclusion

Data sheet

Item Value
Geometry Spherical inclusion of radius aa in an infinite medium (same material). On the portal/CSVs: a=1ma=1\,\mathrm{m} (convenient scale). In the article §8.3 the drawing uses a=0.40ma=0.40\,\mathrm{m}; in r/ar/a coordinates the map gg is identical
Readouts r/a=0.5r/a=0.5 (inside) and r/a=2r/a=2 (outside)
Loading ΔT=10C\Delta T=10\,^{\circ}\mathrm{C} at z0=3dz_0=3\,\mathrm{d}; σ\sigma frozen
Response εθ(r,t)=σθ(r)J(t,z0)\varepsilon_\theta(r,t)=\sigma_\theta(r)\,J(t,z_0)

Input files

Output figures

Maps · Contours

Output files