Material deformation and flow

$$\rho \dot{v_i} = \frac{\partial \sigma_{ij}}{\partial x_j} + (1-... ...o g_i - d {\frac{\partial v_i}{\partial x_i}}_{\rm no ~ sum ~ on ~ i} + f_i$$

Notations: $\rho$ group_materi_density; $v_i$ materi_velocity in $i$-direction; $\sigma_{ij}$ materi_stress matrix; $x$ space coordinate; $\beta$ group_materi_expansion_volume; $T$ (optional) condif_temperature; $g_i$ force_gravity; $d$ group_materi_damping coefficient; $f_i$ force_volume. The equation is given for space coordinates following the material velocities $v_i$.

TOCHNOG allows you to build your favorite material, by adding separate contributions to the stresses $\sigma_{ij}$. In this way you can build solids or fluids or things in between. The separate contributions will be listed below. First two typical examples are given.

Nearly incompressible Navier Stokes:

...
materi_velocity
materi_stress
end_initia
...
mesh -fixed_in_space -fixed_in_space
timestep_predict_velocity 0 -yes
...
group_type 0 -materi
group_materi_elasti_compressibility 0 1.0
group_materi_viscosity 0 1.2
...

Linear solid:

...
materi_velocity
materi_strain_total
materi_stress
end_initia
...
group_type 0 -materi
group_materi_elasti_young 0 1.e10
group_materi_elasti_poisson 0 0.2
group_materi_memory 0 -updated_linear