Hi Hongwei Wu,

On 1/16/24 17:07, Hongwei Wu wrote:

Hi, everyone. I am starting to solve a chemomechanical problem, but I don't know whether the fully coupled equations can be solved in sfepy or not. Could you have a look at them?

The equation are as followed:

Governing Equations

∇∙σ+ρb=ρu ̈ Where σ is the stress tensor, ρ is the mass density, b is the body force per unit mass, u is the displacement vector.

∂c/∂t+∇∙j=∂r/∂t, where j=-(D*c_0)/RT ∇Ψ Where c is the concentration, D is the diffusion coefficient, c0 is the reference concentration, R is Boltzmann constant (gas constant), T is the absolute temperature, Ψ is the chemical potential.

Constitutive relations

σ=2Gε+(λe+bc)I Ψ=be+gc Where b=-β(2G+3λ), β is the chemical dilation coefficient, e is the volumetric strain and g represents the scalar chemistry modulus.

I have no experience with this particular physics, but the structure of the problem seems very similar to piezo-elasticity, where the electrical potential is in place of the chemical potential, see [1, 2], or to Biot problem, where the scalar variable is the fluid pressure [3].

Does it help?

r.

[1] http://sfepy.org/doc-devel/examples/multi_physics-piezo_elastodynamic.html [2] http://sfepy.org/doc-devel/examples/multi_physics-piezo_elasticity.html [3] http://sfepy.org/doc-devel/examples/multi_physics-biot.html