Discussion Forum

Hi,

I need your help in implementing the system of PDEs containing the rate dependent constitutive equation.

There are two PDEs with dependent variables: p and u

PDE#1: d/dt(p) = k*d^2/dx^2(p) - c1*G(p) ....(1)
PDE#2: rho d^2/dt^2(u) = d/dx(sigma) + fx ....(2)

with the rate dependent constitutive equation as
d^2/dxdt(u) = c2 d/dt(sigma) + c3 d/dt(G(p)) ....(3)

where G(p) is a polynomial function of p, c1, c2, c3, rho, and fx are constants.

In the case where the constitutive equation is not rate dependent, like d/dx(u) = c2 sigma + c3 G(p)), and the equation can be rearranged to write sigma as sigma = 1/c2*(d/dx(u) - c3 G(p)). However, in the case of rate dependent constitutive equation as in Eq. (3), the equation cannot be rearranged to obtain a value of sigma.

The equations (1) and (2) are easy to implement in general form. I need help especially in modeling the equations 3 in Comsol. Please share your inputs on how to model the above system of equations?

Thanks,
Rakesh