Combine ode and pde equations in Matlab to solve a thermal-mechanical coupled problem

Good morning,

I am new to Matlab and I have to solve the following equation in Matlab, considering a bunch of constraints:

where zita is a phase fraction, sigma star is the Tresca/VonMises stress on the thin sample, T is the temperature, t is time. It might imply a combination of pde and ode and a combination of a thermal and mechanical problem. Plus:

• zeta is a function of sigma star
• the temperature variation depends on a suite of heat transfer mechanisms + zeta prime.

Forgive my vagueness but I am not sure about what details you need to help me approach this problem. Please let me know any additional information you need.

Thank you in advance for any help you could give me.

Answer 1

[SaiDileep Kola]

You may refer to the documentation attached on PDE and ODE equations of MATLAB.

PDE Equations: https://www.mathworks.com/help/matlab/math/partial-differential-equations.html

ODE Equations: https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html