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Irreversible temperature dependence process

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Hi,

I want to simulate irreversible thermal process same like phase change but in one direction. For the "phase change" I used alpha parameter which described by tanh (depends on T). however I want the process to be irreversible so when the matiral is heated the material properties will changed according to alpha but when the temp. goes down the materias parameter wouldn't change (not like alpha) How can I write this?


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