a rational method for defining damage variables in one dimension

To address the issue of whether it is rational to define damage variables through the degradation of elastic modules, we essentially clarified which material module should be used to describe the damage variables in unidimensional cases, and pointed out that the reference undamaged working state of material was needed firstly in order to measure the degree of damage if the strain equivalence hypothesis was used. We maintained it was baseless to consider the linear stressstrain working state as an undamaged reference state. We deduced a rational definition of elastic and elastoplastic damage variables. We stated that the degradation of an unloading module can be used to define the damage variables. To illustrate the definition of damage variables, we presented an example of establishing a damage constitutive equation of concrete in compression, validate the elastic strain equivalence hypothesis, and provide an appropriate approach for establishing a damage constitutive model.

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