 ## Material Properties

#### What is the difference in plasticity definition for bilinear vs. multilinear models?

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Question: What is the difference in plasticity definition for bilinear vs. multilinear models? Is the bilinear stress-strain definition based on total strain or plastic strain? What does the multilinear stress-strain input require plastic strain? Answer: Please note that the definition of multilinear vs. bilinear stress-strain curves in Engineering Data are different. When we define bilinear stress-strain curves, we define the tangent modulus “E_T” based on total strain. It is the slope of stress (“sigma”) vs. total strain (“epsilon_total”) curve after yielding. We do this because the input is simple from the user’s standpoint. If we take E_T as the tangent modulus of stress vs. total strain, we have the following relationship for plastic strain (“epsilon_plastic”): delta(sigma) = E_T * delta(epsilon_total) delta(sigma) = E_T * (delta(epsilon_elastic) + delta(epsilon_plastic)) delta(sigma) = E_T * (delta(sigma)/E + delta(epsilon_plastic)) delta(sigma) * (1 – E_T/E) = E_T * delta(epsilon_plastic) delta(sigma) = E*E_T / (E – E_T) * delta(epsilon_plastic) and you will see here that “C” is the slope of stress vs. plastic strain, but it is not the input tangent modulus “E_T”. Instead, “C” is equal to “E*E_T/(E- E_T)”. For multilinear stress-strain curves, in Engineering Data, however, we define stress vs. plastic strain. This is because, if you define stress vs. total strain, the stress-strain data contains elastic information that must be consistent with the elastic modulus (i.e., yield point defined by (sigma_y, epsilon_y) must line on the elastic modulus slope). There are some cases where users have temperature-dependent data for E and nuxy that are different than the temperature-dependent stress-strain data, and when the solver does the interpolation, E(T_i) may not match with (sigma(T_i), epsilon(T_i)) – we would have a problem since we would end up with two different yield points, and it’s not clear which to use. To prevent this type of inconsistent definition, we only define stress vs. plastic strain in Engineering Data. If you have true stress vs. total strain, in Excel, simply add another column for elastic strain calculations, which would be your current stress divided by elastic modulus. Then, subtract your column of elastic strain from total strain to get plastic strain, which would be used for input into Engineering Data. A common mistake is to determine the elastic strain at yield and subtract this constant value from the total strain, but this is not correct; after initial yield, as long as there is strain hardening, your stress will increase, which implies that elastic strains increase as well. 