To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

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Mn-Cu high damping alloy is a twin-type damping alloy. Owing to its martensite twin structure at room temperature, it can convert vibration energy into heat energy, thereby reducing vibration. Although essentially a nonlinear elastic material, Mn-Cu damping alloys are treated as linear elastic materials in current engineering practice. However, introducing a constant damping coefficient alone will produce significant errors when modeling vibration reduction characteristics of the material, especially under impact loading. In this study, vibration test was performed on Mn-Cu damping alloy cantilever beam subjected to an impact load and deviation between the test result and the one of existing modeling method was analyzed. A generalized fractional-order Maxwell model was established to describe the nonlinear constitutive relation of the Mn-Cu damping alloy. Then, the model was extended to the three-dimensional state and a secondary development was performed. Finally, various applications for the damping alloy were explored and the effects of the damping alloy on the vibration characteristics of composite cantilever beam structures subjected to impact loads were investigated with the aim of better understanding the dynamic characteristics and improving the effectiveness of vibration reduction applications using Mn-Cu damping alloy in the future.