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.