Crumpling wires in two dimensions

An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. We varied the bending rigidity and stretching modulus to measure the energy allocation, size-mass exponent, and the stiffness exponent. The mass exponent is shown to be universal at value $D_M=1.33$. We also found that the stiffness exponent $\alpha =-0.25$ is universal, but varies with the plasticity parameters $s$ and ${\theta }_p$. These numerical findings agree excellently with the experimental results.