Molecular dynamics simulation of polyethylene under cyclic loading: Effect of loading condition and chain length

Two nano-blocks of polyethylene (PE) are made and subjected to cyclic deformation with various loading conditions, i.e., strain vs. stress control, zero lateral strain vs. zero lateral stress, and different load amplitude by using the coarse grained molecular dynamics simulation. The one block is filled with 1000 random coil chains of [-CH₂-]³⁰⁰ (long chain), while the other 10 000 chains of [-CH₂-]³⁰ (short chain). The random coil chains are freely grown and relaxed in a simulation box of , then compressed to and relaxed to obtain a stress-free equilibrium. Under the zero lateral stress condition, σ^′=0, the long-chain block shows a leaf-like hysteresis curve both in the stress- and strain-controlled cyclic loading. The area of the hysteresis loop increases as the maximum load is changed to , and , respectively. The “Mullin's effect” is also observed, i.e., the stress-strain curve depicts lower path in the 2nd or later loading, although the target is never a rubber with filler. Under the zero lateral strain condition, ε^′=0, the long-chain block shows little hysteresis with the stress amplitude of 100 MPa, while it shows rapid or unstable elongation around at ε=0.35 in the simulation of ε_max=0.5 and . The short-chain block also shows unstable elongation under the ε^′=0 condition even with the stress amplitude of 100 MPa, noting that it has an upper yield point of at ε=0.35 and lower one around at ε=1.6. On the other hand, the short-chain block is stretched without remarkable stress increase up to the strain around 1.0, under the lateral condition of σ^′=0. Then the block shows “strain hardening” and comes up to the external stress of 100 MPa. It is worth noting that the block shows a leaf-like hysteresis in the 2nd or later cycle; the stress goes back to zero around ε=1.0 in the unloading process and rises up immediately when the load is reversed, as same as the long-chain block.     

Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element

This paper aims at presenting a technique to replace the moving load by an equivalent moving finite element so that both the transverse and the longitudinal inertial effects due to the moving mass may easily be taken into account simultaneously. Where the mass, damping and stiffness matrices of the moving finite element are determined by the transverse () inertia force, Coriolis force and centrifugal force of the moving mass, respectively. From the numerical examples illustrated, it has been found that, in addition to the conventional transverse () responses, the inertial effects of the moving load also affect the longitudinal () responses of the portal-frame structure significantly.