Loading Rate Effect on The Ratio of Yield to Failure Stress for A Simplified Membrane

**Murphy, M. A.**, Prabhu, R., Williams, L. N., & Horstemeyer, M. (2017). Loading Rate Effect on The Ratio of Yield to Failure Stress for A Simplified Membrane. *International Mechanical Engineering Congress & Exposition*. Tampa, FL: American Society of Mechanical Engineers.

INTRODUCTION TBI affects an estimated 10 million people every year resulting in enormous financial and personal loss. Finite element analysis, a common method for studying TBI, needs lower length scale information to be implemented through constitutive material models to accurately replicate the brain’s response to TBI. One important lower length scale mechanism leading to TBI is membrane mechanoporation. Studies have previously explored the stress-strain response of simplified membranes at differing strain rates using molecular dynamics. However, simulations with higher strain rates have shown the shape of the stress-strain curve changes above a certain loading rate resulting in a decline in stress after yield. Additionally, simulations using lower strain rates often have fewer pores that grow, but they become larger. The current study examines the relationship between the stress at yield and at failure with regards to loading rate. METHODS A bilayer consisting of seventy-two 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) phospholipids and 9,070 TIP3P water molecules (original structure sourced from NIH’s Laboratory of Computation Library and 6,828 TIP3P water molecules were added) was equilibrated for ten nanoseconds using the program LAMMPS and the CHARMM36 all-atom lipid force field. The equilibrated structure was subjected to constant velocity tensile deformations in one in-plane dimensions while the other in-plane was held constant to give the strip biaxial strain state. The out-of-plane dimension was allowed to relax freely during deformations. A water chain fully penetrating through both bilayer leaflets was used as the failure criteria. PRELIMINARY RESULTS AND CONCLUSIONS Preliminary results using the strip biaxial strain state show the ratio of the yield and failure stresses became larger as the loading rate was increased. The lower loading rates examined exhibited similar values for the yield and failure stresses. Plotting the stresses for yield and failure independently against loading rate resulted in two linear curves that intersect in the lower range of the examined loading rates. This intersection shows a loading rate where the stresses for yield and failure increasingly diverge as the loading rate increases. This finding shows the bilayer’s damage properties change above a critical loading rate limit for the strip biaxial strain state, as also indicated by the change in pore growth properties noted in previous studies. The equibiaxial strain state will be used to confirm this behavior. The results for the equibiaxial strain state will also be compared to the strip biaxial strain state to determine if strain state changes the critical loading rate.