The current study presents a nanoscale in silico investigation of strain rate dependency of membrane (phospholipid bilayer) failure when placed under strip biaxial tension with two planar areas. The nanoscale simulations were conducted in the context of a multiscale modelling framework in which the macroscale damage (pore volume fraction) progression is delineated into pore nucleation (number density of pores), pore growth (size of pores), and pore coalescence (inverse of nearest neighbor distance) mechanisms. As such, the number density, area fraction, and nearest neighbor distances were quantified in association with the stress–strain behavior. Deformations of a 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer were performed using molecular dynamics to simulate mechanoporation of a neuronal cell membrane due to injury, which in turn can result in long-term detrimental effects that could ultimately lead to cell death. Structures with 72 and 144 phospholipids were subjected to strip biaxial tensile deformations at multiple strain rates. Formation of a water bridge through the phospholipid bilayer was the metric to indicate structural failure. Both the larger and smaller bilayers had similar behavior regarding pore nucleation and the strain rate effect on pore growth post water penetration. The applied strain rates, planar area, and cross-sectional area had no effect on the von Mises strains at which pores greater than 0.1 nm² were detected (0.509 ± 7.8%) or the von Mises strain at failure (ε _failure = 0.68 ± 4.8%). Additionally, changes in bilayer planar and cross-sectional areas did not affect the stress response. However, as the strain rate increased from 2.0 × 10⁸ s⁻¹ to 1.0 × 10⁹ s⁻¹, the yield stress increased from 26.5 MPa to 66.7 MPa and the yield strain increased from 0.056 to 0.226.

Continuum finite element material models used for traumatic brain injury lack local injury parameters necessitating nanoscale mechanical injury mechanisms be incorporated. One such mechanism is membrane mechanoporation, which can occur during physical insults and can be devastating to cells, depending on the level of disruption. The current study investigates the strain state dependence of phospholipid bilayer mechanoporation and failure. Using molecular dynamics, a simplified membrane, consisting of 72 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) phospholipids, was subjected to equibiaxial, 2:1 non-equibiaxial, 4:1 non-equibiaxial, strip biaxial, and uniaxial tensile deformations at a von Mises strain rate of 5.45 × 10⁸ s⁻¹, resulting in velocities in the range of 1 to 4.6 m·s⁻¹. A water bridge forming through both phospholipid bilayer leaflets was used to determine structural failure. The stress magnitude, failure strain, headgroup clustering, and damage responses were found to be strain state-dependent. The strain state order of detrimentality in descending order was equibiaxial, 2:1 non-equibiaxial, 4:1 non-equibiaxial, strip biaxial, and uniaxial. The phospholipid bilayer failed at von Mises strains of .46, .47, .53, .77, and 1.67 during these respective strain path simulations. Additionally, a Membrane Failure Limit Diagram (MFLD) was created using the pore nucleation, growth, and failure strains to demonstrate safe and unsafe membrane deformation regions. This MFLD allowed representative equations to be derived to predict membrane failure from in-plane strains. These results provide the basis to implement a more accurate mechano-physiological internal state variable continuum model that captures lower length scale damage and will aid in developing higher fidelity injury models.

Nanoscale deformation mechanisms of cellular structures could render drastically different results depending on the molecular dynamics (MD) simulator chosen. Due to different available settings, the comparison of these different MD simulators is typically an intricate task, requiring that all configurations be converted appropriately with a variety of reasonable parameter choices. The current study aims to perform and compare MD simulations of biomolecules between two common MD software packages (GROMACS and LAMMPS), in which a phospholipid bilayer is deformed under different strain states (equibiaxial, 2:1 non-equibiaxial, 4:1 non-equibiaxial, strip biaxial and uniaxial tension). The results for the stress–strain, pore nucleation and growth, and damage behavior are compared between the respective GROMACS and LAMMPS simulations. In general, GROMACS and LAMMPS produced similar deformation behavior, including damage evolution and the effect of strain state on phospholipid bilayer failure. However, GROMACS nucleated a greater number of pores at lower strains, produced lower stress values and higher damage values than LAMMPS. Multiple different setting options between GROMACS and LAMMPS, including algorithm variations, have been considered as possible explanations for the observed differences. Overall, this study will aid in the cross-check of parameter settings and simulation results in future MD research, particularly on the mechanical damage of phospholipid bilayers and other biological systems. Based on that, with future efforts, GROMACS and LAMMPS, as well as other MD programs, could be exploited synchronously with better comparability and reproducibility.

Designing protective systems for the human head—and, hence, the brain—requires understanding the brain’s microstructural response to mechanical insults. We present the behavior of wet and dry porcine brain undergoing quasi-static and high strain rate mechanical deformations to unravel the effect of hydration on the brain’s biomechanics. Here, native ‘wet’ brain samples contained ~80% (mass/mass) water content and ‘dry’ brain samples contained ~0% (mass/mass) water content. First, the wet brain incurred a large initial peak stress that was not exhibited by the dry brain. Second, stress levels for the dry brain were greater than the wet brain. Third, the dry brain stress–strain behavior was characteristic of ductile materials with a yield point and work hardening; however, the wet brain showed a typical concave inflection that is often manifested by polymers. Finally, finite element analysis (FEA) of the brain’s high strain rate response for samples with various proportions of water and dry brain showed that water played a major role in the initial hardening trend. Therefore, hydration level plays a key role in brain tissue micromechanics, and the incorporation of this hydration effect on the brain’s mechanical response in simulated injury scenarios or virtual human-centric protective headgear design is essential.

Chronic Traumatic Encephalopathy (CTE) affects a significant portion of athletes in contact sports but is difficult to quantify using clinical examinations and modeling approaches. We use an in silico approach to quantify CTE biomechanics using mesoscale Finite Element (FE) analysis that bridges with macroscale whole head FE analysis. The sulci geometry produces complex stress waves that interact with one another to create increased shear stresses at the sulci depth that are significantly larger than in analyses without sulci (from 0.5 to 18.0 kPa). Sulci peak stress concentration regions coincide with experimentally observed CTE sites documented in the literature.

In this paper, mechano-physiological damage evolution equations are developed to capture the disruption of neuronal membrane integrity and quantify neuronal cell death in the brain during mechanical insult. Traumatic brain injury involves multiscale structure-property relations where the mechanical behavior of the brain is phenomenologically characterized at the macroscale. However, damage largely occurs at the cellular level (microscale and nanoscale) due to the loss of ion homeostasis. To measure this neuronal death mechanism, molecular dynamics simulations were performed on a representative neuronal membrane, a 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer structures. Pore density and pore growth due to membrane deformation were then quantified. The results showed that the pore growth and pore density rates were a function of stress state, but only the pore growth rate was a function of the strain rate. Mechano-physiological damage evolution equations were developed to capture the damage biomechanics of the POPC bilayer based on the pore density and growth rate responses. The proposed damage evolution equations were combined with the Nernst–Planck diffusion equation to produce a criterion based on the change of intracellular calcium ion concentration.