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Multiscale Methods for Protein and Virus Shell Mechanics

Friday, November 18, 10:30AM – 12PM
POB 6.304

Andro Mikelic

With size ranging from a few nanometers to hundreds of nanometers, proteins and protein assemblies like virus shells and microtubules are interesting examples of natural nano-materials, and their mechanical properties play an important role in their functioning. Despite their small size, continuum mechanics has been surprisingly successful for modeling their mechanical responses. However, the assumptions of passive continuum and spatially uniform elastic moduli, which are fit to experiment, do not reflect the dynamic and heterogenous nature of proteins and leaves open the question of at what length-scales continuum homogeneity breaks down. In this work, we present methods that derive information from the atomic structure and try to answer those fundamental issues.

We present two models for virus shell mechanics - a 3D model using meshfree and a thin-shell model using finite elements. In the 3D model, we use Reproducing Kernel Particle Method (RKPM) to define a coarse-graining from the atomic degrees of freedom to a continuum field description. We use that to compute the point-wise elastic modulus at continuum level from equilibrium, all-atom, molecular dynamics (MD) simulation. In the thin shell model, we use the information from imaging techniques to define a martensitic type phase transition and modify the classical elasticity theory by introducing discontinuities in stress/strain fields. We demonstrate that it changes the phase-space diagram of virus shell shapes at a fundamental level by adding another coordinate.

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