A phase field modeling framework is developed to quantify structure evolution of protein fibrils in solution. The modeling framework employs a set of multi-physics constitutive relations to predict time dependent protein fibril structural evolution. The balance relations include chemical potential relations, microforces that govern local protein structure evolution, linear momentum and conservation of mass. Anisotropic formation of protein fibrils is controlled by protein monomer microforces and chemical fluxes to obtain long fibril growth from small seed particles. The theoretical model is implemented numerically using a nonlinear finite element phase field modeling approach which couples nonlinear mechanics with microscopic protein fibril structure evolution and chemical behavior. For comparisons to the model, the self-healing RADA16-I protein fibrils are characterized using transmission electron microscopy before and after ultrasonic radiation. Comparisons illustrate quantitative model predictions that govern spontaneous protein fibril self-healing that is predicted on the time scale of several hundred hours. The underlying physical mechanisms associated with self-assembly of the protein fibrils are discussed.

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