Continuum constitutive models from analytical free energies

We present a critical investigation of the validity of the harmonic approximation for developing constitutive models for multiscale simulations. We examine models using the Cauchy–Born hypothesis within the quasiharmonic, local harmonic, and modified local harmonic approximations in order to characterize the strain and temperature dependence of the Cauchy stress for uniaxial, equibiaxial, and equitriaxial deformations. We compare these predictions with molecular dynamics simulations to evaluate the suitability of each harmonic model over a wide range of strains and temperatures. The various harmonic approximations are found to be very robust over a large temperature range. All the approximations make very similar predictions at small strains and temperatures. At larger strains and temperatures, the quasiharmonic model is the most accurate but also the most computationally expensive. The modified local harmonic model is seen to provide an accurate alternative to the full quasiharmonic model over a wide range of strains while being much less computationally expensive. The local harmonic model is similar in absolute accuracy to the modified local harmonic model, but the modified harmonic model is seen to more accurately predict the elastic moduli.

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