Micromorphic modeling of wave propagation in granular materials: Considering particle nonaffine micro-deformation and kinematics decomposition
2022
Yu, Pengqiang | Liu, Yang
The objective of this study is to develop a micromorphic model for granular materials and then apply it to investigate the wave propagation. The relationship between particle displacement and rotation is firstly decomposed and thus particle displacement and spin are adopted. The effect of the particle displacement due to particle rotation is also considered. The relative deformation tensors are introduced to describe the local fluctuation of particle kinematics. Based on micro–macro energy conservation, the constitutive relations are consequently derived. The motion equations and boundary conditions can further be obtained building on Hamilton’s principle and subsequently the dispersion equations of plane waves are derived. It is indicated that the present model can reflect sixteen dispersion curves and predict the presence of bandgaps. A further discussion on the dispersion characteristics is made. Finally, the performance of the present model is verified by comparison with existing micromorphic models and other gradient models.
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