A 2D granular medium with rotating particles

Abstract

A two-dimensional (2D) model of a granular medium is represented as a square lattice consisting of elastically interacting round particles possessing one rotational and two translational degrees of freedom. The differential equations describing propagation and interaction of waves of various types in such a medium have been derived in the long-wavelength approximation. Accounting for microrotations of the particles and moment interactions between them leads to the consideration of so-called microrotation waves (spin waves). In the absence of microrotations, the governing equations degenerate into 2D Lamé equations for anisotropic media. A one-to-one correspondence has been established between the microstructure parameters and effective elasticity constants of the second-order. Dependence of elasticity constants on the size of grains has been analyzed. The proposed model is compared in the continuous approximation to the equations of the 2D Cosserat continuum possessing macroscopic anisotropy.

Modeling of micropolar type chiral structures

“…В сравнении с широко используемыми при постро-ении моделей микрополярной теории упругости фено-менологическим потенциалом [4], потенциальной энер-гией сложного соединения частиц с симметричными (c 2 =c 3 ) связями [5], соединения балочного типа [6] …”

“…2б) [6], квадратной решетки частиц конечного размера с симметричными сложными соединениями [5], а также модели, которые строятся на основе феноменологического потенциала вида [4]. Урав-нения (5) включают отмеченные модели как частный случай и при выборе параметров (2), (3) описывают хи-ральные решетки (рис.…”

Higher-order gradient continuum modelling of periodic lattice materials

“…The subscripts x and y denote the spatial derivatives with respect to the spatial coordinates x and y. The equations (8), often called equations of micropolar elasticity [6][7][8], differ from the equations of classical theory elasticity by the additional equation of the microrotational wave. Neglecting the terms proportional to ℓ 2 in the third expression of (8) to eliminate the rotational DoF θ from the system yields to the equations of conventional two-dimensional elasticity…”

Modeling of static deformations and dynamics of localized rotation in a chain of finite size particles

“…Structural approach provides in-depth understanding of a developing theory, possibilities for its practical realization, experimental verifications and numerical modelling [8,9].…”