Dynamics of fragmented geomaterials with rotations

An important feature of fragmented geomaterials and fragmented structures is the possibility of mutual rotations of the fragments leading to rotational oscillations. In the process of the oscillations, the fragments impact each other. Partial restitution of the impacts causes dissipation of kinetic energy into heat. This dynamics can be reproduced mathematically using a linear oscillator, i.e. a single mass connected to a stationary object by a linear spring, coupled with a condition on energy dissipation occurring at the neutral points (zero force, maximum velocity) of the mass trajectory. As a result of the presence of energy dissipation, which is characterised by a restitution coefficient, this linear system is converted into nonlinear. Our numerical modelling reveals that the system demonstrates chaotic behaviour in some values of the restitution coefficient, a ratio of the force frequency to the natural frequency and the initial phase. The conditions of non-chaotic and chaotic behaviour are formulated. The obtained results will be used for modelling energy absorption in oscillations and wave propagation in fragmented geomaterials and structures.