Hysteresis and creep in powders and grains

The quasi-static mechanical response of grains under cyclic loading is studied in this contribution by means of a three-dimensional Molecular Dynamics scheme. The response of the system is characterized by an accumulation of plastic deformation with the number of cycles. For the deviatoric stress and strain, a quasi-periodic ratchet-like behavior is observed. Results are presented for different system sizes and coefficients of friction, respectively showing consistent results for more than ~2000 particles and much weaker plastic strain accumulation in the presence of stronger friction. The normal force is, in the simplest case, a linear spring that takes care of repulsion, and a linear dashpot that accounts for dissipation during contact. 0 n i f kδ γ δ = + , (1) with spring constant k and some damping coefficient 0 γ . The half period of a vibration around the equilibrium position can be computed, and one obtains a typical contact duration (response time) / π ω = c t , with 2 0 ( / ) ω η = − ij k m , the eigenfrequency of the contact, the reduced mass /( ) = + ij i j i j m m m m m , and the rescaled damping coefficient 0 0 /(2 ) ij m η γ = . The energy dissipation during a collision, as caused by the dashpot is quantified by the restitution coefficent 0 / exp( ), n c r t η ′ = − = − where the prime denotes the normal velocity after a collision. The tangential force involves dissipation due to Coulomb friction, but also some tangential elasticity that allows for stick-slip behavior on the contact level (Luding, 2004). In the static case, the tangential force is coupled to the normal force, Eq. (1), via Coulomb’s law, i.e. μ ≤ , where for the limit sliding case one has the dynamic friction with