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A closed-form description is proposed to explain nonlinear and slow dynamicseffects exhibited by sandstone bars in longitudinal resonance experiments.Along with the fast subsystem of longitudinal nonlinear displacements weexamine the strain-dependent slow subsystem of broken intergrain andinterlamina cohesive bonds. We show that even the simplest butphenomenologically correct modelling of their mutual feedback elucidates themain experimental findings typical for forced longitudinal oscillations ofsandstone bars, namely, (i) hysteretic behavior of a resonance curve on bothits up- and down-slopes, (ii) linear softening of resonant frequency withincrease of driving level, and (iii) gradual recovery (increase) of resonantfrequency at low dynamical strains after the sample was conditioned by highstrains. In order to reproduce the highly nonlinear elastic features ofsandstone grained structure a realistic non-perturbative form of strainpotential energy was adopted. In our theory slow dynamics associated with theexperimentally observed memory of peak strain history is attributed tostrain-induced kinetic changes in concentration of ruptured inter-grain andinter-lamina cohesive bonds causing a net hysteretic effect on the elasticYoung's modulus. Finally, we explain how enhancement of hysteretic phenomenaoriginates from an increase in equilibrium concentration of ruptured cohesivebonds that are due to water saturation.Comment: 5 pages, 3 figure

Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars