Mechanistic diffusion model for slow dynamic behavior in materials

Infrastructure materials, such as rocks and concrete, exhibit an array of intricate and interrelated dynamic mechanical behaviors that act across a broad range of size scales. Modeling these dynamic behaviors is important for understanding safe design, application, and maintenance practices. One particular and fascinating nonlinear dynamic mechanic response - slow dynamics is characterized by a self-recovering hysteretic stress-strain relationship. Here we formulate a mechanistic model for slow dynamics, which we call a mechanistic diffusion model (MDM), based on coupled mechanical and diffusional processes. Diffusion-driven moisture migration nearby the minuscule regions surrounding granular contact points within a cracked solid serves as the physical foundation of the model. Diffusion physics explains fast conditioning rates, as moisture is vaporized, and relatively slow recovery process rates, as the moisture condenses back to equilibrium conditions. The MDM provides physically-based justification for environment and strain activated observations noted in previous slow dynamic experiments. The MDM is verified against new experimental data of internal humidity and mechanical softening observed in a porous solid during dynamic excitation. The MDM model predicts, and the accompanying experiment successfully exhibits, internal humidity changes with slow dynamic nonlinearity of the test material. The MDM model identifies a physical mechanism of transient nonlinearity and provides a framework to interpret the significance of observed slow dynamic nonlinear behaviors.