Within a closed system of particles, we formulate configurational mechanics for a nonempty subsystem whose membership can change through particle admission or deletion. Using zero–one membership functions and the quantities carried by each particle, we derive the standard open-subsystem balances and the open-subsystem form of a postulated configurational-momentum balance. To describe membership change geometrically, we introduce an auxiliary smooth scalar field and assign velocities to its level sets. For each auxiliary description, we require the working to be invariant under tangential changes of those velocities. Combining this invariance with independent comparisons of membership rates and local normals, we conclude that every membership-weighted standard force must vanish if the working contains only standard forces and standard-momentum transfer. After including configurational forces and configurational-momentum transfer, we instead identify the specific configurational momentum with the negative of the particle velocity and establish that the combined standard and configurational force is normal to the local level surface. Using the stated spatial continuum representation, we recover the known expression for the specific configurational momentum. For nondissipative membership transfer, we use a mechanical energy imbalance to recover the form of the Eshelby stress in the same spatial representation. To interpret the stress thermodynamically, we additionally require a consistent identification of the marginal interaction energy per unit mass with the continuum specific free energy.
Intervertebral disc (IVD) degeneration involves coupled interactions between tissue mechanics, nutrient transport, cellular metabolism, and extracellular matrix (ECM) turnover. This work presents a multiscale mechanobiological framework integrating these processes within a continuous description of degeneration. A multiphasic mechanical model is calibrated and assessed against experimental mechanical and osmotic responses, including independent creep datasets, and subsequently coupled with experimentally informed metabolic and matrix-turnover mechanisms. Depending on the applied load and metabolic configuration, the simulations reveal three distinct model-emergent degeneration regimes characterized by decelerating, fluctuating, and accelerating progression. The decelerating regime exhibits an age-dependent decrease in degeneration rate qualitatively similar to trends reported in cross-sectional and longitudinal clinical studies, whereas the accelerating regime is associated with a cascade involving nutrient depletion, proteoglycan loss, and progressive loss of mechanical function. These findings illustrate how interactions between mechanical, metabolic, and matrix-turnover processes can give rise to nonlinear long-term degeneration trajectories. Long-term simulations rely on sustained compression rather than physiological diurnal loading and do not account for direct mechanotransduction, structural damage, or injury-induced degeneration. Accordingly, the framework is intended to explore the mechanisms underlying long-term IVD degeneration rather than to predict individual degeneration trajectories.
