From cumulative exposure to failure: a unifying modelling framework for nonlinear tissue fatigue in ergonomics

Musculoskeletal injury risk is often assessed using models that assume damage accumulates linearly with loading. However, biological tissues may exhibit history-dependent changes in tolerance, particularly under repeated or variable loading. In this study, we propose a nonlinear cumulative damage model grounded in a mechanistic description of collagen fibril engagement and failure. The model predicts the evolving tissue tolerance over time, with damage rates governed by a Tobolsky-Eyring-type law modulated by prior damage history. The model was calibrated using experimental fatigue data from functional spinal units and evaluated through a series of simulations designed to reflect common ergonomic exposures. These included constant-load cycling, variable-load sequences, and heavy-tailed loading distributions. Notably, the model predicts that tissue already compromised by prior loading is more susceptible to additional damage, even under identical external conditions—a form of path dependence not captured by the classical Miner-Palmgren rule. Perturbation analysis reveals that commonly used fatigue models can be recovered as successive approximations of the proposed framework, offering a formal connection between linear cumulative load theory, including ergonomics tools like LiFFT, and our nonlinear formulation. This unifying perspective helps reconcile chronic and acute injury risk models and highlights the importance of accounting for load history and variability in injury risk assessments. These findings suggest that ergonomic models should be sensitive not only to cumulative load, but also to its temporal structure and variability. Incorporating such nonlinearities could improve predictions of tissue failure and inform guidelines for safer task design.