Path-dependent viscoelastic-hyperelastic response of brain tissue under multistage shear loading

Advancing computational models of repetitive traumatic brain injury (rTBI) requires understanding how prior loading alters the mechanical response of brain tissue. However, most previous studies have relied on single-stage loading or limited preconditioning protocols that do not capture path-dependent behavior. To bridge this gap, multistage simple shear experiments were performed on 14 bovine brain specimens. Successive ramp-and-hold and cyclic loading protocols examined the effects of loading mode, strain amplitude, and loading sequence within the reported sub-damaging loading range. Mechanical behavior was quantified using the shear modulus (μ) and Prony-series viscoelastic parameters (g₁-g₃, g_∞). In the present experiments, prior cyclic loading generally reduced peak stress and shear modulus. From the initial to the final loading stage, μ decreased from 2.94 ± 0.94 to 2.49 ± 0.63 kPa, g₂ increased from 0.14 ± 0.19 to 0.19 ± 0.17, and g₃ decreased from 0.21 ± 0.08 to 0.16 ± 0.06 (all p < 0.05). In contrast, g₁ and g_∞ showed no significant changes (p > 0.05). Cumulative strain was not significantly correlated with final μ (Spearman ρ = - 0.31, p > 0.05), whereas protocol sequence was associated with differences in μ within the investigated multistage loading histories. These findings demonstrate path- and sequence-dependent brain tissue mechanics that may inform constitutive models for repeated loading scenarios, including those relevant to rTBI.