Experimental and Inverse Analysis of Natural Cork Material with Anisotropic Nonlinear Viscoelastic Behavior

Due to its cellular structure, cork from Quercus suber has significant deformability, showing magnificent recovery after being compressed by 50%. Its mechanical characteristics show dependency on the direction of the external load (anisotropy), making it difficult to estimate recoverable large displacements. Here, the mechanical behavior of cork is investigated under loading–unloading cycles (1–15 MPa) in the radial and non-radial directions. Cork demonstrates higher stiffness and higher residual strain in the radial direction, compared to the softer, buckling-dominated behavior in the non-radial direction. Both directions feature significant cycle-by-cycle softening, suggesting a Mullins-type (recoverable) damage mechanism, with residual strain increasing in both directions. According to the data obtained six months after testing, dimensional recovery demonstrates ongoing recovery with varying percentages depending on the direction (92% against 88% of the original height after six months). It supports the theory of softening from cycle to cycle because the damage is primarily pseudo-elastic and therefore recoverable rather than irreversible. A transversely isotropic hyperelastic constitutive model is enriched with Mullins-type (pseudo-elastic) damage and viscoelasticity. The three-dimensional model is based on engineering applications; all parameters are obtained through inverse analysis of loading–unloading tests. Consequently, this model accounts for the anisotropic behavior and increasing recoverable damage of cork, allowing better prediction of its mechanical performance.