Growth-induced crack propagation in biological epidermis: a three-dimensional phase-field-cohesive zone study

During biological epidermal growth, factors such as non-uniform growth rates and tissue differentiation inevitably generate internal stresses, leading to the formation of microcracks. These cracks facilitate the controlled release of such stresses, thereby enhancing the material’s damage tolerance and flexibility. In this paper, a three-dimensional elastic phase-field-cohesive zone model for simulating growth-induced cracks in biological epidermis is established. The growth process is modeled through uniform volumetric expansion. The model successfully captures the crack patterns observed in Tuzoia fossils. Simulation results indicate that tensile stress serves as the primary driving force for both crack initiation and propagation. The influence of interlayer parameters and model variations on crack propagation and fragment area is systematically investigated. Larger differences in interlayer growth rates and thickness, or lower interlayer stiffness and a smaller model curvature radius, promote crack initiation and propagation. An empirical formula is further developed to predict the average fragment area of double-layer thin plates, based on the ratios of interlayer growth rates, elastic modulus, and thickness. The model has the potential to predict and reconstruct the cracking processes of other quasi-brittle biological epidermal structures under growth-induced forces.