Rate-dependent modeling and simulation in engineering and biological systems - Zhang, Shubo (Nanyang Technological University, 2025)
Rate-dependent mechanical behaviors are widely observed across various scales, from the microscopic interactions of nanoscale bonds between atoms and molecules to the macroscopic expanse of mantles and glaciers spanning thousands of kilometers, holding significant importance in the fields of science and engineering. However, fundamental scientific and technical challenges related to these phenomena remain unresolved. For instance, the fracture, interfacial, and adhesive behaviors of soft materials, which often exhibit pronounced rate-dependent characteristics, still require quantitative investigation. Biological materials, which are among the most critical types of soft materials, demand a thorough understanding of their properties to advance biomedical engineering practices, such as the repair and replacement of myocardial, vascular, cartilage, and tendon tissues. In this dissertation, we will explore and address three distinct rate-dependent mechanical issues in engineering and biological systems through modeling and simulation. In Chapter 2, the zero-degree peeling of a viscoelastic tape is addressed. A thin tape, modeled as a standard-linear solid and adhered to a rigid substrate via a triangular-shaped cohesive law, is peeled by a constant stress applied at the end. Both analytical modeling and finite element simulation are performed to investigate this problem. The peeling stress under various crack propagation speed is determined, providing a fully analytical closed-form solution that can serve as a benchmark for more realistic models. We have demonstrated that, for medium-rate detachment, the crack propagation speed under “full stick” assumption grows as the cubic power of the applied stress and depends solely on viscosity and cohesive strength. The instantaneous elastic modulus determines the critical load for rapid detachment. In Chapter 3, two types of rate-dependent 90-degree peeling problems are investigated: a viscoelastic backing tape adhered to a rigid substrate via a conservative cohesive law, and an elastic backing tape adhered to a rigid substrate via a rate-dependent cohesive law. Analytical models are developed for both problems and validated through finite element simulations and experiments, respectively. The model indicates that the enhancement in peeling force for the rate-dependent cohesive law has the same order of magnitude with the enhancement ratio, while that for the viscoelastic backing tape is much smaller. This study can be utilized to further explore the apparent fracture energy of viscoelastic materials under different loading rates. In Chapter 4, the mechanisms of functional loss in injured intervertebral discs and the guidelines for designing injectable hydrogels to reconstruct the biomechanical environment are investigated. A simplified analytical model is established to explain the functional loss mechanisms in injured intervertebral discs. Finite element simulations are performed to study how the injected material can facilitate the biomechanical environment reconstruction. The model indicates that a hydrogel with moderate modulus can restore the supporting and cushioning function of the disc simultaneously, which is validated by the experiment. This study provides guidance for reconstructing the biomechanical environment of similar tissues with rate-dependent behavior.