Multiphysical dynamic fracture analysis of biomimetic composites based on non-Fourier heat conduction
Creators: Yang, Weilin
Publisher: name: University of Alberta Library
Year: 2023

<p>In the world of engineering, strength and toughness are two highly desirable properties to materials design. Biological materials have already mastered both of these properties within the threads they protect themselves in harsh nature. The key to both the biomaterial’s ability to resist external injury and the highly energy dissipative behavior is a type of hierarchical structure called brick-and-mortar structure, which is comprised of soft collagen matrix and hard hydroxyapatite crystals. Recently, researchers have incorporated metal phases into various sizes of polymeric matrix to improve their mechanical properties. However, there is not as much fundamental understanding of how the heterogeneity of these combinations dictates fracture behavior, either in a single- or in multi-physical fields.</p>

<p>In this thesis, we use the non-Fourier heat conduction law to explore biomimetic gradation design under different surrounding environments. The thesis includes three parts of work. First, a multiphysical model was developed to investigate the fracture behavior of biomimetic materials under thermoelectromechanical loading. In particular, a piezoelectric material model is used to mimic the multiphysical behavior of biological materials, such as wood and nacre. A simplified, homogeneous piezoelectric material is used to mathematically model the dynamic multiphysical fracture behavior of biomimetic materials. With the aid of fractional heat conduction equation and Maxwell’s equations, we analyze the effects of temperature and electrical disturbances on the stress-electric displacement intensity factors.  In the second part, a brick-and-mortar graded (BM-GRAD) model was proposed to investigate how material heterogeneity interacts with its crack resistance. It was found that the BM-GRAD always shows a smaller zone of extreme stress localization as well as lower values of the normal stress, which significantly improves the crack resistance. It is also highlighted that BM-GRAD microstructure is easier to form deflecting crack once a fracture happens and the crack propagation is more likely to be terminated. Finally, we combined the gradient design and multiphysical behavior and carried out a comprehensive analysis of various multiphysical, gradient designs in the third part. The results showed that multiphysical conditions have a significant influence on the fracture resistance of heterogeneous material, whiles temperature is a vital factor that cannot be ignored. To describe thermal transport more accurately in biomaterials, the non-Fourier theory incorporated with thermal relaxation effect describes thermal transport more accurately than classical heat conduction equations which indicates the speed of thermal propagation is infinite. The results of a cracked functionally graded piezoelectric strip mimicking biomaterials under thermoelectromechanical loading shows that a sudden temperature fall will cause an opening-mode failure risk, while a positive electric shock will slightly reduce the likelihood of fracture occurrence compared to a negative electric loading.</p>

<p>From our fracture resistance results, a strong dependence of peak stress on the electromechanical gradation coefficient Ω and thermal gradation coefficient Ψ was observed. Except the case of a singular thermal environment, the configuration without gradients demonstrates exceptional crack resistance performance. Incorporating graded design principles into biomimetic piezoelectric structures can effectively enhance their ability to resist crack propagation under single stress, single electric, and thermo-electromechanical environments. Specifically, the symmetric gradient configuration, characterized by a higher order of the electromechanical gradation coefficient Ω and thermal gradation coefficient Ψ, shows remarkable fracture resistance under single stress or single electric environment. For coupled heating-mechanical-electrical and cooling-mechanical-electrical fields, the symmetric functional gradient configuration with (Ω, Ψ) = (1, -0.5) and (1, -1), respectively, displays lower stress intensity in the vicinity of crack tips.</p>

<p>In addition to the theoretical studies, we also first replicated the effect of the multiphysics based on non-Fourier theory within finite element simulations. To do so, we first defined time-dependent thermal partial differential equations in COMSOL Multiphysics platform and further coupled static solid mechanics and electrostatics physics. The temperature and stresses simulation results are in good agreement with our theoretical results for gradation design. </p>

<p>Collectively, these findings provide us with new insights into the correlations between fracture mechanics and heterogenous functional gradations of biomimetic composites for different environments, and guidelines to tune the gradation coefficients of bio-inspired materials under complex environments.</p>