Modeling strategies for analyzing the inelastic behavior of biological and bioinspired materials

The smashing mantis shrimp is a crustacean that uses its dactyl club to defend itself or prey on other animals. This dactyl club is so strong that it can reach accelerations as high as a bullet of a caliber 0.22 gun and impact without breaking. We seek to understand the secrets behind the staggering properties of this club that withstand several high-damage impacts without breaking catastrophically. The dactyl club comprises three parts: the impact region, the periodic region, and the striated region. The first region of interest is the periodic region. This region is made of a helicoidal arrangement of fibers called Bouligand architecture, and in this architecture, cracks only form in the matrix between fibers. The first research project approximates the Bouligand composite with a single helicoidal crack embedded in an isotropic material. The test consists of a disk with a notch under quasistatic biaxial boundary conditions. We found an enhancement of mechanical properties when we increase the pitch angle. In the following section, a coarse-grained model is developed. This model allows multiple crack formation. This approximation tells us that as the initial crack grows, the driving force of crack propagation, the energy release rate, diminishes. The crack stops growing, confining itself, and allowing multiple crack nucleation and delocalization. At the same time, this dissipates more energy as more cracked surfaces appear. Hashin damage model with a cohesive zone model are used under different boundary conditions, geometries, and material properties, to model Bouligand composites. The helicoidal composites outperform the reference ones in peak load and absorbed energy. The next part of this thesis investigates the bicontinuous particles present in the impact surface of the dactyl club. These bicontinuous particles consist of a soft phase (organic) and a hard phase (hydroxyapatite) that can withstand high strain rates. Their stiffness and strength increase with strain rate. On the other hand, preliminary studies suggest that they perform well in cyclic loading. Finally, we proceed to use the helicoidal composites to design structural parts. We introduce a model for simulating the fiber-reinforced composites called LARC05. We verify, validate, and then use models for fiber-reinforced composites.