Targeting the finite-deformation response of wavy biological tissues with bio-inspired material architectures.

The Particle Swarm Optimization algorithm driven by a homogenized-based model is employed to target the response of three types of heart-valve chordae tendineae with different stiffening characteristics due to different degrees of waviness of collagen fibril/fiber bundles. First, geometric and material parameters are identified through an extensive parametric study that produce excellent agreement of the simulated response based on simplified unit cell architectures with the actual response of the complex biological tissue. These include amplitude and wavelength of the crimped chordae microstructure, elastic moduli of the constituent phases, and degree of microstructural refinement of the stiff phase at fixed volume fraction whose role in the stiffening response is elucidated. The study also reveals potential non-uniqueness of bio-inspired wavy microstructures in attaining the targeted response of certain chordae tendineae crimp configurations. The homogenization-based Particle Swarm Optimization algorithm, whose predictions are validated through the parametric study, is then shown to be an excellent tool in identifying optimal unit cell architectures in the design space that exhibits very steep gradients. Finally, defect criticality of optimal unit cell architectures is investigated in order to assess their feasibility in replacing actual biological tendons with stiffening characteristics.