Incorporating Bio-Inspired Sutures Into Curved Structures: Using Finite Element Models to Optimize the Mechanical Response Under Quasi-Static Three-Point Bending

Many animals have protective anatomical structures that allow for growth and flexibility; these structures contain thin seams called sutures that absorb impacts without breaking. Strong materials are well-suited for protective roles, but their rigidity renders them sensitive to brittle fracture. Studies suggest that sutures act as stress concentrators that absorb impact energy, which can help to prevent fracture in, for example, human skulls, woodpecker beaks, and the carapace of turtles. Previous experimental and numerical studies have explored the tensile properties of sutures as a function of geometric variables including suture shape, size, contact area, and degree of interlocking. While these geometric variables have been tuned to optimize the mechanical response (i.e., maximize strength and energy absorption) during pullout, the mechanical response of three-dimensional (3D) structures under more complex loadings can be optimized as well. As many of the naturally-occurring structures that contain sutures are curved and experience impacts at least partially normal to the surface, one potential application of this work is the design of novel protective helmets (e.g., bicycle or sports) that incorporate bio-inspired sutures into their structure. 

In this study, we created finite element models of pairs of curved test pieces linked together to create archway structures in ANSYS Mechanical. The inner radius of the pieces was 10 cm, and the square cross-section was 2.54 cm thick. Quasi-static three-point bending experiments were simulated to determine the suture geometries that would maximize the structure’s toughness (i.e., capacity for energy absorption), which is critical for structures that are subjected to impact. The dovetail design used in this study blends the tensile strength of interlocking jigsaw tabs with the bending strength of longer triangular saw-teeth tabs. Specifically, varying geometric parameters of the suture included tab radii of 1-4.5 mm, tangent lengths of 0-20 mm, and contact angles of 0-40 degrees. The curved arch pieces were modeled as polylactic acid (PLA), as we plan to 3D print these test pieces for future dynamic impact studies. The indenter was modeled as structural steel. Both materials were treated as isotropic and linear elastic. In the simulation, the indenter was displaced downward in 0.5 mm increments such that the contact force as a function of displacement could be plotted. The flat face at the bottom of each arch piece was fixed in place, and frictionless contact was defined between all faces to isolate the geometric effects. Quadratic elements were used throughout the model, and contact sizing was applied at the contacting surfaces between the two archway pieces to ensure stress convergence.

Our results indicate that the overall toughness was a complex function of all three geometric variables. In general, sutures with the largest contact angles led to the toughest structures. Increasing the tangent length also increased the contact force, but less dramatically. Increasing the radius of the jigsaw tabs produced non-monotonic results, with both the smallest and largest radii producing weaker responses. Because of the fixed cross-sectional dimensions, the number of tab repeats in the suture varied in our parametric study, resulting in a significant variation in the contact surface area. This suggests that the addition of frictional contact would further increase the toughness of the cases with higher contact surface area. Lastly, it should be noted that certain parameter combinations could not be achieved. For example, high contact angles with large tangent lengths, which trends suggested would be quite tough, could not be incorporated in the test pieces. The study revealed several suture geometries that hold significant promise for impact applications, and these will be used in future experimental impact studies.