Mechanical modelling of viscoelastic hierarchical suture joints and their optimisation and auxeticity

• Published in: Mechanics of materials 2023-11, Vol.186, p.104785, Article 104785
• Main Authors: Ongaro, F., Pugno, N.M.
• Format: Article
• Language: English
• Subjects: Auxeticity; Effective properties; Hierarchy; Loss factor; Suture joints; Viscoelasticity
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2023.104785

It has been widely recognised that suture joints play a fundamental role in the exceptional mechanical properties of many biological structures like the cranium and ammonite fossil shells. Up to date, many efforts have been devoted to investigate suture interfaces to predict the relations between the characteristics of its two phases, the teeth and the interface layer, and the structure effective properties. However, in very few works the viscoelasticity of the suture components has been taken into account. To provide a contribution in this limitedly explored research area, this paper describes the mathematical formulation and modelling technique leading to explicit expressions for the effective properties of viscoelastic suture joints with a general trapezoidal waveform. It emerges a strong influence of the suture geometric and mechanical characteristics on the effective properties and a parametric analysis reveals that an auxetic behavior can be obtained simply by tailoring the suture parameters. The effects of adding hierarchy into the above system are also explored and closed-form relations for the effective moduli are derived. Optimal levels of hierarchy can be identified and, similarly to the non-hierarchical case, an auxetic behavior emerges for particular values of the suture parameters. Finally, an extension of the theory to the sinusoidal sutures in biology is reported. By considering the examples of the cranium and the woodpecker beak, it emerges that the first is optimised to obtain high stiffness, while the second to obtain high energy dissipation levels. •Explicit expressions for the effective properties of viscoelastic suture joints are presented.•A strong influence of the suture geometric and mechanical characteristics emerges.•A parametric study reveals that auxeticity can be obtained simply by tailoring the suture parameters.•The effects of adding hierarchy are explored and the effective properties are derived in a closed-form.•Optimal levels of hierarchy are found, with auxeticity emerging for certain suture configurations.•The theory is then extended to the sinusoidal sutures in biology and explicit expressions for the effective stiffness are obtained.•Two examples are considered: the sutures of the cranium and the woodpecker beak, respectively optimised to obtain high stiffness and high energy dissipation levels.