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Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies (N) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints.

Section: Introductionmentioning

confidence: 99%

Bioinspired, mechanical, deterministic fractal model for hierarchical suture joints

Ortiz

Boyce

2012

“…The structure of fossilised ammonites have long been appreciated to exhibit a fractal structure in their suture lines [4]. Although other driving factors have been proposed [5], it has been persistently hypothesised that higher degrees of structural hierarchy are responsible for increased resilience to pressure bearing (for a given mass of construction material) [4,6,7]. It has recently been shown that hierarchical and fractal-like suture joints can be used to tailor mechanical properties, load resistance and flaw tolerance [8].…”

Section: Introductionmentioning

confidence: 99%

Optimization of fractal space frames under gentle compressive load

Rayneau-Kirkhope

Farr

2013

The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency is found in certain loading regimes. We show that in the limit of gentle loading, the optimal hierarchical order increases without bound. We show that the scaling of material required for stability against loading to be withstood can be altered in a systematic, beneficial manner through manipulation of the number of structural length scales optimized upon. We establish the relationship between the Hausdorff dimension of the optimal structure and loading for which the structure is optimized. Practicalities of fabrication are discussed and examples of hierarchical frames of the same geometry constructed from solid beams are shown.

“…The wavy, mechanically interdigitating structure of a suture joint can be as simple as a sinusoid [14] or exhibit a complex multiple wavelength pattern and/or a hierarchical fractal-like structure of shorter wavelengths superposed onto longer wavelengths [15][16][17]. A common measure of the degree of interdigitation is the "suture complexity index" or SCI [5,18,19], given in its simplest form as the ratio of the suture contour length to the shortest suture line length [l/l 0 , Fig.…”

mentioning

confidence: 99%

Stiffness and strength of suture joints in nature

Ortiz

Boyce

2011

Suture joints are remarkable mechanical structures found throughout nature composed of compliant interlocking seams connecting stiffer components. This study investigates the underlying mechanisms and the role of geometry governing the unique mechanical behavior of suture joints. Analytical and numerical composite models are formulated for two suture geometries characterized by a single repeating wavelength (e.g., triangular and rectangular). Stiffness, strength, and local stress distributions are predicted to assess variations in deformation and failure mechanisms. A unique homogeneous stress field is observed throughout both the skeletal and interfacial components of the triangular geometry, thus providing advantages in load transmission, weight, stiffness, strength, energy absorption, and fatigue over the rectangular geometry. The results obtained have relevance to biomimetic design and optimization, suture growth and fusion, and evolutionary phenotype diversity.