Statistical shear lag model - unraveling the size effect in hierarchical composites

Numerous experimental and computational studies have established that the hierarchical structures encountered in natural materials, such as the brick-and-mortar structure observed in sea shells, are essential for achieving defect tolerance. Due to this hierarchy, the mechanical properties of natural materials have a different size dependence compared to that of typical engineered materials. This study aimed to explore size effects on the strength of bio-inspired staggered hierarchical composites and to define the influence of the geometry of constituents in their outstanding defect tolerance capability. A statistical shear lag model is derived by extending the classical shear lag model to account for the statistics of the constituents' strength. A general solution emerges from rigorous mathematical derivations, unifying the various empirical formulations for the fundamental link length used in previous statistical models. The model shows that the staggered arrangement of constituents grants composites a unique size effect on mechanical strength in contrast to homogenous continuous materials. The model is applied to hierarchical yarns consisting of double-walled carbon nanotube bundles to assess its predictive capabilities for novel synthetic materials. Interestingly, the model predicts that yarn gauge length does not significantly influence the yarn strength, in close agreement with experimental observations.

Enhanced tendon-to-bone repair through adhesive films

Tendon-to-bone surgical repairs have unacceptably high failure rates, possibly due to their inability to recreate the load transfer mechanisms of the native enthesis. Instead of distributing load across a wide attachment footprint area, surgical repairs concentrate shear stress on a small number of suture anchor points. This motivates development of technologies that distribute shear stresses away from suture anchors and across the enthesis footprint. Here, we present predictions and proof-of-concept experiments showing that mechanically-optimized adhesive films can mimic the natural load transfer mechanisms of the healthy attachment and increase the load tolerance of a repair. Mechanical optimization, based upon a shear lag model corroborated by a finite element analysis, revealed that adhesives with relatively high strength and low stiffness can, theoretically, strengthen tendon-to-bone repairs by over 10-fold. Lap shear testing using tendon and bone planks validated the mechanical models for a range of adhesive stiffnesses and strengths. Ex vivo human supraspinatus repairs of cadaveric tissues using multipartite adhesives showed substantial increase in strength. Results suggest that adhesive-enhanced repair can improve repair strength, and motivate a search for optimal adhesives.

STATEMENT OF SIGNIFICANCE

Current surgical techniques for tendon-to-bone repair have unacceptably high failure rates, indicating that the initial repair strength is insufficient to prevent gapping or rupture. In the rotator cuff, repair techniques apply compression over the repair interface to achieve contact healing between tendon and bone, but transfer almost all force in shear across only a few points where sutures puncture the tendon. Therefore, we evaluated the ability of an adhesive film, implanted between tendon and bone, to enhance repair strength and minimize the likelihood of rupture. Mechanical models demonstrated that optimally designed adhesives would improve repair strength by over 10-fold. Experiments using idealized and clinically-relevant repairs validated these models. This work demonstrates an opportunity to dramatically improve tendon-to-bone repair strength using adhesive films with appropriate material properties.

Shear lag sutures: Improved suture repair through the use of adhesives

Suture materials and surgical knot tying techniques have improved dramatically since their first use over five millennia ago. However, the approach remains limited by the ability of the suture to transfer load to tissue at suture anchor points. Here, we predict that adhesive-coated sutures can improve mechanical load transfer beyond the range of performance of existing suture methods, thereby strengthening repairs and decreasing the risk of failure. The mechanical properties of suitable adhesives were identified using a shear lag model. Examination of the design space for an optimal adhesive demonstrated requirements for strong adhesion and low stiffness to maximize the strength of the adhesive-coated suture repair construct. To experimentally assess the model, we evaluated single strands of sutures coated with highly flexible cyanoacrylates (Loctite 4903 and 4902), cyanoacrylate (Loctite QuickTite Instant Adhesive Gel), rubber cement, rubber/gasket adhesive (1300 Scotch-Weld Neoprene High Performance Rubber & Gasket Adhesive), an albumin-glutaraldehyde adhesive (BioGlue), or poly(dopamine). As a clinically relevant proof-of-concept, cyanoacrylate-coated sutures were then used to perform a clinically relevant flexor digitorum tendon repair in cadaver tissue. The repair performed with adhesive-coated suture had significantly higher strength compared to the standard repair without adhesive. Notably, cyanoacrylate provides strong adhesion with high stiffness and brittle behavior, and is therefore not an ideal adhesive for enhancing suture repair. Nevertheless, the improvement in repair properties in a clinically relevant setting, even using a non-ideal adhesive, demonstrates the potential for the proposed approach to improve outcomes for treatments requiring suture fixation. Further study is necessary to develop a strongly adherent, compliant adhesive within the optimal design space described by the model.