Differential Constitutive Equation of Elytra Cuticle by Nanoindentation

Abstract

Due to size limits in the transverse direction, tensile testing is not appropriate to investigate the mechanical properties of elytra cuticle of the dung beetle (Copris ochus Motschulsky). However, nanoindentation testing can determine a material’s anisotropic properties through a single indentation. In the present study, nanoindentation stress–strain curves were used to characterize the complete mechanical behavior of dung beetle elytra cuticle. A differential constitutive equation has been developed with time-dependent spring constants k and viscosities η . To describe the complex viscoelastic behavior of dung beetle cuticle, a descriptive representation of the linear viscoelasticity law for the multilayer matrix has been formulated. A qualitative model for the relationship between cuticle structure and mechanical properties of elytra may help develop bionic composite materials for micro-aircraft, bionic tribology, bionic medical apparatus, and bionic organs (tissue engineering).

Review of beetle forewing structures and their biomimetic applications in China: (I) On the structural colors and the vertical and horizontal cross-sectional structures

“…These features make beetle forewings an excellent biological model for our biomimetic research. The work described above has primarily been performed by two research groups: LQ Ren at Jilin University [81][82][83][84][85][86][87][88] and ZD Dai at NUAA [47,[89][90][91]. These groups focused on the surface structures of beetle forewings and their friction properties, applications, and nanometer indentation hardness and energy storage.…”

Biomimetic Studies of the Beetle Forewing in China

“…At the beginning of this century, while B. Chen and J. Chen et al continued to engage in the bionic research of beetles, J. Sun et al in Jilin University began to investigate the structural and mechanical properties of beetle forewings [45,[72][73][74][75][76][77][78][79][80][81][82]. They measured the surface morphology and the hardness and elastic modulus of the forewing of dung beetles using an optical profiler and a nanoindenter, respectively [73,74,[76][77][78][79].…”

“…An intrinsic relation was found to exist between the vertical and transverse elastic modulus of beetle forewings. Additionally, the measurement method and technology were discussed [72,75], and an equation was derived between the stress and contact time with the nanoindenter tip [80]. The tensile strength of the forewing was tested, and the failure modes were investigated [78].…”

Avoidance of Catastrophic Structural Failure as an Evolutionary Constraint: Biomechanics of the Acorn Weevil Rostrum

“…The endocuticle is made of aligned α‐chitin nanofibrils whose crystalline structure is enforced by hydrogen bonds between individual chitin chains and through the protein matrix along their length. Macroscopic viscoelastic behavior is thought to be caused by slippage between these chains in response to shearing between the chitin molecules and protein matrix . Repeated strain may have caused such slippage in the endocuticle of the rostral apex during the fatigue test.…”