Instabilities And Applications Of Tubular Structures Composed Of Soft Materials And Kirigami Metamaterials

Stability is a classical problem in mechanics.Instability phenomena are ubiquitous in engineering,natural science and biomedical fields.Due to the effect of curvature,the instability characteristics of tubular structures can be very different from those of planar structures.By combining theoretical analysis,numerical modeling and experimental validation,different types of instabilities and morphology changes are investigated for tubular structures,composed of soft materials or kirigami metamaterials with different load and boundary conditions.Novel soft robots are also developed utilizing the deformation characteristics of soft materials and kirigami metamaterials.The content of the thesis includes the following aspects:Asymptotic analytical solutions of critical growth factor and critical mode number for growth instability of soft tubular structures.In the framework of nonlinear elasticity theory,models of growth instability for single-layer and bilayer tubular structures with external boundary constraints are established,and the bifurcation conditions are obtained by using incremental elasticity theory.In the case of instability with large critical mode number,the bifurcation condition is transformed from the eigenvalue problem of a variable coefficient ordinary differential equation to the eigenvalue problem of a matrix by using WKB method,and the explicit expressions of bifurcation conditions are obtained accordingly.The bifurcation conditions of single-layer and bilayer structures are further analyzed,and the obtained asymptotic solutions qualitatively reveal the effects of geometric and material parameters on the critical bifurcation condition,which can provide guidance for the study of patterns formation in biological soft tissues.A semi-analytical solution for the post-buckling behavior of the soft tubular structures.In the framework of nonlinear elasticity theory,the incremental governing equations are expanded to higher orders.A weakly nonlinear analysis is conducted under the assumption that the incremental perturbation is of small amplitude.A semianalytical solution of the post-buckling amplitude is derived through a solvability condition and virtual work principle at the third order of the successive approximations.Compared with finite element results,the proposed method can determine the relationship between the wrinkle's amplitude and growth factor more efficiently,and it can reveal the effects of geometric and material parameters on the amplitude of the wrinkles.Moreover,the bifurcation types of structures with different material and geometric parameters as well as the imperfection sensitivity of instability are discussed.Finally,the rationality of the conclusion for post-buckling analysis was verified by swelling experiments on PDMS tubular structures.Different types of instabilities and the propagation of instability interface for kirigami metamaterial tubular structures.By means of experimental test,numerical simulation and theoretical analysis,the instability types and morphological differences after buckling are studied for both planar and tubular kirigami structures under uniaxial tensile load.The instability morphologies of planar and tubular kirigami structures are compared in experiments,which reveal the deformation mechanism of instability phenomena for different structures.By combining Maxwell construction with finite element analysis,a phase diagram is conducted to distinguish different types of instability.For tubular structures with limit point instability,the relationship between the width of the instability interface(the interface between the tube segment with inplane deformation and the tube segment with out-of-plane deformation)and the geometric parameters are obtained by using a strain gradient theory.The results of this study are applied to crawling robots,which significantly improve the crawling efficiency.A bistable kirigami structure is also designed,whose sustainable propagation process of the instability interface is further investigated.By combining the deformation characteristics of soft material and kirigami metamaterial,new types of soft robots are designed.An inflatable kirigami structure is designed by combining the tubular kirigami structure with silicone rubber,whose deformation can be regulated by changing the geometric parameters of the kirigami structure.The relationships between geometric parameters and structural deformation of orthogonal patterns are investigated,and an inverse design model is proposed accordingly for axisymmetric and non-axisymmetric structures.Using modular design and fluid viscosity characteristics,the pressure drops between different modules are introduced to transform the quasi-static deformation process of the structure into a dynamic sequential deformation process,which can benefit the design of soft robots.Our study on instability of tubular structures for soft materials can provide guidance for the morphological evolution of soft tissues as well as the diagnosis of some diseases in clinical medicine.The investigation on the instability of the tubular structure for kirigami metamaterials will provide theoretical supports for the design of mechanical metamaterials.Furthermore,the combination of soft materials and metamaterials can further enrich the applications of mechanical metamaterials in flexible electronics and soft robots.