Theoretical Analysis And Numerical Simulation Study On Surface Instability Of Soft Materials Film Substrate System With Negative Gauss Curvature

The surface instability of soft material film-substrate system is not only widely existed in nature,but also widely used in engineering.Previous studies focused on planar systems,cylindrical and spherical systems.It is of great theoretical significance and practical engineering value to study the evolution process of surface instability mode of negative Gauss curvature film-substrate system.In the paper,based on the elastic stability theory,the evolution process of surface instability morphology that under uniaxial compression,equal biaxial compression and unequal biaxial compression of negative Gauss curvature film-substrate system is analyzed,and the effect of curvature on the evolution process of surface instability morphology is discussed by Fourier simulation.The main research work is as follow.Based on the Koiter elastic stability theory,the critical buckling analysis that negative Gauss curvature film-substrate system under uniaxial compression and negative Gauss curvature film-substrate system under biaxial compression is analyzed.The relation between critical buckling stress,critical wavenumber and curvature and the phase diagram of critical buckling mode selection are obtained.The potential energy of sinusoidal and hexagonal instability modes that negative Gauss curvature film-substrate under uniaxial compression is derived,the expression of overstress at sinusoidal to hexagonal transition point is solved by ignoring the higher order term of amplitude in energy expression,and the relation between critical overstress and curvature is discussed.The potential energy of square,hexagonal and herringbone instability modes that negative Gauss curvature film-substrate system under biaxial compression was established.After optimizing the energy by the principle of minimum potential energy,the evolution process of instability modes that real state and the variation of buckling wavenumber,buckling amplitude were obtained.The phase diagrams of post-buckling mode selection that negative Gauss curvature under axial compression and negative curvature film-substrate system under equal biaxial compression were given respectively.The potential energies of the negative Gauss curvature film-substrate system under unequal axial loads are calculated.It is proved that the morphology evolution under unequal axial compression is the same as that under uniaxial compression when the load biaxiality is small.Fourier spectrum method was used to simulation the evolution of surface instability morphology that negative Gauss curvature film-substrate system under uniaxial compression and negative curvature film-substrate system under biaxial compression.The finite element simulation of negative Gauss curvature film-substrate system under equal biaxial compression verifies the morphology evolution obtained from theoretical analysis and spectral simulation.It is proved that Gauss curvature plays an important role in the morphology evolution of filmsubstrate system by the uniaxial compression experiments and finite element analysis of zero and negative Gauss curvature film-substrate systems.