Numerical simulations of local and global buckling of hyperelastic tubes with different cross-sections

Introduction. An approach to the application of finite element programs (FEM) ABAQUS/Standard and ABAQUS/Explicit with various equations of state of incompressible isotropic hyperelastic materials is presented when analyzing compressed and stretched shell elements of elastomers. Elastomers are commonly used in construction as well as in structural shell elements, in particular pipes of different cross sections. Materials and methods. Three FEM models for pipes with the same length and initial stiffness were created. Pipes with elliptical, square and triangular cross sections are considered. Three types of structural models of rubber-like material (elastomer) were used - with a polynomial elastic energy function in the form of the MV model and the standard models of Neo - Hooke and Mooney - Rivlin. In the FEM models of the analyzed pipes, not enter initial imperfections. Numerical modeling buckling of pipes was performed for two types of initial and boundary conditions - for quasistatic and dynamic problems. Results. It is shown that the type of buckling depends on the cross section of the pipe. Comparison of buckling solutions for simulated pipes with different structural models demonstrated a good correlation of the results. An approximate history of the deformation of an elliptical sample analyzed by ABAQUS/Standard, loaded by moving the boundary, is given. Conclusions. It has been established that the ABAQUS/Standard program allows the use of incompressible hyperelastic materials, the ABAQUS/Explicit program does not provide this possibility. This implies the need to set the parameters of the material associated with the spherical part of the stress tensor. The parameter should not be too small, otherwise it will lead to numerical errors. Solving problems on the stability of pipe models with different physical models give good correlations of results.