Elastostatic shocks and shear localization problems in incompressible hyperelastic materials are analyzed by newly developed assumed stress finite elements. The element formulation is derived from the discretized form of a mixed variational principle which includes unsymmetric stress, rotation (drilling degrees of freedom), hydrostatic pressure, and displacement as independent variables. The numerical examples demonstrate that the present numerical procedures capture the formation of shear bands successfully and the results are in good agreement with analytical solutions. It is also found that the numerical solutions become quite sensitive to the initial and boundary conditions if the ellipticity of the material fails. The arclength method, in conjunction with the Newton-Raphson procedure, plays a crucial role in dealing with these problems to pass through the limit loads and bifurcation points in the solution paths.
|Number of pages||16|
|Journal||American Society of Mechanical Engineers, Applied Mechanics Division, AMD|
|State||Published - 1994|
|Event||Proceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA|
Duration: Nov 6 1994 → Nov 11 1994