Instabilities in hyperelastic softening materials

W. Seki, S. N. Atluri

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish
Pages (from-to)151-166
Number of pages16
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
StatePublished - 1994
EventProceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA
Duration: Nov 6 1994Nov 11 1994


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