Plane-stress analysis of rubber at high strains using finite elements

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Abstract
A finite-element programme has been developed for the analysis of stretched rubber sheets. The elastic energy of each of the homogeneously deformed triangular elements into which the sheet is divided can be determined from the displacements of its nodal points and a suitable strain-energy function. Each nodal point of the sheet is considered in turn and moved to a position which minimizes the energy of all the elements local to it. This iterative process is continued until the total energy of the sheet is minimized. A modified classical-elasticity-theory programme provides the first approximation. The boundary conditions are specified displacements, assumed to arise from the use of rigid clamps. The results are in good agreement with experiment for peak strains of about 150 per cent. Computation time on a CDC 6600 computer is about 0.005 × (nodal points)2 seconds.

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