A marked characteristic of rubberlike materials is the nearly incompressible behaviour. This type of behaviour is best modelled by mixed finite elements with separate interpolation functions for the displacements and the pressure. In this contribution the performance of threedimensional elements is investigated using a twotiered strategy. First, the ability of some linear and quadratic threedimensional elements to deform correctly under nearly isochoric conditions is estimated using the wellknown constraintcounting method, in which the ratio of the number of degreesoffreedom over the number of kinematic constraints present in the finite element mesh is determined. Next, the performance of the elements is assessed by numerical simulations for three cuboidal rubber blocks with different shape factors. The results turn out to be quite sensitive with respect to the ratio of the number of degreesoffreedom over the number of kinematic constraints, since too many pressure degreesoffreedom make the element overstiff, while too few pressure degreesoffreedom may cause the occurrence of spurious kinematic modes. This observation appears to be not only valid for the global structural behaviour, but also with respect to the specific parts in the structure, where the abovementioned ratio is different from the global number, e.g., in corners of the structure.
Engineering Computations – Emerald Publishing
Published: Jan 1, 1991
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