Constitutive sensitivity of end effects in slabs under compression

摘要

Constitutive sensitivity of end effects induced in a rectangular elastomeric slab subjected to compression is investigated in the context of plane-strain incremental finite elasticity. A separation of variables in the eigenfunction formulation is used for the perturbed field within the slab. Numerical results for the leading decay exponent, supported by asymptotical expansion, are given for four rubbers. It was found that the lowest decay rate exhibits different patterns of dependence on the prestrain for compressible and for nearly incompressible solids. Compressible solids are characterized by low sensitivity of the decay rate to prestrain level up to moderate compression, beyond which, an abrupt decrease of decay rate brings it to zero. Nearly incompressible solids, on the other hand, exhibit interchange of modes with no decrease of decay rate to zero. Both patterns show that the decay rate obtained from linear elastic analysis can be considered as a good approximation for a pre-buckled, slightly compressed slab, which is long enough in comparison to its width.