Biaxial shear behaviour of HDNR with Mullins effect and deformation-induced anisotropy

High damping natural rubber (HDNR) bearings, commonly employed to isolate structures, are subjected to biaxial horizontal deformations by the seismic motion. If they have virgin material properties, biaxial models including the stress softening due to the Mullins effect should be used for describing their force–deformation behaviour. Specific studies oriented at characterizing and modelling the biaxial behaviour of HDNR bearings accounting for the stress-softening are very few in number because they would require a large number of virgin isolators or long times of rest between two consecutive tests. Moreover, available studies consider the Mullins effect as an isotropic phenomenon, whereas experimental investigations have shown that it is direction-dependent and thus induces anisotropy of the rubber behaviour. This paper describes an extensive experimental campaign carried out on a large number of small material test pieces aimed at achieving a satisfactory characterization of the biaxial anisotropic response of a highly dissipative rubber compound. These results are then used to develop a two-dimensional constitutive model for the virgin HDNR material accounting for the direction-dependence of the Mullins effect, based on the concept of representative directions applied to the biaxial shear deformation state. Because for commonly employed laminated HDNR bearings under design actions the approximation of uniform simple shear is realistic, the proposed material model can also be used to simulate the global bidirectional horizontal response of the bearings.