SentryGlas® (SG) (a transparent ionomer from Kuraray) and Transparent Structural Silicon Adhesive (TSSA) (a transparent silicon from Dow Corning) are two of the adhesive materials used in laminated adhesive connections for structural glass applications. Although they have been used in several projects worldwide, failure criteria for these materials are currently not available in literature. This work gives an introduction to the theoretical development of a novel failure a criterion for TSSA and SG under varying stress state conditions. The main output of this work is a four-dimensional Generalized Triaxial Model (GTM) that accounts for a generic stress state by a governing equation expressed as a function of the three-dimensional stress tensor. Both deviatoric and hydrostatic energetic components are taken into consideration by means of a non-linear function of the two contributions. The effects of the model parameters are investigated by a parametrical study. The proposed model is then analytically compared to existing failure criteria. It is shown that many of the existing models available in the literature can be seen as particular cases of the proposed model. Although the GTM was theoretically developed specifically for SG and TSSA, the model can be generically used as failure criterion for many isotropic materials.