Modelling of Flexible Adhesives in Simple Mechanical States with the Use of the Darijani–Naghdabadi Strain Tensors and Kirchhoff–de Saint-Venant Elastic Potential

Abstract

Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters α,β in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents α,β are discussed regarding its bijectivity in a limited range of variation of principal stretches.