Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

Abstract

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden's expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/ polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

Optimization of transparent laminates for specific energy dissipation under low velocity impact using genetic algorithm

“…The thermo-elasto-visco-plastic material model developed by Mulliken and Boyce [20] and modified by Varghese and Batra [21] is used for the PMMA and the PC. The DFA4700 and the IM800A are modeled as nearly incompressible viscous rubbery materials with the elastic response represented by the Ogden energy potential and the viscoelastic response by a hereditary type integral e.g., see [30]. Effects of both geometric and material nonlinearities are considered.…”

Numerical simulation for behind armor blunt trauma of human torso under non-penetrating ballistic impact

“…The expandable polyethylene (EPE) buffer layer was added between human torso and BCS to weaken the blunt impact of BCS on human torso, and the effect of the thickness of the buffer layer on BABT was studied. The material models and material parameters of pistol cartridge [26], AlSi 10 Mg [27], TPU [28] and EPE [29] were given in Table 2∼5, respectively.…”

Soft impacts on aerospace structures

“…23 dealing with deviatoric stresses. Nonlinear constitutive models for describing the large deformations can be developed considering the interlayer material to be hyperelastic following some of the well-known models from rubber elasticity (e.g [140][142]…”

“…21. To account for rate effects, the other terms in the Prony series are added[142].In the analysis of bird strikes on windshields, the bird is usually modeled as an inviscid fluid (s ij =0 in Eq. 4).…”