Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

Impact Mechanics and High-Energy Absorbing Materials: Review

“…For example, the viscoplasticity theories are developed to account for hydrostatic stress in the nonlinear deformation response by applying variation of the Drucker-Prager yield criterion through modifying the definitions of the effective stress and effective inelastic strain (Li and Pan, 1990;Chang and Pan, 1997;Goldberg et al, 2005). Using the above-mentioned modification, Goldberg et al (2005) develop the nonlinear constitutive model to account for the strain rate dependence and nonlinearity of the matrix and then implement it into a micromechanics model to obtain the effective composite deformation response under different loading rates. Goldberg et al (2008) revise the analytical model in Goldberg et al (2005) to account for the nonlinear unloading behavior, simultaneously including the effects of hydrostatic stresses on the nonlinear deformation.…”

“…Daniel et al (1995) study the strain rate dependence and nonlinearity of carbon/epoxy composites and conclude that the strain rate-dependence and nonlinearity is primarily driven by the epoxy matrix. The constitutive equations of metals based on plasticity and viscoplasticity are often adapted to model the nonlinear and strain rate-dependent deformation of polymer (Bordonaro, 1995;Goldberg et al, 2005). For example, the viscoplasticity theories are developed to account for hydrostatic stress in the nonlinear deformation response by applying variation of the Drucker-Prager yield criterion through modifying the definitions of the effective stress and effective inelastic strain (Li and Pan, 1990;Chang and Pan, 1997;Goldberg et al, 2005).…”

“…Using the above-mentioned modification, Goldberg et al (2005) develop the nonlinear constitutive model to account for the strain rate dependence and nonlinearity of the matrix and then implement it into a micromechanics model to obtain the effective composite deformation response under different loading rates. Goldberg et al (2008) revise the analytical model in Goldberg et al (2005) to account for the nonlinear unloading behavior, simultaneously including the effects of hydrostatic stresses on the nonlinear deformation. Gilat et al (2005) use small dog-bone-shaped samples for tensile tests and short hollow cylinders for shear tests to obtain the stress-strain curves of epoxy resins at both low and high strain rates.…”

“…The constitutive equations of metals based on plasticity and viscoplasticity are often adapted to model the nonlinear and strain rate-dependent deformation of polymer (Bordonaro, 1995;Goldberg et al, 2005). For example, the viscoplasticity theories are developed to account for hydrostatic stress in the nonlinear deformation response by applying variation of the Drucker-Prager yield criterion through modifying the definitions of the effective stress and effective inelastic strain (Li and Pan, 1990;Chang and Pan, 1997;Goldberg et al, 2005). Using the above-mentioned modification, Goldberg et al (2005) develop the nonlinear constitutive model to account for the strain rate dependence and nonlinearity of the matrix and then implement it into a micromechanics model to obtain the effective composite deformation response under different loading rates.…”

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites

“…20) to create effective unidirectional lamina stiffness matrices for the composite laminates employed to represent each subcell. This model is a micromechanics model developed for use in calculating effective composite properties (Ref.…”