A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Abstract

A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach.The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure.

A micro-mechanical model of reinforced polymer failure with length scale effects and predictive capabilities. Validation on carbon fiber reinforced high-crosslinked RTM6 epoxy resin

“…The mechanical behavior of the high-crosslinked RTM6 epoxy was studied experimentally in [10] with a set of mechanical tests at various levels of triaxiality (such as shear, uniaxial tension, uniaxial compression) as well as of strain rates. Rate-dependent behavior of this epoxy resin can be modeled either by a viscoelastic-viscoplastic model [11], by a viscoplastic-damage model [10] or by a viscoelastic-viscoplasticnonlocal damage model [12]. This epoxy resin can be used as the matrix of a unidirectional composite of carbon fibers and experimental testing of cubic samples made of this composite was performed under uniaxial compression at various strain rates [8].…”

“…This epoxy resin can be used as the matrix of a unidirectional composite of carbon fibers and experimental testing of cubic samples made of this composite was performed under uniaxial compression at various strain rates [8]. The manufacturing of the tested cubic samples was made through a resin transfer molding (RTM) process in order to perfectly replicate the curing conditions of the bulk matrix (high-crosslinked RTM6 epoxy resin) which was considered in [10,12]. As a result, the constitutive model developed for the RTM6 epoxy resin in [10,12] could have been used to represent the matrix behavior under the assumption that the responses of the RTM6 epoxy as a bulk material and as a composite material phase are identical.…”

“…The manufacturing of the tested cubic samples was made through a resin transfer molding (RTM) process in order to perfectly replicate the curing conditions of the bulk matrix (high-crosslinked RTM6 epoxy resin) which was considered in [10,12]. As a result, the constitutive model developed for the RTM6 epoxy resin in [10,12] could have been used to represent the matrix behavior under the assumption that the responses of the RTM6 epoxy as a bulk material and as a composite material phase are identical. However, using the constitutive model developed and identified by [10] within a composite material leads to FE predictions underestimating the experimental values of the peak stress [8].…”

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

“…Fourth order tensors are denoted by blackboard bold symbols other than R, e.g., C and I. Components of tensors of order M are with respect to the Euclidean tensorial basis e (1) ⊗ e (2) ⊗ · · · ⊗ e (M) , e.g., A ij , B ij for second order tensors A, B and C ijkl ,C ijkl for C, C . The following contractions are defined:…”

“…They are characterized by stored energy density functions W = W(F). The first Piola-Kirchhoff stress P(F) = ∂W ∂F (F) (2) and the corresponding fourth-order stiffness tensor…”