The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites

Abstract

A finite strain micromechanical model is generalized in order to incorporate the effect of evolving damage in the metallic and polymeric phases of unidirectional composites. As a result, it is possible to predict the response of composites with ductile and brittle phases undergoing large coupled inelastic-damage and viscoelastic-damage deformations, respectively. For inelastic composites, both finite strain elastoplastic (time-independent) and viscoplastic (time-dependent) behaviors are considered. The ductile phase exhibits initially a hyperelastic behavior which is followed by an inelastic one, and its analysis is based on the multiplicative split of its deformation gradient into elastic and inelastic parts. The embedded damage mechanisms and their evolutions are based on Gurson’s (which is suitable for the modeling of porous materials) and Lemaitre’s finite strain models. Similarly, the polymeric phase exhibits large viscoelastic deformations in which the damage evolves according to a suitable evolution law that depends on the amount of accumulated deformation. Evolving damage in hyperelastic materials can be analyzed as a special case by neglecting the viscous effects. The micromechanical analysis is based on the homogenization technique for periodic multiphase materials, which establishes the strong form of the Lagrangian equilibrium equations. These equations are implemented together with the interfacial and periodic boundary conditions, in conjunction with the current tangent tensor of the phase. As a result, the instantaneous strain concentration tensor that relates the local deformation gradient of the phase to the externally applied deformation gradient is established. This provides also the instantaneous effective stiffness tangent tensor of the composite as well as its current response. Results are given that exhibit the effect of damage on the initial yield surfaces, response and possible failure of the composite.

Uncertainty Quantification in Damage Modeling of Heterogeneous Materials

“…Previous works have investigated the behavior of composites using rate-independent and ratedependent phenomenological models [23,24,25]. In this study, a viscous damage model is used to describe the evolution of microcrack damage within the fiber and matrix phases of the composite to capture the rate-dependence observed in experiments.…”

Visco-Hyperelastic Model with Damage for Simulating Cyclic Thermoplastic Elastomers Behavior Applied to an Industrial Component

“…Another important mechanical feature exhibited by this type of materials is the damage effect. Two main types of damage theories exist, which are classified in micromechanical and phenomenological damage models, respectively [36]. Although both try to describe the same effect, several differences exist between them: micromechanical models allow micro-mechanisms to be captured explicitly by introducing internal variables such as dislocations, slips, etc., and hence are generally more accurate than phenomenological models.…”