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.
Highlights
In [1], a review of finite strain micromechanical analyses of multiphase materials have been presented.It was shown that it is possible to predict the microscopic and macroscopic response of composites undergoing large deformations in which the constituents in these composites can be modeled as hyperelastic, thermoelastic, viscoelastic (including quasilinear viscoelasticity (QLV) which is suitable for the modeling of biological tissues), thermoviscoelastic, rate-dependent thermoinelastic and rate-independent thermoinelastic materials
The extension of Lemaitre elastoplastic model [9], [10] that includes an evolving damage to large deformations was presented by de Souza Neto et al [11]
In the present section we briefly present the constitutive behavior of finite strain viscoelastic materials that exhibit evolving damage
Summary
In [1], a review of finite strain micromechanical analyses of multiphase materials have been presented. Fidelity Generalized Method of Cells (HFGMC), provide the instantaneous mechanical, thermal and inelastic concentration tensors that relate the local induced strain in the phase to the current externally applied strains and temperature These micromechanical analyses yield the macroscopic constitutive equations of the multiphase composite in terms of its instantaneous stiffness (tangent) and thermal stress tensors. The consistency parameter which appears in the flow rule is not one of the unknowns but it is prescribed in advance in terms of the other unknown field variables [12] (cf Perzyna’s [18]) Both the finite strain Gurson’s and Lemaitre’s models are presently extended and applied to investigate the behavior of composites that consist of viscoplastic coupled with evolving damage constituents. The paper is concluded by some suggestions for further generalizations in a future research
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