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The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites
Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
Received: 14 October 2009; in revised form: 15 November 2009 / Accepted: 17 November 2009 / Published: 18 November 2009
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 compostes. 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.
Keywords: large deformations; ﬁnite inelasticity; ﬁnite viscoelasticity; evolving damage; micromechanical analysis; ﬁnite strain high ﬁdelity generalized method of cells
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MDPI and ACS Style
Aboudi, J. The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites. Materials 2009, 2, 1858-1894.
Aboudi J. The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites. Materials. 2009; 2(4):1858-1894.
Aboudi, Jacob. 2009. "The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites." Materials 2, no. 4: 1858-1894.