A Constitutive Model for Arbitrary Fiber-Reinforced Composite Materials Having Micro-cracks Based on Continuum Damage Mechanics

Melek Usal, Mustafa Reşit Usal, Ayşe Hilal Erçelik

Abstract


A continuum damage mechanics model for composites having micro-cracks consisting of an isotropic matrix reinforced by independent and inextensible two families of arbitrarily fibers is proposed. The composite medium is assumed to be incompressible, having micro-cracks and showing linear elastic behavior. The reaction of the composite material subject to external loads is expressed in stress tensor and strain-energy density release rate. The matrix material made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions and the existence of micro-cracks has been assumed as an isotropic medium. The theory is formulated within the scope of continuum damage mechanics. As a result of thermodynamic constraints, it has been determined that, the stress potential function is dependent on the deformation tensor, the damage tensor; the fiber fields vectors and the temperature. It is expressly understood from obtained constitutive relations that the stress and the strain energy density release rate are derived from the stress potential. To determine arguments of the stress potential, findings relating to the theory of invariants have been used as a method because of that isotropy constraint is imposed on the material. Finally the constitutive equations of stress and strain-energy density release rate have been written in terms of material coordinate description.


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