Overall damage and elastoplastic deformation in fibrous metal matrix composites.

*(English)*Zbl 0816.73040A phenomenological constitutive model for the analysis of overall damage and plastic deformation is formulated for a composite system consisting of elastic fibers and an elastoplastic matrix. The formulation is based on the assumption of small strains and an associated flow rule for the matrix material. In this formulation all types of damage experienced by the composite are characterized by a fourth rank damage tensor \(M_{ijkl}\) which transforms the Cauchy stress in the damaged configuration into the stress in the (fictious) deformed configuration without damage.

From the assumptions of elastic fibers and (isotropic) yield function and associated flow rule for the elastoplastic matrix, closed form expressions are derived for the elastoplastic stiffness tensor of the composite system which involve the damage tensor \(M_{ijkl}\). Some interesting features of the analysis include: an anisotropic yield function for the composite based on using a von Mises type yield criterion for the undamaged matrix material, a nonassociated flow rule for the composite, and a generalized kinematic hardening rule resulting from the assumption of a Ziegler-Prager rule for the undamaged matrix.

From the assumptions of elastic fibers and (isotropic) yield function and associated flow rule for the elastoplastic matrix, closed form expressions are derived for the elastoplastic stiffness tensor of the composite system which involve the damage tensor \(M_{ijkl}\). Some interesting features of the analysis include: an anisotropic yield function for the composite based on using a von Mises type yield criterion for the undamaged matrix material, a nonassociated flow rule for the composite, and a generalized kinematic hardening rule resulting from the assumption of a Ziegler-Prager rule for the undamaged matrix.

Reviewer: W.-L.Yin (Atlanta)

##### MSC:

74E30 | Composite and mixture properties |

74R99 | Fracture and damage |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74A60 | Micromechanical theories |

74M25 | Micromechanics of solids |