About Damage and Failure for Fiber-Reinforced Composites Using Multiscale Modeling

Compared to the composite-level damage model (see About Damage and Failure for Fiber-Reinforced Composites), the multiscale approach takes into account the constituent material behavior and the microstructure of the composite (see Mean-Field Homogenization). The multiscale approach has an advantage over the traditional composite-level approach because it can:

• determine composite properties for any given volume fraction and other geometry specifications before the composite is even manufactured, which facilitates the design process of new composite materials;

• capture damage and failure at a more fundamental scale (the constituent level);

• allow you to specify simpler constitutive models for the constituents;

• allow you to specify simpler and more fundamental damage and failure criteria; and

• capture progressive damage of the composite with simpler evolution laws at the constituent level.

Unidirectional fiber-reinforced composite materials exhibit elastic-brittle behavior; damage in these materials is initiated without significant plastic deformation. Consequently, plasticity is often neglected when modeling the behavior of these materials. You must specify material properties in a user-defined local coordinate system with the local 1-direction aligned with the fiber direction. In addition, you must specify isotropic or transversely isotropic elasticity in the constituent materials. You can also specify isotropic or transversely isotropic thermal expansion in the constituent materials.

The example below shows how to define a multiscale material for a unidirectional fiber-reinforced composite (continuous fiber):

Input file template

MATERIAL, NAME=MatMatrix
…
MATERIAL, NAME=MatFiber
…
MATERIAL, NAME=COMPOSITE
MEAN FIELD HOMOGENIZATION, FORMULATION=MT
CONSTITUENT, TYPE=MATRIX, MATERIAL=MatMatrix, NAME=MATRIX_MAT1
CONSTITUENT, TYPE=INCLUSION, MATERIAL=MatFiber, NAME=FIBER_MAT2, SHAPE=CYLINDER, DIRECTION=FIXED
$v_f^{}$, , 1.0,0.0,0.0

Abaqus supports woven composite materials that are made of orthogonal yarns (weave and weft) and matrix material. The yarns are unidirectional fiber-reinforced composites and are considered to have a continuous cylindrical inclusion with an elliptical cross-section shape. You must specify a multilevel multiscale material model to specify damage and failure properties in the fiber and matrix constituents of the yarn. The yarn directions must align with the local 1- and 2-directions of the composite material.

The example below shows how to define a multilevel multiscale material for a woven composite:

Input file template

MATERIAL, NAME=MatMatrix
…
MATERIAL, NAME=YarnMatrix
…
MATERIAL, NAME=YarnFiber
…
MATERIAL, NAME=Yarn
MEAN FIELD HOMOGENIZATION, FORMULATION=MT
CONSTITUENT, TYPE=MATRIX, MATERIAL=YarnMatrix, NAME=MATRIX_MAT1
CONSTITUENT, TYPE=INCLUSION, MATERIAL=YarnFiber, NAME=FIBER_MAT2, SHAPE=CYLINDER, DIRECTION=FIXED
$v_f^{}$, , 1.0,0.0,0.0

MATERIAL, NAME=COMPOSITE
MEAN FIELD HOMOGENIZATION, FORMULATION=MT
CONSTITUENT, TYPE=MATRIX, MATERIAL=MatMatrix, NAME=MATRIX_MAT1
CONSTITUENT, TYPE=INCLUSION, MATERIAL=Yarn, NAME=FIBER_MAT2, SHAPE=ELLIPTIC CYLINDER, DIRECTION=FIXED
$v_{yarn1}^{}$, $ar$
, 1.0,0.0,0.0
CONSTITUENT, TYPE=INCLUSION, MATERIAL=Yarn, NAME=FIBER_MAT2, SHAPE=ELLIPTIC CYLINDER, DIRECTION=FIXED
$v_{yarn2}^{}$, $ar$
, 0.0,1.0,0.0

You must specify isotropic or transversely isotropic elasticity in the constituent materials. Abaqus/Standard does not support thermal expansion in woven composites when you specify progressive damage.

Abaqus/Standard offers the following damage initiation criteria for constituents inside the unidirectional fiber-reinforced composites and woven composites:

• Constituent-level failure criterion based on the work of Mayes (2001).

• Matrix failure criterion based on the work of Shultz (2013).

These models include initiation criteria for various failure mechanisms commonly observed in fiber-reinforced composites, such as fiber fracture in tension, fiber buckling/kinking under compression, and matrix cracking/crushing under tension/compression, all at the constituent level.

Once a particular damage initiation criterion is satisfied, the material stiffness of the constituent is degraded according to the specified damage evolution law for that criterion. The effective material behavior of the composite can then be determined through homogenization. In the absence of a damage evolution law, the material stiffness is not degraded.

The damage evolution law describes the rate of degradation of the material stiffness once the corresponding initiation criterion is reached. At any given time during the analysis, the stress tensor in the material is given by

where ${\mathbf{C}}_{\mathbf{d}}$ is the damaged elasticity matrix. The evolution of the elasticity matrix arising from damage is discussed in more detail in Damage Evolution for Fiber-Reinforced Composites Using Multiscale Modeling; that section also discusses viscous regularization (Viscous Regularization).