1. Modeling Composite Material Impact with Abaqus/Explicit
Lecture 13

2. Overview Introduction Composite Damage Models in Abaqus/Explicit
Unidirectional Fiber
Example – Composite Plate Impact
Woven Fabric
Example – Corrugated Beam Crushing
Modeling Techniques

3. Introduction

4. Introduction
Impact resistance of composite materials is of primary importance in many industries
Automotive
Road debris
Vehicle crashworthiness
Aerospace
Aircraft crashworthiness
Bird strike
Defense
Ballistics
With the increasing use of composite materials in automobiles and aircraft, the ability of these structures to withstand impact is an important design consideration. Impact can be encountered both during automotive or aircraft crash, or as a result of debris from roads or runways. The top figure here depicts a head on collision test of two automobiles. The bottom figure shows the damage that can occur to a composite aircraft radome after a bird strike event.

5. Composite Damage Models in Abaqus/Explicit

6. Composite Damage Models in Abaqus/Explicit
Abaqus/Explicit provides additional damage models for fiber-reinforced composite materials.
The built-in damage model discussed in Lecture 9 can only be used with elements that have a plane stress formulation.
Plane stress, membrane, and shell elements.
User-defined material subroutines (VUMATs) are available to extend this capability to elements with other stress states (3D, for example).
Composite damage VUMATs
Two routines are available:
Unidirectional fiber VUMAT (extension of built-in capability to include 3D)
Available via SIMULIA Answer 3123
Woven fabric VUMAT
Available as a built-in user subroutine
Both of these routines require user input to specify how the composite materials will behave under load.

7. Unidirectional Fiber VUMAT

8. Unidirectional Fiber VUMAT
The primary assumption is that elastic stress/strain relations are given by orthotropic damaged elasticity
Four damage variables are introduced
Two associated with fiber tension and compression
Two associated with matrix tension and compression
C_{ij} are damaged elastic constants.
Damaged elasticity refers to a gradual decrease in the material stiffness as damage accumulates. Once a material is fully damaged, the stiffness has decreased to zero. In this VUMAT, damage can occur in either tension or compression, and is calculated separately for the fiber and matrix components.

9. Unidirectional Fiber VUMAT
These four damage variables are used to define global fiber and matrix damage variables.
The damaged elastic constants, Cij, are defined in terms of the undamaged elastic constants and the damage variables.
The factors smt and smc control the loss of shear stiffness by matrix tensile and compressive failure, respectively.
The tension and compression components of damage are used to define a global damage parameter for the fiber and matrix as seen here. The global damage variables are then used to reduce the value of the elastic constants from their undamaged state (denoted by a superscript 0).

10. Unidirectional Fiber VUMAT
The undamaged elastic constants are functions of the undamaged Young’s moduli and Poisson’s ratios
The undamaged elastic constants are calculated from user defined material properties at the start of the simulation.

11. Unidirectional Fiber VUMAT
19 user material constants must be specified for this subroutine
Young’s moduli in the three primary axes
E011, E022, E033
Poisson’s ratios
n12, n13, n23
Shear moduli
G012, G013, G023
Shear strengths
S12, S13, S23
Tensile and compressive failure stress in each primary direction
X1t, X1c, X2t, X2c, X3t, X3c
Damping (optional) b
19 material constants are required for use with the unidirectional fiber VUMAT. While this seems like a significant amount of information, we can see from looking at the inputs that these values are fairly straightforward. The elastic and shear moduli, as well as the values of Poisson’s ratio are required. Information is then needed to tell the VUMAT how strong the material is in shear, as well as in tension and compression in each primary direction. An optional damping parameter can be input as well to include material damping effects is they are significant to the problem under consideration.

12. Unidirectional Fiber VUMAT
Data input
*MATERIAL, NAME=matName
*DENSITY r
*USER MATERIAL, CONSTANTS=27
*DEPVAR, DELETE=5 17
Why did the previous slide indicate 19 constants are required?
The input data for the unidirectional fiber VUMAT is shown here. Note that the number of material constants listed is 27, not 19. This is simply due to the fact that each data line must have eight values, however for some of these data lines (2 and 3) less than eight are used. Therefore 27 must be specified, with some of these values being “0” to fill out the inputs. The VUMAT also requires the user to tell it how many solution dependent variables are required. This VUMAT requires 17, and uses variable number 5 to control element deletion.

13. Unidirectional Fiber VUMAT
Output
In addition to the standard output variables for stress-displacement elements, the following output variables have a special meaning for this VUMAT:
SDV1 Tensile damage along direction 1 (fiber direction)
SDV2 Compressive damage along direction 1
SDV3 Tensile damage along direction 2 (transverse direction)
SDV4 Compressive damage along direction 2 (transverse direction)
SDV5 Material point status; 1 if active, 0 if failed
SDV6-11 Components of viscous stresses if beta-damping is active
SDV12-17 Components of elastic strain tensor
By including “SDV” as an output variable in the Abaqus output requests, solution dependent outputs can be included as shown above. These variables allow you to determine the amount of tensile and compressive damage has occurred in the fiber and matrix at any point in the simulation.

14. Unidirectional Fiber VUMAT
Example: Composite laminate plate ballistic impact
A view of the undamaged plate geometry. The plate has been fixed in all degrees of freedom around the edges. The ball velocity has been specified to impact the plate normal to the top surface.

15. Unidirectional Fiber VUMAT
Results:
A view of the underside of the plate after penetration. The significant amount of damage done to the plate material is clearly evident. Many areas of the plate lower surface have been damaged even though they do not directly interact with the projectile. This occurs due to the extreme stress waves propagating through the plate material.

16. Unidirectional Fiber VUMAT
Using cohesive elements for delamination prediction
While modeling at the ply level is an advantage when a detailed knowledge of failure behavior is desired, this is often not possible on real-life large structures. The model size would soon become unmanageable. Therefore it is typical to model a laminate using a coarse mesh and global material properties rather than individual lamina properties. In the example shown here, a 20 layer laminate plate was modeled using only 6 elements through the thickness. However, to include delamination in the model, cohesive elements were used in areas where significant delamination was expected. This is an economical way to minimize model size and yet include additional detailed physical failure mechanisms.

17. Woven Fabric VUMAT

18. Woven Fabric VUMAT
A schematic of the assumed woven material is shown to the right.
The fiber directions are assumed to be, and to remain, orthogonal (no wrinkling due to shear).
The constitutive stress-strain relations are formulated in a local Cartesian coordinate system with base vectors aligned with the fiber directions.
The fabric reinforced ply is modeled as a homogeneous orthotropic elastic material with the potential to sustain progressive stiffness degradation due to fiber/matrix cracking, and plastic deformation under shear loading. 1 2

19. Woven Fabric VUMAT
It is assumed that the elastic stress-strain relations are given by orthotropic damaged elasticity.
Three global damage variables are used and are associated with fiber fracture along the 1- and 2-directions and matrix micro-cracking due to shear deformation.
The model differentiates between tensile and compressive fiber failure modes by activating the corresponding damage variable depending on the stress state in the fiber directions
The woven fabric VUMAT again uses damaged elasticity to account for degradation of material stiffness.

20. Woven Fabric VUMAT Fiber response
The material response along the fiber directions is characterized with damaged elasticity. It is assumed that the fiber damage variables are a function of the corresponding effective stress
The criterion for initiation of fiber failure is assumed to take the form
Shear response
The shear response is dominated by the non-linear behavior of the matrix, which includes both plasticity and stiffness degradation due to matrix microcracking
The criterion for initiation of shear failure is assumed to take the form

21. Woven Fabric VUMAT Element deletion
The VUMAT provides an option to delete elements when any one tensile/compressive damage variable along the fiber directions reaches a maximum specified value, or when the plastic strain due to shear deformation reaches a maximum specified value.
Calibration
The elastic constants and the fiber tension/compression strengths are easily measured from standard coupon tests in uniaxial tension/compression loading of 0/90 laminates.
The calibration of damage evolution in the fiber failure modes is based on the fracture energy per unit area of the material, which can be measured experimentally.
The shear response is usually calibrated with a cyclic tensile test on a ±45 laminate, where the strains along the fiber directions can be neglected.
As in most simulations of complex material behavior, it is important to calibrate the model using available data. This is often obtained from coupon tests of the constituent materials.

22. Woven Fabric VUMAT E1+/-, E2+/- G12 S X1+/-, X2+/-
26 user material constants must be specified for this subroutine
Young’s moduli in fiber 1- and 2-directions
E1+/-, E2+/-
Poisson’s ratio
n12+, n12-
Shear modulus
G12
Shear stress at the onset of shear damage S
Tensile and compressive strength along fiber directions
X1+/-, X2+/-
Shear equation parameters
a12, d12max
24 user defined material constants are required for use with the woven fabric VUMAT. As we saw before, while this is a non-trivial amount of data, the inputs are straightforward. The elastic modulus in the two fiber directions for both tension and compression are required. In addition, Poisson’s ratios, the shear moduli and strength, as well as tensile and compressive failure stresses are required. Two additional inputs are required for use in the shear representation, however default values are provided for these inputs.

23. lDelFlag, dmax, eplmax, emax, emin
Woven Fabric VUMAT
Energy per unit area for tensile and compressive fracture along fiber directions
Gf1+/-, Gf2+/-
Shear plasticity coefficients
sy0, C, p
Controls for material point failure
lDelFlag, dmax, eplmax, emax, emin
24 user defined material constants are required for use with the woven fabric VUMAT. As we saw before, while this is a non-trivial amount of data, the inputs are straightforward. The elastic modulus in the two fiber directions for both tension and compression are required. In addition, Poisson’s ratios, the shear moduli and strength, as well as tensile and compressive failure stresses are required. Two additional inputs are required for use in the shear representation, however default values are provided for these inputs.

24. Woven Fabric VUMAT Data input *MATERIAL, NAME=ABQ_PLY_FABRIC_matName
To activate the model for fabric reinforced composites the material name must start with the string ABQ_PLY_FABRIC
*MATERIAL, NAME=ABQ_PLY_FABRIC_matName
*DENSITY r
*USER MATERIAL, CONSTRANT=40
** Line 1:
** Line 2:
** Line 3:
** Line 4:
** Line 5:
lMpFail
*DEPVAR, DELETE=16 16

25. Woven Fabric VUMAT Output
In addition to the standard output variables for stress-displacement elements, the following output variables have a special meaning for this VUMAT:
SDV1 Tensile damage along fiber direction 1
SDV2 Compressive damage along fiber direction 1
SDV3 Tensile damage along fiber direction 2
SDV4 Compressive damage along fiber direction 2
SDV5 Shear damage
SDV6 Tensile damage threshold along fiber direction 1
SDV7 Compressive damage threshold along fiber direction 1
SDV8 Tensile damage threshold along fiber direction 2
SDV9 Compressive damage threshold along fiber direction 2
SDV10 Shear damage threshold

26. Woven Fabric VUMAT Output (cont’d) SDV11 Equivalent plastic strain
SDV12 Elastic strain component 11
SDV13 Elastic strain component 22
SDV14 Not used
SDV15 Elastic strain component 12
SDV16 Material point status: 1 if active, 0 if failed

27. Woven Fabric VUMAT Example: Composite woven fabric beam crush
This is an example of a sine-wave beam fabricated from a hybrid woven fabric/Kevlar composite. This type of structure is typical in areas where energy absorption for crashworthiness is desired. This type of beam would typically be found in the subfloor of a helicopter cockpit to absorb energy in the event of hard landing. Here a semi-circular impactor, defined as a rigid body, is dropped onto the top of the beam. The gold stripe is a ply drop-off location to initiate the desired crushing response.

28. Woven Fabric VUMAT Results:
The results of the crushing analysis are shown here. The extreme amount of damage is clearly evident as the solution progresses. This is a desired result. The damage to the beam means that this energy will not be transferred to the pilot’s spine.

29. Modeling Techniques

30. Modeling Techniques Stable time increment
For Abaqus/Explicit, the concept of the stable time increment is important to understand
When modeling composites at the laminate level, very small element dimensions can be encountered
This can lead to a very small stable time increment, requiring a large number of increments to complete an analysis
For a typical composite where Le=0.2 mm, r =1.5e-9, E=65 GPa, and n =0.3, Dt is on the order of 1e-10 seconds.
To simulate 1 millisecond will require 10 million increments!
Some ideas for dealing with this follow.

31. Modeling Techniques Stable time increment
Use double precision if the number of increments will exceed 300,000
To attempt a more time economical solution, the following may be helpful
Mass scaling can be used to speed up the simulation for the purposes of checking model setup
Dynamic response will be affected
Group layers of common material orientation together and model as one layer
Use continuum macroscopic (i.e., anisotropic global) properties to model the composite instead of using a mixed modeling technique

32. Modeling Techniques Interior surfaces for erosion
If erosion will be considered in an impact analysis, care must be taken when defining contact
Interior mesh surfaces must be included in the contact definitions
The inclusion of interior faces is not currently supported in Abaqus/CAE, and requires a manual edit to the input file. For example:
*SURFACE, NAME=interior_elems, TYPE=ELEMENT all_elems, interior
This creates a surface named interior_elems consisting of the interior faces of the element set all_elems, which can now be used in the contact domain