Methods and systems for manufacturing products/parts made of carbon fiber reinforced composite based on numerical simulations

1. A method of numerically simulating manufacturing procedure of a product or part made of carbon fiber reinforced composite (CFRC) comprising:

receiving, in a computer system having finite element analysis (FEA) based application module capable of analyzing CFRC installed thereon, a first FEA mesh model representing a three-dimensional (3-D) geometry of a product or part made of CFRC that includes carbon fibers and binding matrix, a pre-forming fiber orientation of a workpiece and a reference fiber direction at a location on the product or part;

obtaining, with the FEA based application module, a pre-forming two-dimensional (2-D) shape of the workpiece used for manufacturing the product or part by conducting a simulation that numerically expands the first FEA mesh model to a second FEA mesh model based on numerically-calculated structural behaviors that include nonlinear elastic deformations of the carbon fibers coupled with piecewise linear plastic deformations of the binding matrix, wherein the nonlinear elastic deformations are calculated in accordance with a formula based on a local deformation gradient between the first FEA mesh model and the second FEA mesh model;

superimposing, with the FEA based application module, the pre-forming fiber orientation on the second FEA mesh model with the reference fiber direction being preserved; and

determining, with the FEA based application module, relative angles amongst all of the carbon fibers on the product or part by correlating the superimposed pre-forming fiber orientation of the second FEA mesh model to the first FEA mesh model.

2. The method of claim 1 , wherein the second FEA mesh model represents the pre-forming 2-D shape and contains same number of finite elements of the first FEA mesh model in a one-to-one corresponding relationship.

3. The method of claim 2 , wherein said obtaining the pre-forming 2-D shape of the workpiece comprises projecting all of the finite elements of the first FEA model to a flat surface to create an initial stat of the second FEA mesh model; and expanding those deformed finite elements in the initial state to a dimension of corresponding finite elements in the first FEA mesh model such that a force equilibrium condition is met.

4. The method of claim 3 , wherein each finite element of the second FEA mesh model is horizontally expandable on the flat surface.

5. The method of claim 1 , wherein the formula comprises

V

2

=

F

c

-

1

⁢

V

1

L

c

⁢

⁢

and

⁢

⁢

L

c

=





⁢

F

c

-

1

⁢

V

1

⁢





,

where V 1 is a unit vector representing the reference fiber direction, F c is a tensor representing the local deformation gradient from a finite element in the second FEA mesh model to a corresponding finite element in the first FEA mesh model, L c is a magnitude used for calculating V 2 , and V 2 is an unknown unit vector representing fiber direction in the finite element of the second FEA mesh model.

6. The method of claim 1 , wherein each finite element comprises a two-dimensional shell finite element.

7. A system for numerically simulating manufacturing procedure of a product or part made of carbon fiber reinforced composite (CFRC) comprising:

A bus;

a memory for storing computer readable code for a finite element analysis (FEA) based application module capable of analyzing CFRC;

at least one processor coupled to the bus and the memory, said at least one processor executing the computer readable code from the memory to perform a method comprising:

receiving a first FEA mesh model representing a three-dimensional (3-D) geometry of a product or part made of CFRC that includes carbon fibers and binding matrix, a pre-forming fiber orientation of a workpiece and a reference fiber direction at a location on the product or part;

obtaining a pre-forming two-dimensional (2-D) shape of the workpiece used for manufacturing the product or part by conducting a simulation that numerically expands the first FEA mesh model to a second FEA mesh model based on numerically-calculated structural behaviors that include nonlinear elastic deformations of the carbon fibers coupled with piecewise linear plastic deformations of the binding matrix, wherein the nonlinear elastic deformations are calculated in accordance with a formula based on a local deformation gradient between the first FEA mesh model and the second FEA mesh model;

superimposing the pre-forming fiber orientation on the second FEA mesh model with the reference fiber direction being preserved; and

determining relative angles amongst all of the carbon fibers on the product or part by correlating the superimposed pre-forming fiber orientation of the second FEA mesh model to the first FEA mesh model.

8. The system of claim 7 , wherein the second FEA mesh model represents the pre-forming 2-D shape and contains same number of finite elements of the first FEA mesh model in a one-to-one corresponding relationship.

9. The system of claim 8 , wherein said obtaining the pre-forming 2-D shape of the workpiece comprises projecting all of the finite elements of the first FEA model to a flat surface to create an initial state of the second FEA mesh model; and expanding those deformed finite elements in the initial state to a dimension of corresponding finite elements in the first FEA mesh model such that a force equilibrium condition is met.

10. The system of claim 9 , wherein each finite element of the second FEA mesh model is horizontally expandable on the flat surface.

11. The system of claim 7 , wherein the formula comprises

V

2

=

F

c

-

1

⁢

V

1

L

c

⁢

⁢

and

⁢

⁢

L

c

=





⁢

F

c

-

1

⁢

V

1

⁢





,

where V 1 is a unit vector representing the reference fiber direction, F c is a tensor representing the local deformation gradient from a finite element in the second FEA mesh model to a corresponding finite element in the first FEA mesh model, L c is a magnitude used for calculating V 2 , and V 2 is an unknown unit vector representing fiber direction in the finite element of the second FEA mesh model.

12. The system of claim 7 , wherein each finite element comprises a two-dimensional shell finite element.

13. A non-transitory computer readable medium containing instructions which, when executed in one or more processors, perform a method for numerically simulating manufacturing procedure of a product or part made of carbon fiber reinforced composite (CFRC) comprising:

receiving, in a computer system having finite element analysis (FEA) based application module capable of analyzing CFRC installed thereon, a first FEA mesh model representing a three-dimensional (3-D) geometry of a product or part made of CFRC that includes carbon fibers and binding matrix, a pre-forming fiber orientation of a workpiece and a reference fiber direction at a location on the product or part;

obtaining, with the FEA based application module, a pre-forming two-dimensional (2-D) shape of the workpiece used for manufacturing the product or part by conducting a simulation that numerically expands the first FEA mesh model to a second FEA mesh model based on numerically-calculated structural behaviors that include nonlinear elastic deformations of the carbon fibers coupled with piecewise linear plastic deformations of the binding matrix, wherein the nonlinear elastic deformations are calculated in accordance with a formula based on a local deformation gradient between the first FEA mesh model and the second FEA mesh model;

superimposing, with the FEA based application module, the pre-forming fiber orientation on the second FEA mesh model with the reference fiber direction being preserved; and

determining, with the FEA based application module, relative angles amongst all of the carbon fibers on the product or part by correlating the superimposed pre-forming fiber orientation of the second FEA mesh model to the first FEA mesh model.

14. The non-transitory computer readable medium of claim 13 , wherein the second FEA mesh model represents the pre-forming 2-D shape and contains same number of finite elements of the first FEA mesh model in a one-to-one corresponding relationship.

15. The non-transitory computer readable medium of claim 14 , wherein said obtaining the pre-forming 2-D shape of the workpiece comprises projecting all of the finite elements of the first FEA model to a flat surface to create an initial state of the second FEA mesh model; and expanding those deformed finite elements in the initial state to a dimension of corresponding finite elements in the first FEA mesh model such that a force equilibrium condition is met.

16. The non-transitory computer readable medium of claim 15 , wherein each finite element of the second FEA mesh model is horizontally expandable on the flat surface.

17. The non-transitory computer readable medium of claim 13 , wherein the formula comprises

V

2

=

F

c

-

1

⁢

V

1

L

c

⁢

⁢

and

⁢

⁢

L

c

=





⁢

F

c

-

1

⁢

V

1

⁢





,

where V 1 is a unit vector representing the reference fiber direction, F c is a tensor representing the local deformation gradient from a finite element in the second FEA mesh model to a corresponding finite element in the first FEA mesh model, L c is a magnitude used for calculating V 2 , and V 2 is an unknown unit vector representing fiber direction in the finite element of the second FEA mesh model.

18. The non-transitory computer readable medium of claim 13 , wherein each finite element comprises a two-dimensional shell finite element.