Author Contributions
Conceptualization, M.W.; Data curation, M.W.; Formal analysis, M.W.; Funding acquisition, X.H.; Investigation, M.W.; Methodology, M.W.; Project administration, M.W.; Resources, M.W.; Software, M.W.; Supervision, M.W.; Validation, M.W.; Visualization, X.H.; Writing—original draft, M.W.; Writing—review & editing, M.W. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Finite element discretization for the macroscale model.
Figure 1.
Finite element discretization for the macroscale model.
Figure 2.
Local orientation for the first four plies.
Figure 2.
Local orientation for the first four plies.
Figure 3.
Fiber diamond distribution microscale RVE considering interface. (a) geometrical model; (b) finite element model.
Figure 3.
Fiber diamond distribution microscale RVE considering interface. (a) geometrical model; (b) finite element model.
Figure 4.
Fiber random distribution microscale RVE considering interface.
Figure 4.
Fiber random distribution microscale RVE considering interface.
Figure 5.
Flowchart for deriving cluster distribution patterns.
Figure 5.
Flowchart for deriving cluster distribution patterns.
Figure 6.
Schematic description of the FFNN.
Figure 6.
Schematic description of the FFNN.
Figure 7.
Analysis flow of the modified MMF-based multiscale method.
Figure 7.
Analysis flow of the modified MMF-based multiscale method.
Figure 8.
Stress distribution patterns for the fiber diamond distribution model. (a) longitudinal tensile loading; (b) transverse tensile loading; (c) longitudinal shear loading; (d) transverse shear loading.
Figure 8.
Stress distribution patterns for the fiber diamond distribution model. (a) longitudinal tensile loading; (b) transverse tensile loading; (c) longitudinal shear loading; (d) transverse shear loading.
Figure 9.
Stress distribution patterns for the model under unit stress loading along transverse direction.
Figure 9.
Stress distribution patterns for the model under unit stress loading along transverse direction.
Figure 10.
Stress distribution patterns for the model under unit stress loading along transverse direction in Ref. [
37].
Figure 10.
Stress distribution patterns for the model under unit stress loading along transverse direction in Ref. [
37].
Figure 11.
Cluster distribution pattern for the fiber diamond distribution model. (a) fiber cluster; (b) matrix cluster; (c) interface cluster.
Figure 11.
Cluster distribution pattern for the fiber diamond distribution model. (a) fiber cluster; (b) matrix cluster; (c) interface cluster.
Figure 12.
Illustration for one failure pattern of matrix and interface.
Figure 12.
Illustration for one failure pattern of matrix and interface.
Figure 13.
Linear regression of the elastic modulus between those from the FFNN and FEM.
Figure 13.
Linear regression of the elastic modulus between those from the FFNN and FEM.
Figure 14.
Stress distribution patterns for the fiber random distribution model. (a) longitudinal tensile loading; (b) transverse tensile loading; (c) longitudinal shear loading; (d) transverse shear loading.
Figure 14.
Stress distribution patterns for the fiber random distribution model. (a) longitudinal tensile loading; (b) transverse tensile loading; (c) longitudinal shear loading; (d) transverse shear loading.
Figure 15.
Cluster distribution pattern for the fiber diamond distribution model. (a) interface cluster; (b) matrix cluster; (c) fiber cluster.
Figure 15.
Cluster distribution pattern for the fiber diamond distribution model. (a) interface cluster; (b) matrix cluster; (c) fiber cluster.
Figure 16.
Predicted compressive responses of the open-hole laminates.
Figure 16.
Predicted compressive responses of the open-hole laminates.
Figure 17.
The initiations regions for fiber–matrix interface debonding.
Figure 17.
The initiations regions for fiber–matrix interface debonding.
Figure 18.
Intralaminar shear stress distribution pattern.
Figure 18.
Intralaminar shear stress distribution pattern.
Figure 19.
Failure indices and traction force states for the interface. (a) failure indices; (b) normal traction; (c) longitudinal shear traction; (d) tangential shear traction.
Figure 19.
Failure indices and traction force states for the interface. (a) failure indices; (b) normal traction; (c) longitudinal shear traction; (d) tangential shear traction.
Figure 20.
Damage propagation in the interface of fiber diamond distribution model.
Figure 20.
Damage propagation in the interface of fiber diamond distribution model.
Figure 21.
The initiations regions for matrix damage.
Figure 21.
The initiations regions for matrix damage.
Figure 22.
Failure indices and stress states in the matrix for fiber diamond distribution model. (a) failure indices; (b) equivalent stress; (c) first stress invariant.
Figure 22.
Failure indices and stress states in the matrix for fiber diamond distribution model. (a) failure indices; (b) equivalent stress; (c) first stress invariant.
Figure 23.
Matrix damage propagation in the matrix for fiber diamond distribution model. (a) at displacement loading 0.66mm; (b) at displacement loading 0.7 mm.
Figure 23.
Matrix damage propagation in the matrix for fiber diamond distribution model. (a) at displacement loading 0.66mm; (b) at displacement loading 0.7 mm.
Figure 24.
The initiations regions for fiber breakage.
Figure 24.
The initiations regions for fiber breakage.
Figure 25.
Failure indices and stress states in the fiber for fiber diamond distribution model. (a) failure indices; (b) compressive stress in the fiber direction.
Figure 25.
Failure indices and stress states in the fiber for fiber diamond distribution model. (a) failure indices; (b) compressive stress in the fiber direction.
Figure 26.
Final failure areas of fiber and matrix. (
a) fiber failure; (
b) matrix failure; (
c) experimental result, reprinted with permission from [
16], 2020, © Taylor & Francis.
Figure 26.
Final failure areas of fiber and matrix. (
a) fiber failure; (
b) matrix failure; (
c) experimental result, reprinted with permission from [
16], 2020, © Taylor & Francis.
Figure 27.
The initiations regions for interface debonding based on FFNN method.
Figure 27.
The initiations regions for interface debonding based on FFNN method.
Figure 28.
The initiations regions for matrix damage based on FFNN method.
Figure 28.
The initiations regions for matrix damage based on FFNN method.
Figure 29.
The initiations regions for fiber breakage based on FFNN method.
Figure 29.
The initiations regions for fiber breakage based on FFNN method.
Figure 30.
Predicted compressive responses considering different fiber arrangement patterns.
Figure 30.
Predicted compressive responses considering different fiber arrangement patterns.
Figure 31.
Failure indices and traction force states for the interface. (a) failure indices; (b) normal traction; (c) longitudinal shear traction.
Figure 31.
Failure indices and traction force states for the interface. (a) failure indices; (b) normal traction; (c) longitudinal shear traction.
Figure 32.
Interface debonding in the 45° ply. Reprinted with permission from [
16], 2020, © Taylor & Francis.
Figure 32.
Interface debonding in the 45° ply. Reprinted with permission from [
16], 2020, © Taylor & Francis.
Figure 33.
Damage propagation in the interface of fiber random distribution model.
Figure 33.
Damage propagation in the interface of fiber random distribution model.
Figure 34.
Failure indices and stress states in the matrix of fiber random distribution model. (a) failure indices; (b) equivalent stress; (c) first stress invariant.
Figure 34.
Failure indices and stress states in the matrix of fiber random distribution model. (a) failure indices; (b) equivalent stress; (c) first stress invariant.
Figure 35.
Matrix damage propagation in the matrix of fiber random distribution model. (a) at displacement loading 0.4 mm; (b) at displacement loading 0.54 mm.
Figure 35.
Matrix damage propagation in the matrix of fiber random distribution model. (a) at displacement loading 0.4 mm; (b) at displacement loading 0.54 mm.
Figure 36.
Failure indices and stress states for the fiber. (a) failure indices; (b) compressive stress in the fiber direction.
Figure 36.
Failure indices and stress states for the fiber. (a) failure indices; (b) compressive stress in the fiber direction.
Table 1.
Elastic parameters for the composites and constituents [
14,
16].
Table 1.
Elastic parameters for the composites and constituents [
14,
16].
Material Parameters | E11 (Gpa) | E22 = E33 (GPa) | G12 = G13 (GPa) | G23 (GPa) | v12 = v13 | v23 | Vf |
---|
Ply | 136 | 10 | 4.7 | 3.2 | 0.35 | 0.56 | 0.56 |
Fiber | 240 | 42 | 23 | 12 | 0.33 | 0.71 | |
Interface | 15.9 | 15.9 | 5.76 | 5.76 | 0.38 | 0.38 | |
Matrix | 3 | 3 | 1.087 | 1.087 | 0.38 | 0.38 | |
Table 2.
Strength parameters for the constituents [
14,
16].
Table 2.
Strength parameters for the constituents [
14,
16].
Strength Parameters (MPa) | Tf | Cf | Tm | Cm | N | S |
---|
Values | 3710 | 3430 | 155 | 207 | 18 | 11.4 |
Table 3.
Performance of the trained FFNN for fiber diamond distribution model.
Table 3.
Performance of the trained FFNN for fiber diamond distribution model.
Samples | RMSE (MPa) | R2 |
---|
Training | 131.9 | 0.999 |
Validation | 623.9 | 0.977 |
Testing | 808.5 | 0.964 |
Table 4.
Performance of the trained FFNN for fiber random distribution model.
Table 4.
Performance of the trained FFNN for fiber random distribution model.
Samples | RMSE (MPa) | R2 |
---|
Training | 304.7 | 0.996 |
Validation | 979.1 | 0.967 |
Testing | 718.8 | 0.978 |
Table 5.
The comparison of the predicted strength values.
Table 5.
The comparison of the predicted strength values.
Model | Average Experimental Value | In Ref. [16] | In Ref. [14] | With Sudden Degradation Model | With FFNN Model |
---|
Strength (KN) | 18.6 | 17.1 | 18.4 | 18.0 | 18.5 |
Difference percentage (%) | — | −8.065 | −1.075 | −3.226 | −0.538 |
Table 6.
Critical displacement values for the initiation of different failure modes.
Table 6.
Critical displacement values for the initiation of different failure modes.
Models | Interface Debonding | Matrix Damage | Fiber Breakage |
---|
Fiber diamond distribution | 0.06 mm | 0.64 mm | 0.62 mm |
Fiber random distribution | 0.04 mm | 0.34 mm | 0.58 mm |