Elastoplastic Analysis of Perforated Metal Sheets using Transformation Field Analysis and Finite Element Method

Várady Filho, Christiano Augusto Ferrário; Cavalcante, Márcio André Araújo

doi:10.1590/1679-78256650

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Latin American Journal of Solids and Structures

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ORIGINAL ARTICLE • Lat. Am. j. solids struct. 18 (06) • 2021 • https://doi.org/10.1590/1679-78256650 copy

Elastoplastic Analysis of Perforated Metal Sheets using Transformation Field Analysis and Finite Element Method

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This investigation analyzes the cost-benefit ratio of the Transformation Field Analysis to compute the elastoplastic behavior of periodically perforated metal sheets. Evaluation of accuracy and computational cost are analyzed by implementing a finite element approach coupled with the Transformation Field Analysis technique for different meshes and finite element orders. Numerical studies are employed to compare Transformation Field Analysis accuracy with standard Finite Element Analysis for elastoplastic analysis of periodically perforated metal sheets. Additionally, experimental data is employed to validate the Transformation Field Analysis results. The Transformation Field Analysis requires calculating the strain concentration and influencing tensors employing the finite element method. The numerical results show the technique's capabilities and favorable scenarios, besides the influence of domain discretization and finite element order.

Keywords:
Transformation Field Analysis; Perforated Metal Sheets; Finite Element Method; High Order Elements; and Computational Performance

Graphical Abstract

	Discretizations
	18x3	30x5	90x15
Elements	54	150	1350
Nodes (Linear Element)	72	180	1440
Nodes (Quadratic Element)	252	660	5580
Nodes (Fifth-Order Element)	1440	3900	34200

Uniaxial Tension
Macroscopic Strain	0.5%	1%	1.5%	2%	2.5%	3%
Q4 18x3	2.50%	4.23%	5.78%	7.17%	8.34%	9.34%
Q4 30x5	1.11%	2.35%	3.26%	4.06%	4.77%	5.40%
Q4 90x15	0.16%	0.40%	0.61%	0.81%	0.98%	1.14%
Q9 18x3	2.57%	4.60%	5.80%	6.86%	7.79%	8.59%
Q9 30x5	1.42%	2.35%	3.10%	3.70%	4.22%	4.68%
Q9 90x15	0.17%	0.34%	0.49%	0.61%	0.73%	0.83%
Q36 18x3	2.58%	4.69%	5.89%	6.90%	7.78%	8.55%
Q36 30x5	1.44%	2.28%	3.02%	3.62%	4.13%	4.58%
Q36 90x15	0.18%	0.34%	0.48%	0.60%	0.72%	0.82%

Pure Shear
Macroscopic Strain	0.5%	1%	1.5%	2%	2.5%	3%
Q4 18x3	1.81%	5.56%	8.69%	11.14%	13.08%	14.66%
Q4 30x5	1.02%	3.98%	5.77%	7.31%	8.52%	9.53%
Q4 90x15	0.15%	0.77%	1.29%	1.70%	2.05%	2.35%
Q9 18x3	1.89%	8.90%	11.58%	13.59%	15.29%	16.60%
Q9 30x5	1.72%	4.96%	6.41%	7.59%	8.55%	9.38%
Q9 90x15	0.19%	0.73%	1.11%	1.40%	1.64%	1.85%
Q36 18x3	2.03%	8.87%	11.15%	12.86%	14.29%	15.59%
Q36 30x5	1.72%	4.84%	6.21%	7.30%	8.20%	8.98%
Q36 90x15	0.19%	0.72%	1.08%	1.37%	1.60%	1.81%

	Coarse Mesh (C)	Intermediate Mesh (I)	Fine Mesh (F)
Number of Nodes	440	1680	3720
Linear Elements	400	1600	3600
Quadratic Elements	100	400	900
5th Order Elements	16	64	144

Macroscopic Strain (%)	FEA			TFA			Difference
Macroscopic Strain (%)	Q4	Q9	Q36	Q4	Q9	Q36	Q4	Q9	Q36
0.4	3.64%	3.57%	3.56%	3.70%	3.77%	4.59%	0.06%	0.19%	1.03%
0.7	7.01%	6.95%	6.94%	7.12%	7.23%	8.51%	0.10%	0.29%	1.57%
1	6.06%	5.99%	5.98%	6.23%	6.38%	7.98%	0.17%	0.40%	1.99%
1.3	5.55%	5.47%	5.47%	5.79%	5.97%	7.87%	0.24%	0.49%	2.40%
1.6	5.08%	5.00%	5.00%	5.39%	5.58%	7.81%	0.31%	0.58%	2.81%
2	5.65%	5.57%	5.57%	6.05%	6.26%	8.88%	0.39%	0.69%	3.32%
2.3	5.12%	5.03%	5.03%	5.57%	5.80%	8.63%	0.45%	0.77%	3.60%
2.8	5.88%	5.79%	5.79%	6.42%	6.68%	9.85%	0.55%	0.89%	4.06%

Macroscopic Strain (%)	FEA			TFA			Difference
Macroscopic Strain (%)	Q4	Q9	Q36	Q4	Q9	Q36	Q4	Q9	Q36
0.4	9.69%	9.60%	9.58%	9.73%	9.81%	10.56%	0.04%	0.20%	0.98%
0.5	9.16%	9.07%	9.06%	9.21%	9.29%	10.28%	0.05%	0.23%	1.22%
0.7	9.08%	8.99%	8.98%	9.16%	9.29%	10.57%	0.08%	0.30%	1.58%
1	9.74%	9.65%	9.65%	9.88%	10.02%	11.52%	0.13%	0.37%	1.87%
1.2	8.92%	8.83%	8.82%	9.08%	9.24%	10.81%	0.16%	0.41%	1.99%
1.4	8.62%	8.53%	8.52%	8.81%	8.97%	10.66%	0.19%	0.45%	2.14%
1.8	8.59%	8.49%	8.49%	8.83%	9.01%	10.93%	0.25%	0.51%	2.44%
2.2	7.93%	7.83%	7.83%	8.23%	8.41%	10.54%	0.30%	0.58%	2.71%
2.7	8.74%	8.64%	8.64%	9.11%	9.30%	11.71%	0.38%	0.66%	3.08%

	Coarse Mesh			Intermediate Mesh			Fine Mesh
	FEA	TFA SEQ	TFA PAR	FEA	TFA SEQ	TFA PAR	FEA	TFA SEQ	TFA PAR
Q4	86.40	153.00	92.00	452.40	3116.00	1906.00	1119.20	18124.00	25324.00
Q9	52.06	12.50	9.56	209.07	188.50	118.68	592.34	1154.50	661.75
Q36	21.11	0.69	0.79	133.86	4.64	4.20	334.67	20.05	14.69

	Coarse Mesh			Intermediate Mesh			Fine Mesh
	FEA	TFA SEQ	TFA PAR	FEA	TFA SEQ	TFA PAR	FEA	TFA SEQ	TFA PAR
Q4	120.60	243.000	155.000	588.00	4512.000	2854.000	1467.10	24536.000	41281.000
Q9	71.35	17.400	15.838	323.47	272.500	176.808	848.31	1632.700	874.656
Q36	26.02	0.773	0.696	162.12	4.832	4.699	459.14	33.185	24.309

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[1] * Corresponding author