II ,, i I I · ii ,, i i i contractor report brl-cr-608 brl nonlinear analysis of a tm-46 00d...

,, i II I I

CONTRACTOR REPORT BRL-CR-608

BRLNONLINEAR ANALYSIS OF A TM-46

00D SOVIET LAND MINE

DTICAN 11 98 JAN WALCZAK

K. J. BATHE

APRIL 1989

APPROVE') 1I01 IllW(" R1.1,ASE: DISTRI!IIt:VION t NIIMI 11.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

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4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANI7ATION REPORT NUMBER(S)

BRL- CR-608

6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

ADINA Engineering, Inc. (f applicable) U.S. Army Ballistic Research Laboratory

6c. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City, State, and ZIP Code)

71 Elton Avenue, Watertown, MA 02172 U.S.A. Aberdeen Proving Ground, MD 21005-5066U.S.A.

Ba NAME OF FUNDING/ SPONSORING 8b OFFICE SYMBOL 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (If applicable) DAAA15-86-C-0029

U.S. Army BRL SLCBR-TB--B

8c. ADDRESS (City, State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERSPROGRAM PROJECT TASK WORK UNITELEMENT NO NO NO. ACCESSION NO

Aberdeen Proving Ground, MD 21005-5066 61102A L!6110MA1-61

11 TITLE (Include Security Classification)

Nonlinear Analysis of a TM-46 Soviet Land Mine

12. PERSONAL AUTHOR(S)

Jan Walczak and K.J. Bathe13a. TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year, Month, Day) 15 PAGE COUNT

Final FROM /2/6oJ3.8/ 1 29 March 1988 49

16. SUPPLEMENTARY NOTATION

17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)

FIELD GROUP I SUB-GROUP Mine Neutralization Finite Element Analysis

13 13 TNT and Tetryl Fxplosives Contact Algorithm

15 1 06 Kinematic Hardening Failure Criteria19. ABSTRACT (Continue on reverse if necessary and identify by block number)

A static and dynamic analysis of a TM-46 land mine is presented.

The objective of this study was to establish a finite clement analysis of themine including an accurate modeling of the contact conditions.

The report presents the finite element modeling and solution results for thestatic buckling response and the dynamic response under blast pressure loading.

20. DISTRIBUTION /AVAILABILITY OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIEDE UNCLA SIF;ED/UNLIM:TED 0 SAME AS RPT. C- DTIC USERS

22. NAME OF RESPONSIBLF n Area Code) 22c OFFICE SYMBOL0. Form 147,Ur. ron D. Guodta o Tet SECRT SLCBR-TB- BDD Form 1473, JUN 86 Previous editions are obsolete SECURITY CLASSIFICATION OF THIS PAGE

TAE OF OONTENTS

Page

LIST CF FIGMR S ............................................... .

LIST OF TABL S ................................................ iv

1. I'rI ................................................. 1

2. TMM Fn = I EBL M L ..................................... 2

3. SO CcU R U S ............................................. 3

a. Static Analysis of the Mine ............................... 4

b. Dynamic Analysis of the Mine ............................... 4

4. DISCUSSICK .................................................... 6

5. OCN=SINS AN REC DATI ................................ 7

P1 E E C S.................................................... ).11

DISTRIBUIN LIST ............................................. 41

Acceso;, For

NTIS CRA&I

DTDC tAB

D T! "' 8 y .... ...

tNSPECTcE -

iis

LIST OF FIGURES

Figure Page

1. Cross-section of mine ...................................... 12

2. Perspective view of mine structure .......................... 13

3. Material elastic-plastic uniaxial test response ............. 14

4. Material for the TNT explosive .............................. 15

5. Loading applied to top plate of mine ........................ 16

6. Finite element mesh used in static analysis ................. 17

7. Load displ t response of top plate of mine ............. 18

8. Deformation of mine at load level corresponiing to2

point 1 in Fig. 7, p - 0.08 N/mm ........................... 19

9. Deformation of mine at load level oorrespondig to2

point 2 in Fig. 7, p - 0.16 N/rm ............................ 20

10. Deformation of mine at load level oorresponding to2

point 3 in Fig. 7, at load level p - 16 N/mm ............... 212

11. Main body of mine at load level p - 500 N/rn ............... 22

12. Finite element mesh used in dynamic analysis, 4-node

elements in the stepped region .............................. 23

13. Deformation of mine at time t - 0.026 ms .................... 24

14. Deformation of mine at time t - 0. 035 ms .................... 25

15. Deformation of mine at time t = 0.0407 ms ................... 26

16. Deformation of mine at time t - 0.0457 ms ................... 27





21. Large strains in the stepped part of the mine attim t - 0.061 me ........................................... 32

ii

LIST OF FIGURES (continued)

Figure Page


23. Deformation of mine at tine t - 0.0749 me .................... 3424. Deformation of mine at time t - 0.0763 us ................... 35

25. Deformation of mine at time t - 0.0835 re ................... 36




29. Deformation of mine at time t - 0. 102 ms .................... 30

iii

LISTOF TALS

Table Page

1. ADfITA Input Values for Bulk and Shear ModuLfor Filler Materials ........................................ 9

iv

1. INTRODUCTION

In some previous work Gupta et al analyzed a mine casing for its nonlinearresponse [1,2]. The structure is described in detail in ref. [2]. Thisdescription gives the geometry and material data and the assumed loading on thestructure.

Figures 1 to 5 show the data pertaining to the analysis of the mine.Figure I shows a cross-section of the (almost) axisymmetric structure. Thecasing consists of steel, the secondary booster fuzewell explosive is the tetrylmaterial and the central cavity in the main body is filled with the TNT explosivepowder. Figure 2 gives a perspective view of the mine and ihdicates'6w tinesteel material properties have been determined from measurements on tensilespecimens. Some test results to determine the uniaxial stress-strain responseof the steel are given in Fig. 3. Gupta used these test results to determine abilinear approximation and a multilinear approximation has been used for hisanalysis. Figure 4 gives the material relationship used to describe the fillermaterial, as established in ref. [2]. Finally, Fig. 5 shows the loading on thetop plate of the mine.

The material relationships for the TNT and filler material are also givenin Table 1.

In their study, Gupta et al established a finite element discretization ofthe mine and solved for the geometric and material nonlinear response. A majordifficulty in their study was to model the contact that is established betweenthe top plate of the mine and the cover plate of the filler material. Sincethe deformations of the top plate are very large and contact is establishedover practically the whole cover plate at an early time of the response, themodeling of the contact conditions is an important ingredient of the analysisprocess.

The reason that Gupta et al had difficulty modeling the contactconditions accurately was that the ADINA program at the time of study dia notoffer an automatic contact algorithm.

The objective of the present study was to establish a finite elementanalysis including a more accurate modeling of the contact conditions. In thisstudy ADINA 84 was used with some improvements, as described below (versus theuse of ADINA 81 by Gupta et al).

The report is presenting the following information. In the next sectionthe finite element model is described with special emphasis on the elementselection and the boundary conditions used. In Section 3 the solution resultsare then given, as obtained in a static analysis and a dynamic analysis. Theseresults are discussed and interpreted in Section 4. The discussion includes adescription of the difficulties encountered in the analysis. Finally, in thelast section, the major results are summarized and recommendations for furtherwork on the problem are given.

• I l I I I I P1

2. THE FINITE ELEMENT MODEL

The finite element model used for the analysis is shown in Fig. 6.

- Eight-node elements were used to model the main cylindrical steel bodyand the top cover and stepped section.

- Five and four-node elements were used to model the TNT explosive andTetryl explosive materials in the mine.

This model was used for the static analysis. For the dynamic solution itwas found that the stepped part of the top plate was more appropriately modeledusing 4-node elements. As a result, two 4-node elements were used to replaceone 8-node element used in static analysis, see Fig. 12.

Since an axisymmetric structure is considered, only half of the mine wasdiscretized. This model was assumed to be supported by a rigid foundation.

The stress-strain relationships used for the materials are given in Figs.3 and 4.

The contact conditions between the top plate and the cover plate weremodeled using the contact algorithm of ADINA 84 [3]. However, since theautomatic load stepping for solution of response had to be used for the staticanalysis, a modification to the standard algorithm was necessary. Thismodification now allows the solution of the equations

it+At(i-1) K AUi) t+At

L T (i)i

T0 AX 0

t+AtF(i-1) t+AtR (i-i)F R-c

0+

2

where

t+AtK('-) = tangent stiffness matrix

KX = contact constraint matrix

R = externally applied load vector, corresponding to auniform pressure on the top cover plate of the mine

t+At (i -1) = load factor, scaling the load vector to trace out

the load-displacement response [4]

t+At F(i-1)= nodal point forces corresponding to the internal element

stresses

t+At Rc (i-I) contact forces

(-)

AU i = incremental displacement

A(i) = vector of Lagrange multipliers

The left superscript t+At denotes time at t+At and the iteration counter

is (i).

The modifications necessary in ADINA 84 pertain to the use of the

automatic load stepping with the load factor t+At U(i-1) in Eq. (1), togetherwith the contact conditions. Here the algorithm of ref. [4] was extended toinclude the contact conditions as a constraint.

The solution results in Section 3 show that the automatic load steppingscheme had to bE used because of the successive collapse (limit) points reacheddue to the physical collapse of the stepped section of the top plate. Sincethe automatic load stepping scheme was used in the static analysis, it had tobe assumed that the load was deformation independent.

In the dynamic analysis the standard incremental equations of motion weresolved, with the applied blast pressure shown in Fig. 5.

The finite element large deformation, large strain formulation used forthe steel casing sections was the U.L.H. (updated Lagrangian Hencky) formu-lation described in refs. [5,6]. For the TNT explosive material and thp fuze-well filler material the materially-nonlinear-only formulation was used, sincerelatively small deformations were anticipated in this part of the mine.

3. SOLUTION RESULTS

The static and dynamic solution results are presented in Figs. 7 to 29.

3

a. Static Analysis of the Mine

The static solution results of the mine are given in Fig. 7 as apressure-displacement response. As can be seen from the figure a successivecollapse behavior of the stepped section of the top plate is observed and at a

2pressure of C.'.o N/mm , the stepped part of the top cover can be considered asdestroyed.

Figures 8, 9 and 10 give some overall deformations of the mine atdifferent load levels corresponding to points (1), (2) and (3) in Fig. 6 (point(I) - first contact, point (2) - center top plate comes into contact with themain body, point (3) - final deformations of the top part). As these figuresshow, the main body of the mine is very stiff. Note that Fig. 11 gives the 2response solution for a very high (perhaps impractical) pressure of 500 N/mm

b. Dynamic Analysis of the Mine

A nonlinear dynamic analysis has been performed to find the response ofthe mine for the blast loading using the U.L.H. formulation.

In order to ascertain that the model has been formulated correctly, aneigenfreqency and mode shape analysis was performed first as in Fig. 12. Thefrequencies and corresponding periods are given in Table 2.

Table 2

Frequency Period

(cps) (sec)

0.1147 • 104 0.8718 * 10-3

0.4799 • 104 0.2084 • 10-3

0.8146 • 10 4 0.1228 - 10-3

0.1512 • 105 0.6612 * 10-4

It is noted that these predicted frequencies (cycles per sec) areconsiderably lower than the values reported by Gupta et al [27]. Thedifference is deemed due to the fact that Gupta et al used a stiffer mesh andused springs to model the contact between the top and cover plates.

This conclusion is substantiated by an approximate analysis in which itis assumed that the top plate acts as a single degree of freedom system.

4

Calculating the lowest frequency of a mesh close to Gupta's mesh (but notincluding the springs) gives

(W ) = 6.7 • 10 rad/sec

whereas Gupta reports [2]

2(w1 ) 3.65. 108 rad/sec

However, for a single degree of freedom system, we have

2 KW1 = -M{-

-2 K+K~2 s

u2 =

We now let K be the stiffness of the cover plate, M the corresponding mass

and K be the stiffness due to the applied springs. The stiffness K can bes

evaluated from the static response (Fig. 7):

K= N _ -A = 0.09 • 7 , 1002 - 1414 [N/mm]AL AL 2.0

Having obtained K, we can calculate the corresponding mass:

M = 1414 7 2.1 • 10-5 ,

6.7 • 10

The stiffness of the springs can be evaluated as:

EA 7(100 2- 40 2) + (150 2-100 )S L 25.0 12 1.4 : 6060 [N/mm]

5

where the Young's modulus for the springs has been obtained from Fig. 8,reference [2]

Es = 1 200 psi = 1.4 N/mm2

Hence

-2 1414 + EJ60 8w2 = 2.-0 3.56 • 108

As can be seen the calculated value for - is close to the value obtained byGupta et al [2].

For the nonlinear dynamic analysis, the mesh in Fiq. 12 was used.Figures 13 to 29 show the calculated nonlinear dynamic response of the mine.The response was obtained using the trapezoidal implicit time integrationscheme. The figures show large deformations in the stepped section of the topplate, and that these defo-mations occur in a different manner than in thestatic analysis.

The analysis was conducted with the time steps varying between 0.1E-07 andand 0.IE-05 sec. and a total of 2050 time steps with full Newton equilibriumiterations in each step was used to obtain the solution up to 0.102E-03 sec.(0.102 ms), as in Fig.30. At this point the top plate is considered to bedestroyed and the main body of the mine gives a very stiff further response.

4. DISCUSSION

Several difficulties were encountered in the static analysis of the mine.The stepped part is a thin-walled structure connected to a relatively thickcentral plate and massive solid main body. As a result, the plate responds ina multi-buckling behavior which together with contact conditions and very largedeformations creates solution difficulties.

The large deformations of the mine occur mainly in the area of the topcover plate, and a relatively low pressure is only needed to destroy the upperpart of the mine. The stepped part was subjected to forty percent strain at a

pressure p = 0.16 N/mm2 and at the pressure p = 16 N/mm2 the top central plateis in full contact with the main body. The main body which is supported on arigid roller, did not show significant deformations at this pressure. 2 However, asthe load was inLreased (up to an artificially large value of 500 N/mm ), thedeformation in The main body increased significantly, as can be seen inFig. 11.

As for the dynamic response prediction, the implicit trapezoidal rule timeintegration scheme with the full Newton method was used. The response of thesystem is shown in Figs. 13-29. The flexible stepped part is subjected againto very large deformations and large strains (see Fig. 21), which causes

6

numerical difficulties due to dynamic buckling behavior and contact. In order

to obtain convergence in the iterations a sufficiently small time step had to

be used and the time step size was varied between 10-2 wsec and I ,sec.

The failure in some elements in the stepped part has been observed at arelatively early time beginning with time t = 0.00003 sec (0.03 ms). In orderto continue the computation, (since damage of the stepped part does not meanthat the whole mine is deactivated) very large strains were allowed in theresponse.

The progressive behavior of the top cover can be seen in Figs. 13 - 29.At time t = 0.0001 sec, (0.1 ms) the top part of the mine was severelydistorted and the analysis could not be carried further. However, again nosignificant deformations are found in the main body, which did not show anyevidence of failure at this stage.

These observations are in good agreement with the observations given byGupta et al [2]. The highest strains in the main body were observed near thecorners and in the contact areas between the top plate and the cover plate ofthe mine casing.

5. CONCLUSIONS AND RECOMMENDATIONS

In the present analysis the mine was supported on rigid rollers. Itshould be noted that the mine on an elastic foundation might display adifferent response in some respects from that presented in this work. However,the underlying analysis difficulties and major response can be expected toremain the same and some suggestions can be summarized.

The analysis is difficult to conduct because of the large deformations andhighly inelastic response of the mine. In the study the response of the minewas obtained for very large pressures and a complex collapse response of thetop plate was observed, but the main body underwent relatively smalldeformations.

The modeling and analysis of the mine could be improved by the followingfeatures:

- For the analysis it would be most effective to employ axisymmetric thinshell elements instead of the axisymmetric solid elements. Suchelements should be available in ADINA for this type of analysis.

The major reason is that solid elements becoming too thin as required inthis analysis develop spurious stresses through the thickness of theelements, which in time renders the contact solution difficult.

- Failure criteria should be used in the model that realistically removeselements during the response history. However, such elements removedwill render the analysis (in particular the static solution) moredifficult because of the abrupt change in system properties. In thereported analysis, elements were removed using the element birth anddeath option.

7

- The dynamic analysis might be considerably easier if an effectiveautomatic time step selection were available in ADINA. We anticipatethat in the next release of ADINA such scheme will be available.

The complete analysis was conducted on a MicroVAX computer: this waseffective to construct the model and perform the runs as reported in thisdocument. However, as a next step it would be effective to perform any furtheranalysis on a large frame computer. In this case the computer processing timesfor a run would be measured in minutes rather than in hours (as for theMicroVAX) and parametric studies are possible.

8

Table 1. ADINA Input Values for Bulk and Shear Moduli

for Filler Materials.

TNT EXPLOSIVE

Point No. Lv K KU G

(%) (GPa) (GPa) (GPa)

1 0 21.72 21.72 10.62

2 1.0 23.03 23.03 11.24

3 3.0 25.65 25.65 12.55

4 5.0 28.68 28.68 14.01

5 9.0 35.85 35.85 17.51

6 11.0 40.20 40.20 19.65

TETRYL

1 0 10.5 10.5 4.03

2 1.0 11.15 11.15 4.27

3 3.0 12.59 12.59 4.83

4 5.0 14.24 14.24 5.46

5 8.0 17.2 17.2 6.60

6 10.0 19.56 19.56 7.50

9

REFERENCES

1. F.H. Gregory and A.D. Gupta, "The Use of ADINA for Analysis of Mines

with Explosive Fills", Computers & Structures, Vol. 17, No. 5-6,

pp. 625-633, 1983.

2. A.D. Gupta, "Structural Analysis of a Mine with Two Viscoelastic

Explosive Fills". Trans. of the Twenty-eighth Conference of Army

Mathematicians, ARO Report 81-3, August 1981.

3. ADINA 84 Users Manual, Report AE 84-1, ADINA Engineering, Inc.

4. K.J. Bathe and E. Dvorkin, "On the Automatic Solution of Nonlinear

Finite Element Equations", Computers & Structures, Vol. 17, No. 5-6,

pp. 871-879, 1983.

5. K.J. Bathe, R. Slavkovi( and M. Koji(, "On Large Strain Elasto-Plastic

and Creep Analysis", in Finite Element Methods for Nonlinear Problems

(P.G. Bergan et al, eds.), Springer-Verlag, 1986.

6. K.J. Bathe, M. Kojic and J. Walczak, "Some Developments in Methods for

Large Strain Elasto-Plastic Analysis", Proceedings, Conference Compu-

tational Plasticity, Barcelona, April 1987.

11

.... . .. ..

..... .... . . ...

........... 0

.... .... .. .

...... ......

........

. ... ....

LL-

12

TOPI INERMEDIATE '

• 5SIDE WALL

(a) LOCATION OF SPECIMENS, TM-46 MINE

9.5.1 . 2 T 2 .0- 2 .5 :t .2 5

1.3 t±0.2

(b) PREPARATION OF SPECIMEN DIMENSIONS (cm)

Fig. 2 Perspective view of mine structure

13

300

TEST I

,20O-LU

I-

zLU

LU

~100

z

00 5 10 15 20

ENGINEERING STRAIN (%)

Fig. 3 Material elastic-plastic uniaxial test response

14

(eds) sninaow lNV3HS- 0vo SniflUow miOs m

c~c;

m J \J

ci Cl CW

S-

I.- .4-

cs 0

LL-

C

(t-oi-xsd) SnilUow HV3HS -Ho SDnfUow mifis - m

15

14 -- 2000

12

-150010

a. C

1000 ac

a- a

4 - 500

2

0 00.0 0.4 0.8 1.2 1.6 2.0

TIME(i)

Fig. 5 Loading applied to top plate of mine

16

i

-

/ (U/

7U

I4F I C

! I I

26.0 I

Pressure[N/mm 2) 18.0

10.0

2.0

0.20-

0.18

0.16 2

0.14

0.12

0.10

0.08

0.06

0.04

0.02

4 8 12 16 20 24 28 32 3640Displacement, w~mm]

Fig. 7 Load displacement response of top

plate of mine

18

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