1. Mechanical Behaviour of silica filled Silicon Rubber: an Optical two-dimensional Extensometer Application Mechanics of Materials and Structures Lab (2MS) Engineering Materials Center (CMGD) Ales School of Mines (EMA) M. Giton, P. Ienny, R. Piques

2. CompTest 20032 Introduction Tear Strength: Common Approach n Principle: analytical model in Fracture Mechanics n Drawback: – no realistic approximation of the behaviour – dependency of the tear strength on specimen geometry loading conditions (type of the test) Local Approach n Principle: stress concentration analysis – Mechanical behavior of the material – Simulated test by FEA

3. CompTest 20033 Experiment Optimization processus Finite Element Analysis Load and Digital kinematic field constitutive law Boundary Conditions Mesh Optimization Procedure E xperimental D atas D igital I mage C orrelation I mage A nalysis E xperimental R esults FEA BC ED DIC IA ER M E(t) F(t)

4. CompTest 20034 Digital Image Correlation F(t) u(t) Experimental setup FEA BC ED DIC IA ER M Image sequence

5. CompTest 20035 Digital Image Correlation Principle of the method n two-dimensional displacement measurements FEA BC ED DIC IA ER M n Linear fit of displacement field n In-plane tensor of strain

6. CompTest 20036 Digital Image Correlation Image 2 X 1 Y 1 Y X X 2 Y 2 P 1 (x 1 ; y 1 ) M 1 M 2 P 2 (x 2 ; y 2 ) Image 1 Processing method FEA BC ED DIC IA ER M Elastomers: large strain Tear Study: local phenomena

7. CompTest 20037 Digital Image Correlation Image 2 X 1 Y 1 Y X X 2 Y 2 [F] P 1 (x 1 ; y 1 ) M 1 M 2 P 2 (x 2 ; y 2 ) Image 1 Improvement of the processing method FEA BC ED DIC IA ER M

8. CompTest 20038 Digital Image Correlation New correlation functions Iterative fine search method: lower number of intermediate images better localisation measurement u:Pattern of M FEA BC ED DIC IA ER M

9. CompTest 20039 Experimental Tests V UC UT BT B.C. Homogeneous tests FEA BC ED DIC IA ER M

10. CompTest 200310 Experimental Tests Exemple of experimental results in UT FEA BC ED DIC IA ER M

11. CompTest 200311 Experimental Tests Non-homogeneous tests LL RR a L geometry b  Alignment defaults FEA BC ED DIC IA ER M

12. CompTest 200312 Experimental Tests Non-homogeneous tests FEA BC ED DIC IA ER M Realistic mesh Realistic BC

13. CompTest 200313 Experimental Tests Non-homogeneous tests FEA BC ED DIC IA ER M Transverse profiles : axial stretch ratio evolution

14. CompTest 200314 Phenomenological model FEA BC ED DIC IA ER M 4 8 2 4 14

15. CompTest 200315 Experimental Study Numerical Study EXPERIMENTEXPERIMENT Testing  Images Collection Finite Element Analysis Load and Digital kinematic field viscous hyper- elastic law’s parametrers Boundary Conditions Mesh Optimization Procedure Finite Element Analysis Load and Digital kinematic field constitutive law Boundary Conditions Mesh E xperimental D atas D igital I mage C orrelation I mage A nalysis E xperimental R esults FEA BC ED DIC IA ER M

16. CompTest 200316 Finite Element Analysis constitutive law Boundary Conditions Mesh Optimization Procedure Law cost Function FEA BC ED DIC IA ER M

17. CompTest 200317 Results and Discussion Uniaxial Tensile Test

18. CompTest 200318 Results and Discussion Biaxial Tensile Test Pure shear

19. CompTest 200319 Results and Discussion DENT Test

20. CompTest 200320 Results and Discussion DENT Tests

21. CompTest 200321 Concluding and remarks Strain sollicitations diagram Multiaxial tests with localisation zone Fracture criteria

22. CompTest 200322 Concluding and remarks FEA + Two-dimensional Digital Extensometer Realistic Boundary Conditions Identical meshes for FEA/DIC Identification bases on Multiaxial Tests Inverse Approach