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Volume change of heterogeneous quasi-brittle materials in uniaxial compression

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Abstract

The volumetric strain was categorized into elastic and plastic parts. The former composed of axial and lateral strains is uniform and determined by Hooke's law; however, the latter consisting of axial and lateral strains is a function of thickness of shear band determined by gradient-dependent plasticity by considering the heterogeneity of quasi-brittle materials. The non-uniform lateral strain due to the fact that shear band was formed in the middle of specimen was averaged within specimen to precisely assess the volumetric strain. Then, the analytical expression for volumetric strain was verified by comparison with two earlier experimental results for concrete and rock. Finally, a detailed parametric study was carried out to investigate effects of constitutive parameters (shear band thickness, elastic and softening moduli) and geometrical size of specimen (height and width of specimen) on the volume dilatancy.

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References

  1. A Hillerborg, M Modeer, P E Petersson. Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Element[J].Cement and Concrete Research, 1976, 6: 773–782

    Article  Google Scholar 

  2. F Ansari. Stress-strain Response of Microcracked Concrete in Direct Tension[J].ACI Material Journal, 1987, (9–10): 481–490

    Google Scholar 

  3. D Fokwa, Y Berthaud. Heterogeneous Materials: Experimental Analysis of Localization and the Influence of Size of the Heterogeneities on the Behaviour in Tension[J].Materials and Structures, 1993,26: 136–143

    Article  Google Scholar 

  4. A Carpinteri, G Ferro. Size Effect on Tensile Fracture Properties: a Unified Explaination Based on Disorder and Fractality of Concrete Microstructure[J].Materials and Structures, 1994,27:563–571

    Article  CAS  Google Scholar 

  5. C Zhang, G Wang, S Wang,et al. Experimental Tests of Rolled Compacted Concrete and Nonlinear Fracture Analysis of Rolled Compacted Concrete Dams[J].Journal of Materials in Civil Engineering, ASCE, 2002, 14(2): 108–115

    Article  Google Scholar 

  6. A Vervuurt, E Schlangen, J M G Van Mier. Tensile Cracking in Concrete and Sandston: Part 1: Basic Instruments[J].Materials and Structures, 1996, 29: 9–18

    Article  Google Scholar 

  7. H B Muhlhaus, I Vardoulakis. The Thickness of Shear Bands in Granular Materials[J].Géotechnique, 1987, 37: 271–283

    Article  Google Scholar 

  8. Z P BaZant, G Pijaudier-Cabot. Measurement of Characteristic Length of Nonlocal Continuum[J].Journal of Engineering Mechanics, ASCE, 1990, 115(4): 755–767

    Article  Google Scholar 

  9. R J Finno, W W Harris, M A Mooney,et al. Strain Localization and Undrained Steady State of Sand[J].Journal of Geotechnical Engineering, ASCE, 1996, 122, (6): 462–473

    Article  Google Scholar 

  10. S P Shah, R Sankar. Interal Cracking and Strain-softening Response of Concrete under Uniaxial Compression[J].ACI Material Journal, 1987, (5–6): 200–212

    Google Scholar 

  11. D C Jansen, S P Shah, E C Rossow. Stress-strain Results of Concrete From Circumferential Strain Feedback Control Testing [J].ACI Material Journal, 1995, (7–8): 419–428

    Google Scholar 

  12. H Jing, S Li. Experimental Study on Volumetric Strain of Rocks in Full Stress-Strain Process[J].Journal of China University of Mining & Technology, 1999, 9(1): 33–37

    Google Scholar 

  13. R I Borja, R A Regueiro, T Y Lai. FE Modeling of Strain Localization in Soft Rock[J].Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2000, 124(4): 335–343

    Article  Google Scholar 

  14. D J Stevens, D Liu. Strain-Based Constitutive Model with Mixed Evolution Rules for Concrete[J].Journal of Engineering Mechanics, 1992, 118(6): 1 184–1 200

    Article  Google Scholar 

  15. A Bouzaiene, B Massicotte. Hypoelastic Tridimensional Model for Nonproportional Loading of Plain Concrete[J].Journal of Engineering Mechanics, ASCE, 1997, 123(11): 1 111–1 120

    Article  Google Scholar 

  16. P H Bischoff, S H Perry. Impact Behavior of Plain Concrete Loaded in Uniaxial Compression[J].Journal of Engineering Mechanics, ASCE, 1995, 121(6): 685–693

    Article  Google Scholar 

  17. Z P BaZant, Y Xiang, M D Adley,et al. Microplane Model for Concrete: II: Data Delocalization and Verification [J].Journal of Engineering Mechanics, ASCE, 1996, 122 (3): 255–262

    Article  Google Scholar 

  18. H R Lotfi, P B Shing. Interface Model Applied to Fracture of Masonry Structures[J].Journal of Structural Engineering, ASCE, 1994, 120(1): 63–80

    Article  Google Scholar 

  19. G Z Voyiadjis, T M Abu-Lebdeh. Damage Model for Concrete Using Bounding Surface Concept[J].Journal of Engineering Mechanics, ASCE, 1993, 119(9): 1 865–1 885

    Article  Google Scholar 

  20. R de Borst, H B Muhlhaus. Gradient-dependent Plasticity: Formulation and Algorithmic Aspects[J].International Journal for Numerical Methods in Engineering, 1992, 35 (3): 521–539

    Article  Google Scholar 

  21. K Ellen, R Ekkehard, R de Borst. An Anisotropic Gradient Damage Model for Quasi-brittle Materials[J].Computer Methods in Applied Mechanics and Engineering, 2000, 183: 87–98

    Article  Google Scholar 

  22. H Askes, J Pamin. Dispersion Analysis and Element-free Galerkin Solutions of Second-and Fourth-order Gradient Enhanced Damage Models[J].International Journal for Numerical Methods in Engineering, 2000, 49: 811–832

    Article  Google Scholar 

  23. H W Zhang, B A Schrefler. Gradient-dependent Plasticity Model and Dynamic Strain Localization Analysis of Saturated and Partially Saturated Porous Media: One-dimensional Model[J].Eur. J. Mech. A/Solids, 2000, 19: 503–524

    Article  Google Scholar 

  24. P A Cundall. Numerical Experiments on Localization in Frictional Material[J].Ingenigeur-Archiv 1989, 59: 148–159

    Article  Google Scholar 

  25. B E Hobbs, A Ord. Numerical Simulation of Shear Band Formation in a Frictional-dilational Material[J].Ingenigeur-Archiv, 1989, 59: 209–220

    Article  Google Scholar 

  26. D Stephen, G Ivan. Fracture Initation, Growth and Effect on Stress Field: a Numerical Investigation[J].Journal of Structural Geology, 1998, 20(12): 1 673–1 689

    Google Scholar 

  27. X B Wang, Y S Pan, Q Sheng,et al. Numerical Simulation of Development of Dynamic Strain Localization and Size Effect[J].Chinese Journal of Computational Mechanics, 2002, 19(4): 500–503 (in Chinese)

    CAS  Google Scholar 

  28. X B Wang, Y S Pan, Q Sheng,et al. Numerical Simulation on Strain Localization of End Constraint of Rock Specimen [J].Journal of Engineering Geology, 2002, 10(3): 233–236. (in Chinese)

    Google Scholar 

  29. X B Wang, Y S Pan, X Ding,et al. Simulation of Multiple Shear Bands in Strain Softening Rock in Plane Strain [J].Rock and Soil Mechanics, 2002, 23(6):717–720 (in Chinese).

    Google Scholar 

  30. X B Wang, Y S Pan, Q Sheng,et al. Numerical Simulation of Localized Deformation Field for Rock in Plane Strain State[J].Chinese Journal of Rock Mechanics and Engineering, 2003, 22(4): 521–524 (in Chinese)

    Google Scholar 

  31. X B Wang, Y S Pan. Effect of Relative Stress on Post-peak Uniaxial Compression Fracture Energy of Concrete [J].Journal of Wuhan University of Technology-Materials Science Edition, 2003, 18(4): 89–92

    Article  Google Scholar 

  32. X B Wang, S H Dai, L Hai,et al. Analysis of Localized Shear Deformation of Ductile Metal Based on Gradient-dependent Plastioity[J].Trans. Nonferrous Met. Soc. China, 2003, 13(6): 1 348–1 353

    Google Scholar 

  33. X B Wang, M Yang, H J Yu,et al. Localized Shear Deformation During Shear Band Propagation in Titanium Considering Interactions Among Microstructures [J].Trans. Nonferrous Met. Soc. China, 2004, 14(2): 335–339

    CAS  Google Scholar 

  34. X B Wang, X B Yang, Z H Zhang,et al. Dynamic Analysis of Fault Rockburst Based on Gradient-dependent Plasticity and Energy Criterion[J].Journal of University of Science and Technology Beijing, 2004, 11(1): 5–9

    CAS  Google Scholar 

  35. Y S Pan, X B Wang, Z H Li. Analysis of the Strain Softening Size Effect for Rock Specimens Based on Shear Strain Gradient Plasticity Theory[J].International Journal of Rock Mechanics and Mining Sciences, 2002, 39(6): 801–805

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics and Engineering Sciences, Liaoning Technical University, 123000, Fuxin, China

    Wang Xuebin Ph D

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  1. Wang Xuebin Ph D
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Correspondence to Wang Xuebin Ph D.

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Funded by the National Natural Science Foundation of China (No.50309004)

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Xuebin, W. Volume change of heterogeneous quasi-brittle materials in uniaxial compression. J. Wuhan Univ. Technol.-Mat. Sci. Edit. 21, 162–167 (2006). https://doi.org/10.1007/BF02840909

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  • DOI: https://doi.org/10.1007/BF02840909

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