Abstract
Considering strain localization in the form of a narrow band initiated just at peak stress, three analytical expressions for stress — strain curves of quasibrittle geomaterial (such as rock and concrete) in uniaxial tension, direct shear and uniaxial compression were presented, respectively. The three derived stress — strain curves were generalized as a unified formula. Beyond the onset of strain localization, a linear strain-softening constitutive relation for localized band was assigned. The size of the band was controlled by internal or characteristic length according to gradient-dependent plasticity. Elastic strain within the entire specimen was assumed to be uniform and decreased with the increase of plastic strain in localized band. Total strain of the specimen was decomposed into elastic and plastic parts. Plastic strain of the specimen was the average value of plastic strains in localized band over the entire specimen. For different heights, the predicted softening branches of the relative stress — strain curves in uniaxial compression are consistent with the previously experimental results for normal concrete specimens. The present expressions for the post-peak stress — deformation curves in uniaxial tension and direct shear agree with the previously numerical results based on gradient-dependent plasticity.
Similar content being viewed by others
References
TANG Li-zhong, PAN Chang-liang, WANG Wen-xing. Surplus energy index for analyzing rock burst proneness[J]. J Cent South Univ Technol, 2002, 33(2): 129–132. (in Chinese)
WANG Wen-xing, PAN Chang-liang, FENG Tao. Fountain rockburst and inductive rockburst[J]. J Cent South Univ Technol, 2000, 7(3): 129–132.
FENG Tao, PAN Chang-liang, WANG Hong-tu, et al. A new method for determining elastic strain energy index of burst rocks[J]. The Chinese Journal of Nonferrous Metals, 1998, 8(2): 352–355. (in Chinese)
Hudson J A, Crouch S L, Fairhurst C. Soft, stiff and servo-controlled testing mechanics: a review with reference to rock failure[J]. Engrg Geol, 1972, 6(3): 155–189.
Choi S, Thienel K C, Shah S P. Strain softening of concrete in compression under different end constraints [J]. Mag Concrete Res, 1996, 48(175): 193–115.
ZHANG Chu-han, WANG Guang-lun, WANG Shao-min, et al. Experimental tests of rolled compacted concrete and nonlinear fracture analysis of rolled compacted concrete dams [J]. J Mater Civil Engrg, ASCE, 2002, 14(2): 108–115.
van Mier J G M, Shah S P, Arnaud M, et al. Strainsoftening of concrete in uniaxial compression[J]. Mater Struct, 1997, 30(198): 195–209.
Wawersik W, Fairhurst C. A study of brittle rock fracture in laboratory compression experiments [J]. Int J Rock Mech Min Sci, 1970, 7(5): 561–575.
Labuz J F, Biolzi L. Class I vs class II stability: a demonstration of size effect[J]. Int J Rock Mech and Min Sci, 1991, 28(2–3): 199–205.
Jansen D C, Shah S P. Effect of length on compressive strain softening of concrete[J]. J Engrg Mech, ASCE, 1997, 123(1): 25–35.
Jewell R A. Direct shear tests on sand [J]. Géotechnique, 1989, 39(2): 309–322.
Attard M M, Setunge S. Stress — strain relationship of confined and unconfined concrete [J]. ACI Mater J, 1996, 93(5): 432–442.
Popovics S. A review of stress — strain curve of concrete[J]. Cement Concrete Res, 1973, 3(4): 583–599.
Alessandro P F, Daniele F, Ivo I. Mechanical model for failure of compressed concrete in reinforced concrete beams[J]. J Struct Engrg, ASCE, 2001, 128(5): 637–645.
Schreyer H L. Analytical solutions for nonlinear strain-gradient softening and localization[J]. J Appl Mech, ASCM, 1990, 57(3): 522–528.
Bažant Z P, Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum [J]. J Engrg Mech, ASCE, 1990, 115(4): 755–767.
Mühlhaus H B, Vardoulakis I. The thickness of shear bands in granular materials[J]. Géotechnique, 1987, 37(3): 271–283.
de Borst R, Mühlhaus H B. Gradient-dependent plasticity: formulation and algorithmic aspects[J]. Int J Numer Methods Engrg, 1992, 35(3): 521–539.
Pamin J, de Borst R. A gradient plasticity approach to finite element predictions of soil instability [J]. Arch Mech, 1995, 47(2): 353–377.
Li X K, Cescotto S. Finite element method for gradient plasticity at large strains[J]. Int J Numer Methods Engrg, 1996, 39(4): 619–633.
WANG Xue-bin. Shear stress distribution and characteristics of deformation for shear band-elastic body system at pre-peak and post-peak[J]. J Cent South Univ Technol, 2005, 12(5): 611–617.
WANG Xue-bin. Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity[J]. J Cent South Univ Technol, 2004, 11(4): 445–450.
WANG Xue-bin, YANG Xiao-bin, ZHANG Zhi-hui, et al. Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion[J]. J Univ Sci Technol Beijing, 2004, 11(1): 5–9.
WANG Xue-bin, DAI Shu-hong, HAI Long. Quantitative calculation of dissipated energy of fault rock burst based on gradient-dependent plasticity [J]. J Univ Sci Tech Beijing, 2004, 11 (3): 197–201.
WANG Xue-bin, YANG Mei, YU Hai-jun, 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.
WANG Xue-bin, DAI Shu-hong, HAI Long, et al. Analysis of localized shear deformation of ductile metal based on gradient-dependent plasticity[J]. Trans Nonferrous Met Soc China, 2003, 13 (6): 1348–1353.
WANG Xue-bin. Local and global damages of quasibrittle material in uniaxial compression based on gradient-dependent plasticity[J]. Key Engrg Mater, 2005, 293–294: 719–726.
WANG Xue-bin. Calculation of temperature distribution in adiabatic shear band based on gradient-dependent plasticity[J]. Trans Nonferrous Met Soc China, 2004, 14(6): 1062–1067.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(50309004) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Wang, Xb. Unified analytical stress — strain curve for quasibrittle geomaterial in uniaxial tension, direct shear and uniaxial compression. J Cent. South Univ. Technol. 13, 99–104 (2006). https://doi.org/10.1007/s11771-006-0114-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-006-0114-5