Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model. (English) Zbl 1162.74504
Summary: The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74R10 | Brittle fracture |
Keywords:
GB lattice model; compressive test; Mohr-Coulomb criterion; fracture; concrete; lattice modeReferences:
| [1] | Bazant ZP, Tabbara MR, Kazemi MT and Cabot GR (1990). Random particle model for fracture of aggregate or fiber composites. J Eng Mech 116(8): 1686–1705 · doi:10.1061/(ASCE)0733-9399(1990)116:8(1686) |
| [2] | Bolander JE Jr, Shiraishi T, Isogawa Y (1996). An adaptive procedure for fracture simulation in extensive lattice networks. Eng Fract Mech 54(3): 325–334 · doi:10.1016/0013-7944(95)00200-6 |
| [3] | Bolander JE Jr, Saito S (1998). Fracture analysis using spring network with random geometry. Eng Fract Mech 61(5–6): 569–591 · doi:10.1016/S0013-7944(98)00069-1 |
| [4] | Chang CS and Gao J (1996). Kinematics and static hypothesis for constitutive modeling of granulates considering particle rotations. Acta Mech 115: 213–229 · Zbl 0942.74015 · doi:10.1007/BF01187439 |
| [5] | Chang CS, Wang TK, Sluys LJ, van Mier JGM (2002). Fracture modeling using a micro-structural mechanics approach–I. Theory and formulation. Eng Fract Mech 69: 1941–1958 · doi:10.1016/S0013-7944(02)00070-X |
| [6] | Chang QT (1994) Nonlinear dynamic discontinuous deformation analysis with finite element meshed block systems. PhD Thesis, University of California, Berkeley |
| [7] | Chetouane B, Dubois F, Vinches M and Bohatier C (2005). NSCD discrete element method for modeling masonry structures. Int J Numer Meth Eng 64(1): 65–94 · Zbl 1073.74051 · doi:10.1002/nme.1358 |
| [8] | Cundall PA and Strack ODL (1979). A discrete numerical model for granular assemblies. Geotechnique 29(1): 47–65 · doi:10.1680/geot.1979.29.1.47 |
| [9] | Cusatis G, Bazant ZPF and Cedolin LM (2003). Confinement-shear lattice model for conrete damage in tension and compression: I. Theory J Eng Mech 129(12): 1439–1448 |
| [10] | Deng SC, Liu JX, Zhang J and Liang NG (2006). Component assembly model and its application to quasi-brittle damage. Theor Appl Fract Mech 46: 232–242 · doi:10.1016/j.tafmec.2006.09.002 |
| [11] | Deng SC, Liu JX, Zhang J and Liang NG (2007). Validation of component assembly model and its extension to plasticity. Theor Appl Fract Mech 47: 244–259 · doi:10.1016/j.tafmec.2007.01.003 |
| [12] | Diebels S and Steeb H (2002). The size effect in foams and its theoretical and numerical investigation. Proc R Soc Lond A 58: 2869–2883 · Zbl 1116.74322 |
| [13] | Digby PJ (1981). The effective elastic modulli of porous granular rock. ASME J Appl Mech 48: 803–808 · Zbl 0468.73128 · doi:10.1115/1.3157738 |
| [14] | Ferro G (2006). On dissipated energy density in compression for concrete. Eng Fract Mech 73: 1510–1530 · doi:10.1016/j.engfracmech.2006.01.037 |
| [15] | Gao HJ and Klein P (1998). Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46(2): 187–218 · Zbl 0974.74008 · doi:10.1016/S0022-5096(97)00047-1 |
| [16] | Goodman RE and Shi G (1985). Block theory and its application to rock engineering. Prentice-Hall, Englewood Cliffs |
| [17] | Herrmann HJ and Roux S (1992). Statistical models for the fracture of disordered media. Elsevier, Amsterdam |
| [18] | Huang CY and Subhash G (2003). Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids. J Mech Phys Solids 51: 1089–1105 · Zbl 1049.74040 · doi:10.1016/S0022-5096(03)00002-4 |
| [19] | Hughes TJR, Taylor RL and Kanoknukulchai S (1977). A simple and efficient finite element for bending. Int J Numer Eng 11: 1529–1543 · Zbl 0363.73067 · doi:10.1002/nme.1620111005 |
| [20] | Ibrahimbegovic A and Depaplace A (2003). Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material. Comput Struct 81: 1255–1265 · doi:10.1016/S0045-7949(03)00040-3 |
| [21] | Karihaloo BL, Shao PF and Xiao QZ (2003). Lattice modelling of the failure of particle composites. Eng Fract Mech 70: 2385–2406 · doi:10.1016/S0013-7944(03)00004-3 |
| [22] | Kawai T (1978). New discrete models and their application to seismic response analysis of structures. Nucl Eng Des 48: 207–229 · doi:10.1016/0029-5493(78)90217-0 |
| [23] | Krajcinovic D (2000). Damage mechanics: accomplishments, trends and needs. Int J Solids Struct 37: 267–277 · Zbl 1075.74071 · doi:10.1016/S0020-7683(99)00081-5 |
| [24] | Lemaitre J (1996) A course on damage mechanics (in Chinese). Science Press, Beijing |
| [25] | Lilliu G, van Mier JGM(2003). 3D lattice type fracture model for concrete. Eng Fract Mech 70: 927–941 · doi:10.1016/S0013-7944(02)00158-3 |
| [26] | Liu JX, Deng SC, Zhang J and Liang NG (2007). Lattice type of fracture model for concrete. Theor Appl Fract Mech 48: 269–284 · doi:10.1016/j.tafmec.2007.08.008 |
| [27] | Liu JX, Deng SC and Liang NG (2008). Comparison of the quasi-static method and the dynamic method for simulating fracture processes in concrete. Comput Mech 41: 647–660 · Zbl 1162.74503 · doi:10.1007/s00466-007-0221-7 |
| [28] | Liu JX, Deng SC, Zhang J, Liang NG (2007) Beam lattice modeling for the fracture of particle composites. Eng Mech (accepted) |
| [29] | Ostoja-Starzewski M (2002). Lattice models in micromechanics. Appl Mech Rev 55: 35–60 · Zbl 1110.74611 · doi:10.1115/1.1432990 |
| [30] | Ostoja-Starzewski M (2007). Microstructural Randomness and scaling in mechanics of materials. Chapman & Hall/CRC, Boca Raton · Zbl 1148.74002 |
| [31] | Potyondy DO and Cundall PA (2004). A bonded-particle model for rock. Int J Rock Mech Min Sci 41: 1329–1364 · doi:10.1016/j.ijrmms.2004.09.011 |
| [32] | Prado EP, van Mier JGM(2003). Effect of particle structure on mode I fracture process in concrete. Eng Fract Mech 70: 1793–1807 · doi:10.1016/S0013-7944(03)00125-5 |
| [33] | Rots JG, Belletti B, Invernizzi S (2007) Robust modeling of RC structures with an ”event-by-event” strategy. Eng Fract Mech (in press) |
| [34] | Schlangen E, van Mier JGM (1992). Experimental and numerical analysis of the micromechanics of fracture of cement-based composites. Cem Conc Comp 14(2): 105–118 · doi:10.1016/0958-9465(92)90004-F |
| [35] | Schlangen E and Garboczi EJ (1997). Fracture simulation of concrete using lattice models: computational aspects. Eng Fract Mech 57(2–3): 319–332 · doi:10.1016/S0013-7944(97)00010-6 |
| [36] | Schorn H and Rode U (1987). 3-D modeling of process zone in concrete by numerical simulation. In: Shah, SP and Swartz, SE (eds) Fracture of concrete and rock, pp 220–228. Springer, New York |
| [37] | Shi G (1988) Discontinuous deformation analysis–a new numerical model for the statics, dynamics of block systems. PhD Thesis, University of California, Berkeley |
| [38] | Shyu K (1993) Nodal-based discontinuous deformation analysis. PhD Thesis, University of California, Berkeley |
| [39] | Trovalusci P and Masiani R (2003). Non-linear micropolar and classical continua for anisotropic discontinuous materials. Int J solids struct 40: 1281–1297 · Zbl 1062.74514 · doi:10.1016/S0020-7683(02)00584-X |
| [40] | Wvan Mier JGM, van Vliet MRA, Wang TK (2002). Fracture mechanisms in particle composites: statistical aspects in lattice type analysis. Mech Mater 34: 705–724 · doi:10.1016/S0167-6636(02)00170-9 |
| [41] | van Vliet M, van Mier JGM (1995) Softening behaviour of concrete under uniaxial compression. In: Wittmann F (ed) Fracture mechanics of concrete structures. AEDIFICATIO Publishers, Freiburg, pp 383–396 |
| [42] | Walton K (1987). The effective elastic modulli of a random packing of spheres. J Mech Phys Solids 35: 213–226 · Zbl 0601.73117 · doi:10.1016/0022-5096(87)90036-6 |
| [43] | Wang TK, van Mier JGM, Bittencourt TN (2001) Statistical study of fracture in concrete. In: Ravi-Chandar K, Karihaloo BL, Kishi T, Ritchie RO, Yokobori AT Jr, Yokobori T (eds) Advances in fracture research, Proc ICF10 0665OR. Pergamon, New York |
| [44] | Wang XC (2003). Finite element method,1st edn. Tsinghua University Press, Beijing |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
