Abstract
A mathematical model for concrete has been developed by combining a multiple-plane plasticity and fracture model with a cap model for compaction. The model provides for the anisotropy of tensile and shear behavior and also for nonlinear compaction. The model is primarily intended to represent the response of concrete structures to impact loading.
The model shows the usual differences in loading and unloading pressure-volume paths for compaction, and also shear stresses in the model enhance the compaction process. Shear stresses on each of seven planes are computed using a Mohr-Coulomb yield curve. Shear damage on a plane causes loss of shearing and tensile strength. Initially, the model has a macro character for ease in matching experimental data, but is extendable later to have micromechanical features for generality and for guidance in scaling calculations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Drucker, D. C. and W. Prager. Soil Mechanics and Plastic Analysis or Limit Design. Quarterly of Applied Mathematics 10 (1952) 157–165.
Chen, W. F. Plasticity in Reinforced Concrete ( McGraw-Hill, New York, 1981 ).
Chen, W. F. Plasticity in Reinforced Concrete. Proceedings of a Workshop on Constitutive Relations for Concrete, New Mexico Engineering Research Institute, University of New Mexico, Albuquerque, N.M., April 28, 29, 1981.
Lindberg, H. E. and L. E. Schwer. Choice and Construction of Yield Functions for Underground Cavity Analysis. Poulter Laboratory Technical Report (SRI International, Menlo Park, California 94025).
Schleicher, F. The Energy Limit of Elasticity (in German), Zeitschrift fuer Angewandte Mathematik and Mechanik 5, 6 (1925) 478–479.
Seaman, L. One-Dimensional Stress Wave Propagation in Soils. Final Report DASA 1757 by SRI International for Defense Atomic Support Agency (Washington, D.C. 20301, February 1966 ).
Shockey. D. A, D. R. Curran, L. Seaman, J. T. Rosenberg, and C. F. Petersen. Failure of Rock under High Tensile Loads. Int. J. Rock Mech. Sci. Geomech. Abstr. 11 (1974) 303–317.
Linde, R. K., L. Seaman, and D. N. Schmidt. Shock Response of Porous Copper, Iron, Tungsten and Polyurethane. J. of Appl. Phys. 43, 8 (August 1972) 3367.
Bazant, Z. P. Mathematical Modeling of Concrete and Its Experimental Basis. Proceedings of a Workshop on Constitutive Relations for Concrete (New Mexico Engineering Research Institute, University of New Mexico, Albuquerque, N. M., April 28, 29, 1981 ).
Seaman, L., D. R. Curran, and D. A. Shockey. Computational Models for Ductile and Brittle Fracture. J. Appl. Phys. 47 (1976) 4814–4826.
Murri, W. J., C. Young, D. A. Shockey, R. E. Tokheim, and D. R. Curran. Determination of Dynamic Fracture Parameters for Oil Shale. SRI International Final Report to Sandia Laboratories (Alburquerque, New Mexico, 1977.).
Gupta, Y. M. and L. Seaman. Local Response of Reinforced Concrete to Missile Impact. SRI International Final Report No. EPRI NP-1217 (Electric Power Research Institute, Palo Alto, California, October 1979 ).
Curran, D. R., D. A. Shockey, and L. Seaman. Dynamic Fracture Criteria for a Polycarbonate. J. Appl. Phys. 44 (1973) 4025.
Batdorf, S. B. and B. Budiansky. A Mathematical Theory of Plasticity Based on the Concept of Slip. National Advisory Committee for Aeronautics Technical Note No. 1871 ( Washington, April 1949 ).
Como, Mario and Salvatore D’Agostino. Strain Hardening Plasticity with Bauschinger Effect. Meccanica 4, 2 (1969) 146–158.
Como, Mario and Antonio Grimaldi. Analytical Formulation of the Theoretical Subsequent Yield Surfaces of Metals with Strain-Hardening and Bauschinger Effect in an Ideal Tension-Torsion Test. Meccanica 4, 4 (1969) 286.–297.
Naghdi, P. M., F. Essenburg, and W. Koff. An Experimental Study of Initial and Subsequent Yield Surfaces in Plasticity. J. Appl. Mech. 25 (1958) 201–209.
Bazant, Z. P. and B. H. Oh. Microplane Model for Fracture Analysis of Concrete Structures. Proceedings of the Symposium on the Interaction of Non-Nuclear Munitions with Structures (U.S. Air Force Academy, Colorado, May 10–13, 1983 ).
Seaman, L., D. R. Curran, and W. J. Murri. A Continuum Model for Dynamic Tensile Microfracture and Fragmentation. J. Appl. Mech. ASME, to appear.
Seaman, L., D. R. Curran. Behavior Under High Stress and Ultrahigh Loading Rates, eds. J. Mescall and V. Weiss ( Plenum Press, New York, 1983 ).
Seaman, L. and J. L. Dein. Representing Shear Band Damage at High Strain Rates, IUTAM Symposium on Nonlinear Deformation Waves (Tallinn, Estonia, August 22–28, 1982 ).
Drucker, D. C., R. E. Gibson, and D. J. Henkel. Soil Mechanics and Work-hardening Theories of Plasticity. Trans of the Amer. Soc. of Civil Eng.. 121 (1956) 338–346.
Sandler, I., F. L. DiMaggio, and G. Y. Baladi. Generalized Cap Model for Geological Materials. J. Geotech. Div., ASCE 102, GT7 (July 1976) 683–699.
Bazant, Z. P. and P. D. Bhat. Endochronic Theory of Inelasticity and Failure of Concrete, J. Eng. Mech. Div., ASCE 102 (1976) 701–722.
Bazant, Z. P. and Sang-Sik Kim. Plastic-Fracturing Theory for Concrete. J. Eng. Mech. Div., ASCE 105 (1979) 407–428.
Wittman F. H. and Yu. V. Zaitsev. Crack Propagation and Fracture of Composite Materials such as Concrete, 5th Int. Conf. on Fracture, ed. D. Francois, 5, 2261–2274 (Cannes, France, Mar. 29–Apr. 3, 1981 ).
Malvern, L. E. The Propagation of Longitudinal Waves of Plastic Deformation in a Bar of Material Exhibiting a Strain-Rate Effect. J. Appl. Mech. 18 (1951) 203–208.
Taylor, G. I. Plastic Strain in Metals. J. Inst. Metals 62 (1938) 307.
Peirce, D., R. J. Asaro, and A. Needleman. Material Rate Dependence and Localized Deformation in Crystalline Solids. Acta Metall. 31 (1983) 1951–1976.
Sneddon, I. N. and M. Lowengrub. Crack Problems in the Classical Theory of Elasticity (John Wiley and Sons, Inc., New York, 1969 ).
He, M. Y. and J. W. Hutchinson. The Penny-Shaped Crack and Plane Strain Crack in an Infinite Body of Power-Law Material. J. Appl. Mech., Trans. of the ASME 48 (Dec. 1981) 830–840.
Bhatt, J. J., M. M. Carroll, and J. F. Schatz. A Spherical Model Calculation for Volumetric Response of Porous Rocks. Paper No. 75-APMW-49, J. Appl. Mech. Trans. of the ASME (March 1975).
Gurson, A. L. Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I — Yield Criteria and Flow Rules for Porous Ductile Media. J. Eng. Materials and Tech., Trans. of the ASME (January 1977) 2–15.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Seaman, L., Gran, J., Curran, D.R. (1985). A Microstructural Approach to Fracture of Concrete. In: Shah, S.P. (eds) Application of Fracture Mechanics to Cementitious Composites. NATO ASI Series, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5121-1_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-5121-1_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8764-3
Online ISBN: 978-94-009-5121-1
eBook Packages: Springer Book Archive