A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

In this work, a rate-dependent model for the simulation of quasi-brittle materials experiencing damage and randomness is proposed. The bi-scalar plastic damage model is developed as the theoretical framework with the damage and the plasticity opening for further developments. The governing physical reason of the material rate-dependency under relatively low strain rates, which is defined as the Strain Delay Effect, is modeled by a differential system. Then the description of damage is established by further implementing the rate-dependent differential system into the random damage evolution. To reproduce the evolution of plasticity under a variety of stress conditions, a multi-variable phenomenological plastic model is proposed and the description of plasticity is then formulated. An explicit integration algorithm is developed to implement the proposed model in the structural simulation. The model results are validated by a series of numerical tests that cover a wide variety of stress conditions and loading rates. The proposed model and algorithm offer a package solution for the nonlinear dynamic structural simulations.

[1]  Jean-François Dubé,et al.  Rate Dependent Damage Model for Concrete in Dynamics , 1996 .

[2]  O. Reynolds.  IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil , 1886, Philosophical Transactions of the Royal Society of London.

[3]  Ignacio Carol,et al.  Viscoplastic approach for rate-dependent failure analysis of concrete joints and interfaces , 2008 .

[4]  Frank J. Vecchio,et al.  Effects of Shear Mechanisms on Impact Behavior of Reinforced Concrete Beams , 2009 .

[5]  Xiaodan Ren,et al.  Stochastic damage model for concrete based on energy equivalent strain , 2009 .

[6]  Jie Li,et al.  Dynamic fracture in irregularly structured systems. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  R. Drathi.  Impact Resistance of Concrete Structures , 2015 .

[8]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .

[9]  S. Sloan,et al.  Refined explicit integration of elastoplastic models with automatic error control , 2001 .

[10]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[11]  J. Takeda,et al.  DEFORMATION AND FRACTURE OF CONCRETE SUBJECTED TO DYNAMIC LOAD , 1972 .

[12]  James O. Jirsa,et al.  Behavior of concrete under compressive loadings , 1969 .

[13]  René de Borst,et al.  Some recent issues in computational failure mechanics , 2001 .

[14]  T. Meinders,et al.  Viscoplastic regularization of local damage models: revisited , 2013 .

[15]  Jeeho Lee,et al.  Plastic-Damage Model for Cyclic Loading of Concrete Structures , 1998 .

[16]  S. H. Perry,et al.  Compressive behaviour of concrete at high strain rates , 1991 .

[17]  Rui Faria,et al.  An energy release rate-based plastic-damage model for concrete , 2006 .

[18]  Xiaodan Ren,et al.  Behavior of High-Performance Concrete Under Uniaxial and Biaxial Loading , 2008 .

[19]  L. J. Sluys,et al.  Viscoplasticity for instabilities due to strain softening and strain‐rate softening , 1997 .

[20]  Oral Büyüköztürk,et al.  Concrete in Biaxial Cyclic Compression , 1984 .

[21]  Rhj Ron Peerlings,et al.  Some observations on localisation in non-local and gradient damage models , 1996 .

[22]  Dusan Krajcinovic,et al.  A micromechanical damage model for concrete , 1986 .

[23]  Thomas T. C. Hsu,et al.  Unified Theory of Concrete Structures: Hsu/Unified Theory of Concrete Structures , 2010 .

[24]  Billie F. Spencer,et al.  Stochastic Damage Model for Brittle Materials Subjected to Monotonic Loading , 1996 .

[25]  J. Ju,et al.  On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects , 1989 .

[26]  Joseph W. Tedesco,et al.  Strain-rate-dependent constitutive equations for concrete , 1998 .

[27]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .

[28]  Ted Belytschko,et al.  Wave propagation in a strain-softening bar: Exact solution , 1985 .

[29]  L. Javier Malvar,et al.  Review of Strain Rate Effects for Concrete in Tension , 1998 .

[30]  J. Klepaczko,et al.  An experimental method for dynamic tensile testing of concrete by spalling , 2001 .

[31]  Joško Ožbolt,et al.  Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads , 2011 .

[32]  P. R. Sparks,et al.  The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression , 1973 .

[33]  Antonio Huerta,et al.  An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model , 2006 .

[34]  J. W. Tedesco,et al.  Effects of Strain Rate on Concrete Strength , 1995 .

[35]  Xiaodan Ren,et al.  A unified dynamic model for concrete considering viscoplasticity and rate-dependent damage , 2013 .

[36]  L. Freund.  Crack propagation in an elastic solid subjected to general loading—III. Stress wave loading , 1973 .

[37]  Xiaodan Ren,et al.  Triaxial Behavior of Concrete Subjected to Dynamic Compression , 2013 .

[38]  Scott W. Sloan,et al.  Substepping schemes for the numerical integration of elastoplastic stress–strain relations , 1987 .

[39]  J. Oliver,et al.  A strain-based plastic viscous-damage model for massive concrete structures , 1998 .

[40]  Yi-Lung Mo,et al.  Unified Theory of Concrete Structures , 2010 .

[41]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[42]  P. Perzyna.  Fundamental Problems in Viscoplasticity , 1966 .

[43]  Dongming Yan,et al.  Dynamic properties of concrete in direct tension , 2006 .