Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 139, Issue -, Pages 250-269Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2018.02.004
Keywords
Damage; Thermodynamics; Quasi-brittle failure; Concrete; Cyclic loading; Microcracks closure-reopening; Unilateral effects
Categories
Funding
- National Key R&D Program of China [2017YFC0803300]
- National Natural Science Foundation of China [51678246]
- State Key Laboratory of Subtropical Building Science [2016KB12]
- Fundamental Research Funds for the Central University [2015ZZ078]
- Scientific/Technological Project of Guangzhou [201607020005]
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The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant importance to the nonlinear responses of engineering structures under cyclic loading, e.g., earthquake excitations. Based on our previous work (Cervera et al., 1995; Faria et al., 1998; Wu et al., 2006) this work addresses a novel thermodynamically consistent unilateral damage model for concrete. In particular, the positive/negative projection (PNP) of the effective stress tensor and the additive bi-scalar damage constitutive relation are maintained owing to the conceptual simplicity and computational efficiency. It is found that the classical PNP widely adopted in the literature is not optimal for this damage model, since the resulting stiffness is not always of major symmetry. Consequently, a well-defined free energy potential does not exist in general cases and the model cannot be cast into the framework of thermodynamics with internal variables. Furthermore, the damage induced anisotropy cannot be captured, exhibiting excessive lateral deformations under uniaxial tension. To overcome the above issues, a novel PNP, variationally interpreted as the closest point projection of the effective stress in energy norm, is proposed with closed-form solution. With the novel PNP, the secant stiffness tensor of the proposed unilateral damage model always possesses major symmetry and exhibits orthotropic behavior under uniaxial tension and mixed tension/compression. The corresponding thermodynamics framework is then given, resulting in an energy release rate based rounded-Rankine type damage criterion appropriate for tensile failure in quasi-brittle solids. Several numerical examples of single-point verifications and benchmark tests are presented. It is demonstrated that the proposed model is capable of characterizing localized failure of concrete under proportional and non-proportional static loading, as well as the MCR effects under seismic cyclic loading. (C) 2018 Elsevier Ltd. All rights reserved.
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