Constitutive model with strain softening

Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ 85721, U.S.A.
Mathematical and Computer Modelling (Impact Factor: 1.41). 01/1987; 23(6):733-750. DOI: 10.1016/0020-7683(87)90076-X


The aim or this paper is to propose a simple yet realistic model for the mechanical behavior of geologic materials such as concrete and rock. The effect of structural changes in such materials is addressed and incorporated in the theory through a tensor form of a damage variable. It is shown that formation of damage is responsible for the softening in strength observed in experiments, for the degradation of the elastic shear modulus, and for induced anisotropy. A generalized plasticity model is incorporated for the so-called topical or continuum part of the behavior, whereas the damage part is represented by the so-called stress-relieved behavior. The parameters required to define the model are identified and determined from multiaxial testing of a concrete. The predictions are compared with observed behavior for a number of stress paths. The model shows very good agreement with the observed response.

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    • "In general, a determination of the entire stress–strain relationship of rock is the most effective manner (Bieniawski 1967a, 1967b, 1967c) of exploring the deformation process and failure mechanism. Investigations performed over the past four decades in this field have merited extensive study (e.g., Cook 1965; Jaeger and Cook 1969; Wawersik and Fairhurst 1970; Hudson et al. 1972; Charles 1976; Hoek and Brown 1980; Desai and Faruque 1984; Kaiser et al. 1985; Frantziskonis and Desai 1987; Kazakidis and Diederichs 1993; Martin 1997). These valuable contributions set the foundation for a comprehensive description of the stress–strain behavior of rocks. "
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    ABSTRACT: With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.
    Canadian Geotechnical Journal 07/2010; 47(8):857-871. DOI:10.1139/T09-148 · 1.33 Impact Factor
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    • "UTILIZATION OF THE HARDENING MODEL FOR SOFTENING RESPONSE DESCRIPTION In DSC, RI can be defined or described by linear elastic, nonlinear elastic, plasto-elastic, or any other suitable model (Erkens, 2002). FA can be defined as a more fragile RI or, in other words, can be supposed to bear loadings like RI does, with the same kind of stress-strain relationship but with a much lower ability (Desai, 2001; Frantziskonis, 1987a). The stress tensor of AR is given by "
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    ABSTRACT: Mesoscopic characteristics of a clayey soil specimen subjected to macroscopic loading are examined using a medical-use computerized tomography (CT) instrument. Disturbed state concept (DSC) theory is based on the utilization of the hardening model. DSC indirectly describes material behavior by claiming that the actual response of the material is expressed in terms of the relative intact (RI) response and the fully adjusted (FA) response. The occurrence of mesoscopic structural changes of material has similarities with the occurrence of a macroscopic response of the material under loadings. In general, the relative changing value of a softening material is three to five times more than that of a hardening material. Whether special zones exist or not in a specimen cross section does not affect the following conclusion: hardening material and softening material show mechanical differences with CT statistical indices values prominently changing, and the change is related to the superposing of a disturbance factor. A new disturbance factor evolution function is proposed. Thus, mesoscopic statistical indices are introduced to describe macroscopic behavior through the new evolution function. An application of the new evolution function proves the effectiveness of the amalgamation of a macroscopic and a mesoscopic experimental phenomenon measurement methods.
    Journal of Zhejiang University - Science A: Applied Physics & Engineering 08/2008; 9(9):1167-1175. DOI:10.1631/jzus.A0720062 · 0.88 Impact Factor
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    • "A procedure for determining the elasticity, plasticity, and damage constants is given in ref.[7]. The values of the constants used for the present analysis are also given in ref.[7]. These constants were determined from test results for concrete[22], where cubical specimens of 100 mm size were tested under multiaxial load. "
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    ABSTRACT: A new mechanics based approach is proposed for scale effects and instabilities on borehole problems. In borehole types of structural systems, two types of instabilities can take place. The first is due to surface degradation growth and results into spalling of layers at the hole wall. The second is due to damage progression, and results into globally unstable response of the structure. The hole size has been found experimentally to be an important parameter in breakout instability initiation. Laboratory size holes may overestimate instability initiation properties by a large factor. At the same time, material properties such as peak stress depend largely on the size and shape of a specimen subjected to uniaxial or triaxial compression. This work attempts to incorporate size and scale effects into the instability initiation conditions. The important task of transferring information from laboratory experiments to actual large scale engineering problems is analysed and discussed. The potential of the theory is demonstrated. The need for further experimental and theoretical work is identified.
    Engineering Fracture Mechanics 01/1991; 39(2):377-389. DOI:10.1016/0013-7944(91)90052-3 · 1.77 Impact Factor
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