Constitutive model with strain softening

Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ 85721, U.S.A.
International Journal of Solids and Structures 01/1987; DOI: 10.1016/0020-7683(87)90076-X

ABSTRACT 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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    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.Dans le cas de roches naturelles incluant des vides ou des pores, le comportement en déformation est fortement affecté par la variation de porosité. Dans cet article, les caractéristiques d'écrouissage et d'anti-écrouissage, en relation avec les vides et les variations de volume, sont investiguées à l'aide d'une approche statistique basée sur les dommages. L'effet des vides et des variations de volume sur le comportement de la roche est analysé premièrement par la détermination de la porosité, ensuite un modèle de dommages associés est développé. Par la suite, une équation d'évolution statistique, qui décrit l'influence du seuil de dommage sur les conditions de propagation des dommages dans la roche, est formulée selon les mesures de résistance mésoscopique des éléments. Un modèle constitutif statistique de dommages, qui reflète les comportements en écrouissage et anti-écrouissage de roches chargées en compression triaxiale conventionnelle, est développé, ainsi qu'une méthode permettant de déterminer les paramètres du modèle. Les résultats obtenus à l'aide du modèle proposé sont comparés aux résultats expérimentaux. Pour terminer, plusieurs aspects du modèle constitutif qui influencent le comportement des roches sont discutés de façon particulière.
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    Procedia Engineering. 28:351–355.

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