# zbMATH — the first resource for mathematics

A comparison of two microplane constitutive models for quasi-brittle materials. (English) Zbl 1228.74069
Summary: We present a comparison of two microplane constitutive models. The basis of the microplane constitutive models are described and the adopted assumptions for the conception of these models are discussed, with regard to: decomposition of the macroscopic strains into the microplanes, definition of the microplane material laws, including the choice of variables that control the material degradation, and homogenization process to obtain the macroscopic quantities. The differences between the two models, with respect to the employed assumptions, are emphasized and expressions to calculate the macroscopic stresses are presented. The models are then used to describe the behavior of quasi-brittle materials by finite element simulations of uniaxial tension and compression and pure share stress tests. The results of the simulations permit to compare the capability of the models in describing the post critical strain-softening behavior, without numerically induced strain localization.

##### MSC:
 74R10 Brittle fracture
Full Text:
##### References:
 [1] Mohr, O., Welche umstande bendingen der bruch und der elastizittsgrenze des materials, Z. vereins deutscher ingenieure, 44, 1-12, (1900) [2] Taylor, G.I., Plastic strain in metals, J. inst. metals, 62, 307-324, (1938) [3] Bazant, Z.P.; Gambarova, P.G., Crack shear in concrete: crack band microplane model, J. struct. eng., 110, 9, 2015-2035, (1984) [4] J.S. Fuina, Formulações de Modelos Constitutivos de Microplanos para Contínuos Generalizados, Ph.D. Thesis (in portuguese), UFMG - Federal University of Minas Gerais, Belo Horizonte, Brazil, 2009. [5] Bazant, Z.P.; Prat, P.C., Microplane model for brittle-plastic material: I - theory, J. eng. mech. (ASCE), 114, 10, 1672-1688, (1988) [6] Ozbolt, J.; Li, Y.; Kozar, I., Microplane model for concrete with relaxed kinematic constraint, Int. J. solids struct., 38, 2683-2711, (2001) · Zbl 1049.74733 [7] Leukart, M.; Ramm, E., Identification and interpretation of microplane material laws, J. eng. mech. (ASCE), 132, 3, 295-305, (2006) [8] Ozbolt, J.; Bazant, Z.P., Microplane model for cyclic triaxial behavior of concrete, J. eng. mech. (ASCE), 118, 7, 1365-1386, (1992) [9] Yang, Y.B.; Shieh, M.S., Solution method for nonlinear problems with multiple critical points, Aiaa j., 28, 12, 2110-2116, (1990) [10] Walsh, S.D.C.; Tordesillas, A., A thermomechanical formulation of finite element schemes for micropolar continua, (2004), Dept. Mathematics & Statistics, The University of Melbourne Melbourne, Australia · Zbl 1064.74048 [11] Carol, I.; Bazant, Z.P., New explicit microplane model for concrete: theoretical aspects and numerical implementation, Int. J. solids struct., 29, 1173-1191, (1992) [12] Carol, I.; Jirasek, M.; Bazant, Z.P., A thermodynamically consistent approach to microplane theory. part I. free energy and consistent microplane stress, Int. J. solids struct., 38, 2921-2931, (2001) · Zbl 0999.74012 [13] Peerlings, R.H.J.; de Borst, R.; Brekelmans, W.A.M.; Geers, M.G.D., Gradient-enhanced damage modelling of concrete fracture, Mech. cohesive-frict. mater., 3, 323-342, (1998) · Zbl 0938.74006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.