Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

Bažant, Zdeněk P.; Caner, Ferhun C.; Carol, Ignacio; Adley, Mark D.; Akers, Stephen A.

doi:10.1061/(asce)0733-9399(2000)126:9(944)

Cited by 252 publications

(182 citation statements)

References 34 publications

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“…Numerous advantages of microplane models were reviewed in and Ba zant et al (2000). One advantageous feature that has generally been overlooked in constitutive modeling but that should be emphasized is that the microplane model automatically captures the vertex effect, i.e., the fact that deformation increments that are parallel to the current loading surface in the stress space are not elastic but inelastic, as experimentally demonstrated in .…”

Section: Introductionmentioning

confidence: 99%

Microplane Model M7 for Plain Concrete. I: Formulation

2013

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Mathematical modeling of the nonlinear triaxial behavior and damage of such a complex material as concrete has been a long-standing challenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit finite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. The microplane models, which use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions among phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which achieves this goal much better than the previous versions M1-M6 developed at Northwestern University since 1985. The basic mathematical structure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the frictional slip regime. Given that the volumetric-deviatoric (V-D) split of strains is inevitable for distinguishing between compression failures at low and high confinement, the key idea is to apply the V-D split only to the microplane compressive stress-strain boundaries (or strain-dependent yield limits), the sum of which is compared with the total normal stress from the microplane constitutive relation. This avoids the use of the V-D split of the elastic strains and of the tensile stress-strain boundary, which caused various troubles in M3-M6 such as excessive lateral strains and stress locking in far postpeak uniaxial extension, poor representation of unloading and loading cycles, and inability to represent high dilatancy under postpeak compression in lower-strength concretes. Moreover, the differences between high hydrostatic compression and compressive uniaxial strain are accurately captured by considering the compressive volumetric boundary as dependent on the principal strain difference. The model is verified extensively in the companion paper.

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Section: Introductionmentioning

confidence: 99%

Microplane Model M7 for Plain Concrete. I: Formulation

2013

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“…In the first version, the microplane model of concrete was only devised for tensile fracturing, but now it has been updated to the fourth version which can characterize the complicated nonlinear triaxial behavior as well as the deformation behavior under the cyclic load. The results of the numerical analysis for basic loading types with the microplane model have been compared with many actual test results and it is shown that microplane models can characterize the responses of concrete under different loading types [2] .…”

Section: Microplane Constitutive Model For Concretementioning

confidence: 99%

“…The traditional elasto-plastic-fracture constitutive models for concrete are macroscopic models. Although great success has been reached in the past, the macroscopic models now seem to have entered a period of diminishing returns, in which a great effort yields only little improvement [2] . When the concrete is under complicated stress condition, these models often can't give satisfying performance for the concrete material.…”

Section: Microplane Constitutive Model For Concretementioning

confidence: 99%

“…By integrating over the all the spatial directions, the microplane model can satisfy the tensor invariant requirement automatically on the macroscopic and conceptual simplicity is achieved. Due to the research work of P. Bazant et al [2,3,4,5] , there have been much progress on microplane model during the last 20 years. In the first version, the microplane model of concrete was only devised for tensile fracturing, but now it has been updated to the fourth version which can characterize the complicated nonlinear triaxial behavior as well as the deformation behavior under the cyclic load.…”

Section: Microplane Constitutive Model For Concretementioning

confidence: 99%

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Nonlinear FE Model for RC Shear Walls Based on Multi-Layer Shell Element and Micro-Plane Constitutive Model

Miao

Lü

Jiang

et al. 2006

Computational Methods in Engineering &Amp; Science

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Nonlinear simulations for structures under disasters have been widely focused on in recent years. However, precise modeling for the nonlinear behavior of reinforced concrete (RC) shear walls, which are the major lateral-force-resistant structural member in high-rise buildings, still has not been successfully solved. In this paper, based on the principles of composite material mechanics, a multi-layer shell element model is proposed to simulate the coupled in-plane/out-plane bending and the coupled in-plane bending-shear nonlinear behaviors of RC shear wall. The multi-layer shell element is made up of many layers with different thickness. And different material models (concrete or rebar) are assigned to various layers so that the structural performance of the shear wall can be directly connected with the material constitutive law. And besides the traditional elasto-plastic-fracture constitutive model for concrete, which is efficient but does not give satisfying performance for concrete under complicated stress condition, a novel concrete constitutive model, referred as microplane model, which is originally proposed by Bazant et al., is developed to provide a better simulation for concrete in shear wall under complicated stress conditions and stress histories. Three walls under static push-over load and cyclic load were analyzed with the proposed shear wall model for demonstration. The simulation results show that the multi-layer shell elements can correctly simulate the coupled in-plane/out-plane bending failure for tall walls and the coupled in-plane bending-shear failure for short walls. And with microplane concrete constitutive law, the cycle behavior and the damage accumulation of shear wall can be precisely modeled, which is very important for the performance-based design of structures under disaster loads.Keywords: shear wall, nonlinear analysis, microplane, finite element, multi-layer shell element INTRODUCTION:Nonlinear simulations for structures under disasters have been widely focused on in recent years. However, precise modeling for the nonlinear behavior of reinforced concrete (RC) shear walls, which are the major lateral-force-resistant structural member in high-rise buildings, still has not been successfully solved. As the cross section of the shear wall member is much bigger than that of the beam and column member, its deformation behavior under the lateral load is more complicated and the research has focused on the nonlinear analysis model for shear wall at home and abroad until now. In this paper, based on the principles of composite material mechanics, a multi-layer shell element model is proposed to simulate the coupled in-plane/out-plane bending or the coupled in-plane bending-shear nonlinear behaviors of RC shear wall. At the element level, the model uses the shell element that is made up of multiple layers with different thickness and different material models (concrete or rebar) are assigned to various layers. Since the model relates the nonlinear behaviors of the shear wall elemen...

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“…The model rests on two basic ideas: ͑1͒ describe these microstructural phenomena by a constitutive relation expressed not in terms of stress and strain tensors of the macroscopic continuum, but in terms of stress and strain vectors acting on planes of all possible orientations at a given point of the continuum; and ͑2͒ use a variational principle to relate the microplane vectors ͑the micro͒ to the continuum tensors ͑the macro͒. Despite increased computer time requirements, this approach has many advantages, described in detail in Bažant et al ͑2000a͒.…”

Section: Background On Microplane Approach and On Models M4 And M5mentioning

confidence: 99%

Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

et al. 2007

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Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete ͑FRC͒ are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening-softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress-strain curves, and on multiaxial failure envelopes.

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Microplane Model M4 for Concrete. I: Formulation with Work-Conjugate Deviatoric Stress

Cited by 252 publications

References 34 publications

Microplane Model M7 for Plain Concrete. I: Formulation

Microplane Model M7 for Plain Concrete. I: Formulation

Nonlinear FE Model for RC Shear Walls Based on Multi-Layer Shell Element and Micro-Plane Constitutive Model

Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

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