Chloe Zhang
Concrete damaged plasticity theory is a continuum, plasticity-based damage model for concrete. It is used to analyse the behaviour of concrete and other quasi-brittle materials such as rock, mortar, and ceramics under cyclic and/or dynamic loading conditions. The theory assumes that the two main failure mechanisms are tensile cracking and compressive crushing of the concrete material. The evolution of the yield surface is controlled by two hardening variables linked to failure mechanisms under tension and compression loading, respectively. Concrete damaged plasticity theory has been the subject of extensive research in recent decades, with various mathematical models and constitutive theories being proposed to predict concrete behaviour, crack propagation, and microcrack coalescence.
| Characteristics | Values |
|---|---|
| Purpose | To provide a general capability for the analysis of concrete structures under cyclic and/or dynamic loading |
| Applicability | Concrete and other quasi-brittle materials such as rock, mortar, and ceramics |
| Failure mechanisms | Tensile cracking and compressive crushing |
| Behaviour under low confining pressure | Brittle |
| Behaviour under high confining pressure | Ductile with work hardening |
| Stiffness recovery effect | More pronounced when load changes from tension to compression |
| Modelling approach | Finite element modelling |
| Constitutive theory | Captures effects of irreversible damage associated with failure mechanisms under low confining pressures |
| Scalar damage elasticity equation | Includes initial (undamaged) elasticity matrix and scalar stiffness degradation variable |
| Tension stiffening | Allows for the simulation of reinforcement interaction with concrete |
| Novel stress decomposition | Decomposes tensile and compressive parts into pure biaxial shear and pure tensile/compressive biaxial stresses |
| Plasticity yield criteria | Includes non-associative plastic flow rule with multiple hardening functions |
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What You'll Learn
Concrete damaged plasticity model
Concrete damaged plasticity (CDP) theory is a continuum, plasticity-based damage model for concrete. The CDP model is used to analyse the behaviour of concrete structures under cyclic and/or dynamic loading. It is also suitable for the analysis of other quasi-brittle materials, such as rock, mortar and ceramics. The CDP model assumes that the two main failure mechanisms are tensile cracking and compressive crushing of the concrete material.
The CDP model is based on the models proposed by Lubliner et al. (1989) and by Lee and Fenves (1998). The model describes the elastic-plastic response of concrete in terms of effective stress and hardening variables. The Cauchy stress is calculated in terms of the stiffness degradation variable and the effective stress. The constitutive relations for the elastic-plastic response are decoupled from the stiffness degradation response, making the model attractive for an effective numerical implementation.
The evolution of the yield (or failure) surface is controlled by two hardening variables linked to failure mechanisms under tension and compression loading, respectively. These hardening variables are referred to as equivalent plastic strains in tension and compression. Microcracking and crushing in the concrete are represented by increasing values of the hardening variables, which control the evolution of the yield surface and the degradation of the elastic stiffness.
The stress-strain relations for the general three-dimensional multiaxial condition are given by the scalar damage elasticity equation. The previous expression for the scalar stiffness degradation variable, d, is generalized to the multiaxial stress case by replacing the unit step function with a multiaxial stress weight factor.
The post-failure behaviour for direct straining is modelled with tension stiffening, which allows for the definition of the strain-softening behaviour for cracked concrete. This behaviour also allows for the effects of the reinforcement interaction with concrete to be simulated. Tension stiffening is specified by means of a post-failure stress-strain relation or by applying a fracture energy cracking criterion.
An improved CDP model has been developed to simulate high-strength concrete under static and dynamic loading conditions. This model is based on recent studies that improved and developed the original CDP model in ABAQUS software. The stress-strain curves in compressive behaviour and tensile behaviour during the softening phase consider the effect of mesh size in the Finite Element model.
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Stiffness recovery effect
Concrete damaged plasticity (CDP) is a theory that models the behaviour of concrete under cyclic and/or dynamic loading. It is used to analyse concrete structures and other quasi-brittle materials such as rock, mortar, and ceramics. The theory is particularly useful for understanding the behaviour of concrete under low confining pressures, where concrete exhibits brittle behaviour and fails through cracking in tension and crushing in compression.
The stiffness recovery effect is an important aspect of the concrete damaged plasticity model, particularly under cyclic loading. This effect is also known as the "unilateral effect" and is more pronounced when the load changes from tension to compression. The stiffness recovery effect involves the closing of tensile cracks, which results in the recovery of compressive stiffness.
The concrete damaged plasticity model assumes that the reduction in elastic modulus is given in terms of a scalar degradation variable, which can range from zero (undamaged material) to one (fully damaged material). During the tensile and compressive phases of the cycle, the evolution equations of the equivalent plastic strains are generalized to the uniaxial cyclic conditions. If the compression stiffness recovery parameter is equal to one, the material fully recovers its initial, undamaged compressive stiffness. On the other hand, if the parameter is equal to zero, there is no stiffness recovery. Intermediate values result in partial stiffness recovery.
The stiffness recovery effect is influenced by the rate of straining and can be modelled in conjunction with a viscoplastic regularization of the constitutive equations to improve the convergence rate in the softening regime. The concrete damaged plasticity model also allows for user control of stiffness recovery effects during cyclic load reversals.
Overall, the stiffness recovery effect is a critical aspect of the concrete damaged plasticity theory, helping to understand and predict the behaviour of concrete under cyclic loading conditions.
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Shear-induced damage
Concrete damaged plasticity theory is a model for analysing the behaviour of concrete and other quasi-brittle materials, such as rock, mortar, and ceramics, under cyclic and/or dynamic loading. The theory is particularly concerned with the effects of irreversible damage associated with failure mechanisms that occur under low confining pressures.
The shear-normal decomposition procedure decomposes the stress tensor into two components: a shear stress tensor representing the shear state, and a normal stress tensor representing the tensile/compression state. This decomposition introduces four additional scalar damage parameters, which are responsible for the different damages induced under loading. The two traditional damage criteria (tensile/compressive) are further decomposed into four criteria: tensile/compressive shear and tensile/compressive pure.
The shear stress-shear strain curve of concrete is calibrated by experiments and is independent of the tensile and compressive stress-strain curves. Simplified shear stress-shear strain relationships are available to reduce complexity, but they can lead to an overestimation of the shear-bearing capacity in cases with large reinforcement ratios. The degradation of the mechanical performance of concrete is accounted for through shear, tension, and compression damage variables.
In summary, the concrete damaged plasticity model, with its shear-normal decomposition procedure, provides a comprehensive framework for understanding shear-induced damage in concrete and reinforced concrete structures. By considering the unique effects of shear stress and strain, this model improves our ability to design and analyse reinforced concrete structural components that are susceptible to shear failure.
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Constitutive modelling of concrete
Concrete damaged plasticity (CDP) theory is a constitutive model for concrete that can be used to analyse concrete structures under cyclic and/or dynamic loading. The theory is also suitable for the analysis of other quasi-brittle materials such as rock, mortar and ceramics. The CDP model captures the effects of irreversible damage associated with the failure mechanisms that occur in concrete under low confining pressures.
The constitutive model for concrete should be compatible with valid experimental information to achieve objectivity. Several mathematical models have been created to analyse the behaviour of concrete, considering factors such as inelasticity, time dependence, cracking, and the interactive effects between reinforcement and concrete.
The proposed elastic-plastic-hardening-softening constitutive model is based on plasticity theory, where the strain-hardening behaviour is modelled by stress-space plasticity, and the strain-softening behaviour is modelled by strain-space plasticity. The model can predict the work-hardening stress-strain behaviour of concrete, including brittle failure in tension, ductile behaviour in compression, hydrostatic sensitivities, and volumetric dilation under compressive loadings.
The constitutive model for concrete can be further developed and improved by coupling it with other models, such as elastic damage models or elastic-plastic constitutive laws, to capture the behaviour of reinforced concrete beams through numerical modelling.
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Concrete failure mechanisms
Concrete is a highly durable material used in construction. However, it can fail in several ways, and these failures can be attributed to various factors.
One of the most common failure mechanisms in concrete is cracking. Cracks can form due to temperature changes, with the concrete expanding in hot weather and contracting in cold weather. This temperature-related expansion and contraction cause pressure within the concrete slab, leading to cracks. Additionally, cracks can occur due to the presence of heavy loads, such as vehicles on a concrete bridge or parked in a concrete parking structure. These loads create compressive and tensile stresses that the concrete may not be able to withstand over time.
Another failure mechanism is crushing, which occurs when the concrete cannot withstand high compressive loads. This can happen when the concrete is subjected to high-impact loads, such as a vehicle collision with a column. The concrete may also crush under compression due to the consolidation and collapse of its microporous microstructure, especially under low confining pressures.
The composition and installation of concrete can also lead to failure. Imperfections in the design, such as faulty proportions of ingredients or misapplied designs, can weaken the concrete. Installation errors, such as improper mixing, curing, or transportation, can further compromise its integrity.
Environmental factors, such as weather and soil conditions, also play a significant role in concrete failure. Flooding and rain can cause the soil under the concrete to become soft and weak, leading to erosion and the formation of voids that cannot support the weight of the concrete. Additionally, human activities, such as moving and replacing soil during construction, can result in loose, poorly compacted soil that is more susceptible to water infiltration and subsequent expansion and contraction, causing concrete slabs to sink.
Concrete failure is a degenerative issue, and early intervention is crucial to prevent minor problems from escalating into major repair projects. Addressing the root cause of the failure with the help of professionals can ensure a safe and long-lasting solution.
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Frequently asked questions
The concrete damaged plasticity theory is a continuum, plasticity-based, damage model for concrete. It is used to analyse the behaviour of concrete structures under cyclic and/or dynamic loading.
The two main failure mechanisms of concrete are tensile cracking and compressive crushing.
The concrete damaged plasticity model is used to analyse the behaviour of concrete structures, particularly under cyclic and/or dynamic loading conditions. It can also be used to analyse other quasi-brittle materials such as rock, mortar and ceramics.
The concrete damaged plasticity model is not suitable for modelling the behaviour of concrete under large hydrostatic pressures. It is also limited in its ability to capture the behaviour of reinforced concrete beams.
