Biaxial Strength Envelope Research Articles

Numerical prediction of beam capacity using the new constitutive model based on concrete biaxial behavior

The biaxial strength of concrete exhibits intriguing nonlinearity and scattering, posing challenges to the assessment of building structural safety. Experiments have confirmed that biaxial strength envelopes can manifest concave, quasi-linear, and convex shapes. Despite various empirical formulas being proposed to describe this behavior, they cannot be applied to finite element simulations due to the absence of a constitutive perspective. To study the mechanisms forming the shape of strength envelopes, a novel three-invariant model constitutive model is proposed, which reveals the characteristics of the envelopes resulting from the coupling effect of hydrostatic pressure and Lode angle. By adjusting the model parameters, it effectively describes concave, quasi-linear, and convex envelopes. The model's accuracy and compatibility were validated against experimental data spanning various concrete types, with compression strengths ranging from 19.29 to 96.5 MPa and tension-compression ratios form 0.056 to 0.095. To investigate how biaxial strength impacts the capacity of beams, numerical experiments were conducted on notched and intact beams based on the proposed model. The results underscored that beams prepared using concrete with convex envelopes exhibited higher capacity compared to those with quasi-linear envelopes. Therefore, conducting biaxial tension-compression experiments is recommended to accurately evaluate beam bearing capacity. The proposed model is expected to have further applications in the safety evaluation of building structures.

Development of a poly-axial platen for testing true-triaxial behavior of rocks

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ1 ≠ σ2 ≠ σ3 with special case of σ3 = 0 and σ1, σ2 ≠ 0 at its boundary, where σ1, σ2, σ3 are major, intermediate, minor principal stress, respectively. The conventional triaxial testing does not represent the actual in situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of a biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ1 = σ2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea sandstone specimens with other biaxial–triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimens of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimens. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For the true-triaxial strength envelope, we found the three-dimensional (3D) failure criterion to be a good fit with R2 of 0.964.

CONSTITUTIVE MODEL FOR ENGINEERED CEMENTITIOUS COMPOSITES UNDER BIAXIAL COMPRESSION

Based on the Darwin-Pecknold method considering the biaxial behavior of concrete, a two-dimensional constitutive model for engineered cementitious composites (ECC) is developed, taking into account the nonlinear mechanical behavior and the variation of compressive strength under biaxial compression. A nonlinear stress-equivalent uniaxial strain relationship is established after introducing the equivalent uniaxial strain in two orthotropic directions caused by biaxial loading to account for the biaxial nonlinear behavior of ECC. A biaxial strength envelope is used to determine the compressive strengths of the two directions. An explicit numerical algorithm of the model is derived, and user-defined material subroutine UMAT containing the numerical algorithm is coded and implemented in finite element procedure ABAQUS v6.14. The efficiency of the proposed model is validated through numerical simulations of two sets of ECC specimens with different mix proportions under biaxial compression loading at various biaxial stress ratios. The stress-strain curves and the compressive strengths in the major compressive stress direction obtained by numerical simulations are in a good agreement with the experimental results. It is shown that the proposed constitutive model can effectively predict the biaxial nonlinear mechanical behavior and the failure strengths of ECC under biaxial compression.

Inelastic orthotropic model for blast analysis of RC slabs

An improved numerical model for the nonlinear analysis of reinforced concrete (RC) slabs subjected to blast loadings is proposed. Instead of using a plastic-based model, which has been popularly used in the blast analyses but has the limitation in describing the strain-softening behaviors, a strain-rate-dependent orthotropic constitutive model that directly determines the stress state from the stress-strain relations defined from the biaxial strength envelope is considered. To minimize the mesh-dependency of FE analysis, in advance, the ultimate strains in the stress-strain relations are determined on the basis of the fracture energy concept, and additional considerations for the strain rate effect are implemented. Moreover, to cope with the development of large deformation concentrated within the plastic hinge region after yielding of reinforcement, the bond-slip effect is also taken into consideration by introducing modified bending stiffness, which is determined from the energy conservation law. Finally, to verify the validity of the proposed numerical model, correlation studies between the numerical results and experimental data for RC slabs are conducted.

Optimization of Theory of Failures of Multi-directional Composite Laminates: AHP approach

The composite materials have been increasingly used in the various field of engineering over the past few decades due to their excellent engineering characteristics. Henceforth, the efforts have been made for the development of reliable theories to examine the failure strength of multidirectional composite laminates. In this research, the analysis has been made among the different failure theories for composite materials. The comparison of failure theories is based on test cases which include stress–strain curves for multi-directional laminates, biaxial strength envelopes for multi-directional laminates, loaded under uniaxial or biaxial conditions. The predictions and experimental results have been analyzed, to identify the strengths and weaknesses of each failure theory. An effort has been made to provide designers with a ranking of the overall effectiveness of each failure theory. A Multi-Criterion Decision making (MCDM) tool has been used to analyze the theories which will be a readily available tool for the readers/researchers to select the appropriate theory for a design situation.

Assessment of Theories of Failure for Multi-Directional Composites Laminates: A Fuzzy - AHP Approach

In this research, the analysis has been made amongst the different 'theories of failure' for composite materials. All theories which include bi-axial strength envelopes and stress–strain curves for a range of multi-directional laminates, loaded under uni-axial or bi-axial conditions.The predictions and experimental data have been analyzed, to identify the strengths and weakness, together with a ranking of the overall effectiveness of each theory, which has been made by the AHP-MCDM tool to facilitate the reader to select the best theory for given design situation.

Evaluation of directional mesh bias in concrete fracture simulations using continuum damage models

In the present comparative study, we investigate the influence of directional mesh bias on the results of failure simulations performed with isotropic and anisotropic damage models. Several fracture tests leading to curved crack trajectories are simulated on different meshes. The isotropic damage model with a realistic biaxial strength envelope for concrete is highly sensitive to the mesh orientation, even for fine meshes. The sensitivity is reduced if the definition of the damage-driving variable (equivalent strain) is based on the modified von Mises criterion, but the corresponding biaxial strength envelope is not realistic for concrete. The anisotropic damage models used in this study capture reasonably well arbitrary crack trajectories even if the biaxial strength envelope remains close to typical experimental data. Their superior performance can be at least partially attributed to their ability to capture dilatancy under shear, which is revealed by a comparative analysis of the behavior of individual models under shear with restricted or free volume expansion.

Elasto-damage Model for High Strength Concrete Subjected to Multiaxial Loading

An effective compliance matrix Č is proposed to model the behavior of concrete based on phenomenological evidence and physical insight. Three parameters α, β, and γ are introduced in the effective compliance matrix Č. α and β are introduced to model the different behavior of concrete in tension and compression, while the third parameter γ is introduced to account for volumetric change. The predictive capability of the proposed elasto-damage model for uniaxial and multiaxial stress paths is investigated for uniaxial compression, biaxial compression, triaxial compression, uniaxial tension, and tension—compression— compression. The simulative capability of the model to capture the phenomenological behavior of concrete such as strain softening, stiffness degradation, biaxial strength envelope, volumetric dilatation, different behavior in tension and compression, and gain in strength under increasing confinement is reflected. The predicted results correlate well with the available experimental data.

Micro‐mechanical damage and rough crack closure in cementitious composite materials

AbstractA micro‐mechanics based damage model is presented which uses the solution of an elastic body with penny‐shaped cracks. The major new aspect of the work is the inclusion of a rough crack closure component in the model. The model uses a damage‐surface, described in terms of transformed strain components. Inelastic strain components in each direction are computed by considering the total directional strains on an equivalent band of elastic material and then removing the elastic component. Details of the model implementation in a Mathcad sheet are given. The results from a series of single point simulations are given for uniaxial and biaxial tension and compression stress/strain paths. Each path is computed with the full model and with a damage only version of the model which does not simulate crack closure effects. It is shown that the incorporation of the rough contact component allows the model to reproduce dilatant post‐peak behaviour in compression and to simulate, with reasonable accuracy, the shape of the biaxial strength envelope for cementitious composite materials. Copyright © 2006 John Wiley & Sons, Ltd.

Modeling of Prestressed Concrete-Filled Circular Composite Tubes Subjected to Bending and Axial Loads

This paper presents a nonlinear model used to predict the load–deflection responses and axial load–moment interaction curves of pretensioned concrete-filled circular composite tubes. The model accounts for the prestressing effect, which not only improves serviceability, but also activates a confinement mechanism of the concrete core restrained by the tube. The enhanced performance of confined concrete is considered. In the compression side, the tube is modeled as a biaxially loaded membrane, subjected to longitudinal compressive and hoop tensile stresses, and failure is detected using the Tsai–Wu biaxial strength envelope. Progressive failure of layers of fibers at various directions within the tube leads to stiffness degradation, and is modeled using the classical lamination theory–ultimate laminate failure approach. The model is verified using experimental results and used in a parametric study to evaluate the effects of prestress level, amount and material type of prestressed reinforcement, and thickne...

A comparison of the predictive capabilities of current failure theories for composite laminates, judged against experimental evidence

This paper draws together the results from a co-ordinated study, known as the World-Wide Failure Exercise, whereby 12 of the leading theories for predicting failure in composite laminates have been tested against experimental evidence. The comparison has been effected through 14 carefully selected test cases, which include biaxial strength envelopes for a range of unidirectional and multi-directional laminates, and stress–strain curves for a range of multi-directional laminates, loaded under uniaxial or biaxial conditions. The predictions were provided by the originators of the theories, not by third parties, and were made without access to the experimental results beforehand. The predictions and experimental data have been compared in a systematic and detailed manner, to identify the strengths and weaknesses of each theory, together with a ranking of the overall effectiveness of each theory. Careful reading of this analysis and study of the figures provided will inform the reader when selecting an appropriate failure theory for use in a given design situation. It will also provide a qualitative assessment of the likely accuracy and reliability of the prediction in a given circumstance.