Simple Constitutive Model Research Articles

A finite element approach for predicting the full resistance profile of a spudcan deeply penetrating in dense sand overlying clay

This paper presents a finite element approach to calculate the full resistance profile of a spudcan deeply penetrating in dense sand overlying clay, in which a potential for an installing spudcan to experience a sudden uncontrolled punch-through failure exists. A modified Mohr-Coulomb model characterized by incorporating a four-phase variation of the mobilized strength and dilation parameters with an equivalent accumulated plastic strain is developed and tested for the overlying dense silica sand. An extended Tresca model is used for the strain softening of the underlying clay. A series of large deformation finite-element (LDFE) analyses are carried out, varying the strength and dilation parameters as well as the spudcan geometries. A fairly good performance of the present approach is verified by validating against groups of centrifuge tests data, allowing the numerical study to be extended parametrically. The four-phase variation of the mobilized strength and dilation parameters involved in the progressive failure of the upper dense sand is parametrically studied and extended to cover the range of sand relative densities that are of practical interest. Additionally, comparisons with the typical existing LDFE analyses using both simple and sophisticated constitutive models are carried out. It shows that the present approach performs fairly well to calculate the full resistance profile of a spudcan deeply penetration in both thin and thick dense sand overlying clay, especially the peak and post-peak resistance, within around 5% of the corresponding centrifuge tests results.

Using a state-dependent constitutive model in strain wedge method for laterally loaded piles in sand

Strain Wedge Method is an effective technique for the analysis of laterally loaded flexible piles in sand. In this method, the three-dimensional soil-pile interaction problem is reduced to the problem of one-dimensional beam on elastic foundation. Various modifications have been applied to the conventional Strain Wedge Method to promote its predictive capacity for different problems. Nevertheless, in the existing Strain Wedge Methods, because the impact of soil state on the stress-strain-strength behavior of granular soils is ignored, multiple calibrations for a wide domain of soil densities are required. To overcome this drawback, a simple but versatile state-dependent constitutive model is implemented in the Strain Wedge Method. It is shown that the modified Strain Wedge Method can effectively simulate the response of laterally loaded model piles embedded in sands of loose, medium, and dense states using a single set of parameters.

Numerical and Experimental Analysis of Damage Evolution and Martensitic Transformation in AISI 304 Austenitic Stainless Steel at Cryogenic Temperature

In this research, ductile damage development and martensitic strain-induced phase transformation in plastic behavior of AISI 304 austenitic stainless steels at cryogenic temperatures are investigated. Nonlinear behavior of hardening and damage evolution could be observed in two-phase material as the result of strain-induced phase transformation. A simplified constitutive model for monotonic loadings, combining the effects of phase transformation and isotropic damage evolution has been introduced. Numerical analysis via implementing the model by means of a user subroutine UMAT in Abaqus/Standard is carried out. In addition, experiments including loading-unloading tensile test and X-ray diffraction test at cryogenic temperature 77[Formula: see text]K have been conducted to identify the parameters of the model and to compare with numerical results.

Predicted and observed settlements induced by the mechanized tunnel excavation of metro line C near S. Giovanni station in Rome

This paper deals with the effects induced by the mechanized excavation of Rome metro line C in the area of an old masonry building, the Carducci school. Class A settlements predictions are obtained performing full 3D soil-tunnel-structure interaction numerical analyses, using a simple elastic perfectly plastic soil constitutive model. The developed model realistically simulates the main excavation and construction features influencing the induced settlements, such as tunnel advancement, front pressure, TBM-EPB design (shield’s weight, overcut and conicity), tail void grouting and grout hardening over time. The measured settlements are reported and compared with the results of numerical analyses performed before (class A prediction) and after tunnelling; the latter carried out to implement in the model the front pressure and TBM conicity actual values, both higher than assumed in the design. Since before the excavation the foundations were reinforced with micropiles, and these were not modelled, the comparison between monitoring data and numerical predictions is limited to the settlements outside the building. Monitoring data are also compared with further analyses conducted using small-strain soil stiffness and using a constitutive model able to reproduce the non-linearity of soil behavior (Hardening Soil). The different predictions of the two models are investigated analyzing the vertical strains distributions and the stress paths around the tunnel. Finally, a reasonable interpretation for the remaining differences between numerical results and field data is proposed and used to back-analyze the settlements, obtaining a satisfactory agreement. The results confirm the effectiveness of the proposed 3D numerical approach, associated with relatively simple soil constitutive models, as a tool to predict tunnelling-induced settlements both in the design and the construction phase, independently of the geotechnical context.

A simple 3D elastoplastic constitutive model for soils based on the characteristic stress

This paper presents a direct method to establish a 3D elastoplastic constitutive model for soils based on the characteristic stress. In the established model, a new yield function is first formulated through an interpolation function in the characteristic stress space. A hardening parameter that suits for monotonic and cyclic loading conditions is established by introducing the concept of the subloading surface. Then, a 3D constitutive model for soils is established by combining the previously proposed plastic potential function. Only seven material parameters with clear physical meanings are included in the proposed 3D elastoplastic model. The deformation behaviours of soils under monotonic and cyclic loading conditions and the critical state properties under true triaxial stress conditions are analysed on the basis of the presented model. The capability of the model is verified by the comparisons between the model responses and the test results of soils under the 3D monotonic and cyclic loading conditions.

Non-invasive in vivo quantification of human skin tension lines

Human skin is a composite tissue that exhibits anisotropic mechanical properties. This anisotropy arises primarily from the alignment of collagen and elastin fibers in the dermis, which causes the skin to exhibit greater tension in one direction, making it appear stiffer. A diverse number of skin tension guidelines have been developed to assist surgeons in making incisions that produce the least conspicuous scars. However, skin anisotropy is believed to vary from subject to subject, and no single guideline is universally recognized as the best to implement for surgical applications. To date, no system exists that can rapidly and non-invasively measure lines of skin tension in vivo. In this article, we evaluate the ability of a new aspiration system to measure the anisotropy of human skin. The device painlessly applies a radial stress of 17 kPa to a region of skin, and captures radially asymmetric skin deformations via a dermal camera. These deformations are used to quantify orientations of strain extrema and the direction of greatest skin stiffness. The ratio of these asymmetric strains varies between 1 and −0.75. A simple 2D transverse isotropic model captures this behavior for multiple anatomical sites. Clinical trials reveal that skin tension line orientations are comparable with existing skin tension maps and generally agree across subjects, however orientations statistically differ between individuals. As such, existing guidelines appear to provide only approximate estimates of skin tension orientation. Statement of SignificanceSkin tension lines (STL) in human skin arise primarily from collagen fiber alignment in the dermis. These lines are used by surgeons to guide incisions that produce the least conspicuous scars. While numerous anatomical STL maps exist, no single guideline is universally recognized as the most reliable. Moreover, manual methods of quantifying STL are imprecise. For the first time, we have developed a device capable of rapidly and non-invasively measuring STL orientations in vivo, using a single test. Our results are used to establish a simple constitutive model of mechanical skin anisotropy. Clinical trials further reveal STL orientations are comparable with existing maps, but statistically differ between individuals. Existing guidelines therefore appear to provide only approximate estimates of STL orientation.

Investigation on True Stress‐Strain Curves of Flat and Corner Regions of Cold‐Formed Section Using 3D Digital Image Correlation Method

The true stress‐strain curve is the critical method to describe the practical material mechanical performance and the essential precondition to develop the advanced numerical simulation. Experimental, analytical, and numerical procedures were performed in present research to investigate the true stress‐strain curves of flat and corner regions of the cold‐formed channel section. The coupon tests with the 3D digital image correlation system were conducted on flat and corner specimens to directly obtain the true stress‐strain curves. The experimental results indicate that the tensile secondary‐hardening phenomenon at the plastic strain stage was observed in the true stress‐strain curves of flat coupons, and initial strain hardening behavior was produced in that of corner coupons. Flat region exhibits a significant improvement of true ultimate strength compared to the engineering value. The stress status of the corner region is developed to ultimate strength at the early strain phase and exhibits a slight increase compared with the nominal values at the plastic phase. Cold‐rolling action limits the ductility performance of the corner region, which highly restrains the tensile strain hardening at the plastic condition. Thus, the true yielding strength of the corner region is obviously higher, but the true ultimate strength is significantly lower than that of the flat region. Together with the optical measuring results, a trilinear model with two‐stage strain hardening and a simplified trilinear models were established for describing the true stress‐strain curves of flat and corner regions, respectively. The load‐displacement curves from numerical simulations fit very well with those of coupon tests, which validate the reliability of the optic measurement and the dependability of the simplified constitutive models.

Permanent Deformation Prediction Model of Unbound Granular Materials for Flexible Pavement Design

Constitutive prediction models in flexible pavement are used to predict the permanent deformation (PD) of the unbound granular materials (UGMs). The most recent flexible pavement structural design guide in Australia does not consider the response of the UGMs layers as a design criterion. Additionally, it referred to the absence of an appropriate prediction model. The available prediction models have complex equations with many variables; the use of some of which has been found to be unsuitable in Australia. Thus, the aim of this study was to develop a new simple constitutive model based on an empirical regression equation, which has two predictor variables and four regression parameters. Repeated load triaxial test data covering many loading cycles and stages of stresses were used in order to validate the proposed model by calibration. The tested materials, specified by VicRoads as high-quality base and subbase crushed rocks, were used to prepare 46 samples with a range of moisture contents, gradations, densities, and stress conditions. Additional validation was conducted by predicting the PD response of recycled crushed concrete for different stress conditions. The proposed model excellently matches the experimental PDs with the sum of squared error less than 0.060 and R2 more than 0.96 over the tested matrix for both the crushed rocks and recycled concrete. This high prediction accuracy could lead to a better design of pavement materials and their thicknesses. A new update is proposed for the current Austroads flexible pavements design procedure by involving two more critical locations as performance criteria in the base and subbase layers based on the developed constitutive model. Adopting the proposed model can better generalise the design procedure to determine the accumulated vertical PD for the whole layer system.

A simple nonlinear constitutive model based on non-associative plasticity for UD composites: Development and calibration using a Modified Arcan Fixture

A simple nonlinear constitutive model based on non-associative plasticity for unidirectional (UD) composites is developed and calibrated using a Modified Arcan Fixture (MAF) and Digital Image Correlation (DIC). The plasticity model accounts for the nonlinear response of unidirectional composites subjected to multiaxial loading, assuming transverse isotropy and negligible plasticity in the fibre direction. The different responses in transverse tension and compression are accounted for by a Drucker–Prager type yield function to include transverse pressure sensitivity. It is shown that using an associative flow rule leads to the prediction of non-physical plastic strain components, whilst the use of a non-associative flow rule resolves the deficiency of the associative model. The non-associative model is calibrated and verified against biaxial test data obtained from glass/epoxy specimens using the MAF, as well as against off-axis test data available in the literature for two additional composite material systems. The nonlinear stress-strain curves for unidirectional composites subjected to multiaxial stress states predicted by the model are in good agreement with all three sets of experimental data, thus demonstrating the predictive capabilities of the proposed model.

A SIMPLE CONSTITUTIVE MODEL FOR UNDRAINED SHEAR CHARACTERISTICS OF SANDY SOILS

A vast amount of past experimental examinations reported that the internal peak angle of sand was jointly affected by the density and effective stress level. Several relationships were proposed between these elements. The dependence of dilatancy characteristics on the internal state of a granular material was examined and revealed. A simple constitutive model framework was established on a basis of several well-proven and experienced relationships for granular materials to simulate their undrained shear behavior. A basic hardening law connecting the varying tendency of the stress ratio with shear strain was employed. This model is capable of predicting the undrained monotonic stress-strain relationship of granular materials at different densities and various confining pressures. A series of parametric studies are conducted to investigate the susceptibility of the simulation results to the selected parameters. The simulation results also confirm the influential influences of dilatancy and deformability on the shear characteristics of granular materials at the critical state.

Elastic-Softening-Plasticity Around a Borehole: An Analytical and Experimental Study

Analytical solutions of near-borehole stress–strain responses are often based on simple elastic-perfectly plastic constitutive models. However, such models are incapable of capturing rock softening, and thus often disagree with observed failure patterns. Therefore, in this study, we present a set of closed-form solutions to estimate the stress–strain response around a borehole in a finite medium obeying elastic-softening-plasticity. Solutions are presented for material subject to either Mohr–Coulomb (M–C) or Hoek–Brown (H–B) failure criteria. The proposed analytical solutions define two failure surfaces to capture the peak and residual stress states, which are linked by a softening law. We demonstrate how to identify these two surfaces by first conducting a set of triaxial tests on a sandstone sample to differentiate the deformation stages. The proposed methodology provides a practical approach to characterize the strain-softening response with good accuracy. Finally, the proposed analytical solutions are validated through comparisons with (a) numerical simulations and (b) hydrostatic experiments on hollow-cylinder sandstone samples analysed using Digital Image Correlation. The strain development and interfaces calculated from the proposed model are in good agreement with the experimental and numerical data.

Effect of the soil–pile–structure interaction in seismic analysis: case of liquefiable soils

The design of earthquake-resistant structures depends greatly on the soil–foundation–structure interaction. This interaction is more complex in the presence of liquefiable soils. Pile and rigid inclusion systems represent a useful practice to support structures in the presence of liquefiable soils in seismic zones. Both systems increase the bearing capacity of soil and allow reducing the settlements in the structure. Numerical models with a 3-storey reinforced concrete frame founded on inclusions systems (soil–inclusion–platform–structure) and pile systems (soil–pile–structure) were analyzed. Finite difference numerical models were developed using Flac 3D. Two different soil profiles were considered. A simple constitutive model for liquefaction analysis that relates the volumetric strain increment to the cyclic shear strain amplitude was utilized to represent the behavior of the sand, and the linear elastic perfectly plastic constitutive model with a Mohr–Coulomb failure criterion was used to represent the behavior of the earth platform. Two earthquakes were used to study the influence of the different frequency of excitation in the systems. The results were presented in terms of maximum shear forces distribution in the superstructure and spectrum response of each system. The efforts and displacements in the rigid elements (piles or rigid inclusions) were compared for the different systems. The bending and buckling failure modes of the pile were examined. The results show that the pile system, the soil profile and the frequency of excitation have a great influence on the magnitude and location of efforts and displacements in the rigid elements.

Fully coupled hydromechanical model for compacted soils

To accomplish a proper conception and further modeling of the mechanical behavior of soils, observations at the micro and macro scales need to be merged. The authors believe that the link between scales can be achieved using the effective stress concept. In this paper, we present a model that quantifies the air and water volumes contained within the pores of a solid when their pore pressure is varied. The macroscopic consequences of this are expressed in terms of a single stress that is used to formulate a simple elastoplastic constitutive model to predict volume strains and shear strength of soils.

Application of Nor Sand Constitutive Model in a Highway Fill Embankment Slope Stability Failure Study

This paper presents a case study of a static load induced liquefaction in a simple roadway widening project constructed in north eastern part of Ohio in 2008. The widening required an embankment fill, which moved nearly 4 feet vertically and 1 foot laterally after two days of installation. The main objective of the work is to demonstrate how a simple Constitutive model, in this case Nor Sand model, can represent the static liquefaction in loose sand layers under specific conditions. A set of parameters is assumed based on the soil properties and an Excel Spreadsheet is used for simulations of triaxial compression of sand. It was considered that the situation which led to the failure, and the situation after the solution adopted. Moreover, slope stability analysis is provided for validation of the original results using a commercial software. It was found that the model can represent through stress strain curves and stress paths the behavior of the soil layer which led to the embankment fill movement. As the original work considered only slope stability analysis to explain this phenomenon, the present study shows a different approach for the case study, and this is the main contribution of this research.

Seismic Behaviors of Concrete Beams Reinforced with Steel-FRP Composite Bars under Quasi-Static Loading

Steel-fiber reinforced polymer (FRP) composite bar (SFCB) is a new composite material with good corrosion resistance and designable post-yield stiffness. Substitution of steel bar with SFCB can greatly increase the durability and ultimate capacity associated with seismic performance. First, the method and main results of the experiment are briefly introduced, then a simplified constitutive model of composite bar material was applied to simulate the seismic behaviors of the concrete beams reinforced with SFCBs by fiber element modeling. The simulation results were found to be in good agreement with test results, indicating that the finite element model is reasonable and accurate in simulating the seismic behaviors of beams reinforced with SFCB. Based on the numerical simulation method, a parametric study was then conducted. The main variable parameters were the FRP type in composite bars (i.e., basalt, carbon FRP and E-glass FRP), the concrete strength, basalt FRP (BFRP) content in SFCBs and shear span ratio. Seismic behaviors such as load-displacement pushover curves, seismic ultimate capacity and its corresponding drift ratio of the SFCBs reinforced concrete beams were also evaluated. The results showed that (1) the fiber type of the composite bar had a great impact on the mechanical properties of the beam, among which the beam reinforced with BFRP composite bar has higher seismic ultimate capacity and better ductility. With the increase of the fiber bundle in the composite bar, the post-yield stiffness and ultimate capacity of the component increase and the ductility is better; (2) at the pre-yield stage, concrete strength has little influence on the seismic performance of concrete beams while after yielding, the seismic ultimate capacity and post-yielding stiffness of specimens increased slowly with the increase in concrete strength, however, the ductility was reduced accordingly; (3) as the shear span ratio of beams increased from 3.5 to 5.5, the seismic ultimate capacity decreased gradually while the ultimate drift ratio increased by more than 50%. Through judicious setting of the fiber content and shear span ratio of the composite bar reinforced concrete beam, concrete beams reinforced with composite bars can have good ductility while maintaining high seismic ultimate capacity.

A simplified constitutive model for corroded steel bars

In this paper a theoretical constitutive model is developed to describe the mechanical properties of corroded steel bars. The model is established based on the assumption that the effect of corrosion on the steel bars only leads to the local reduction of cross-section area of the steel bars. By using a bilinear elastoplastic constitutive equation, a generalized equivalent stress-strain equation is derived for the corroded steel bars, which considers the pitting corrosion nature. The derived stress-strain equation is validated using experimental data. To demonstrate the features of the stress-strain equation, a parametric study is also presented.

Computing the linear viscoelastic properties of soft gels using an optimally windowed chirp protocol

We use molecular dynamics simulations to investigate the linear viscoelastic response of a model three-dimensional particulate gel. The numerical simulations are combined with a novel test protocol (the optimally windowed chirp or OWCh), in which a continuous exponentially varying frequency sweep windowed by a tapered cosine function is applied. The mechanical response of the gel is then analyzed in the Fourier domain. We show that (i) OWCh leads to an accurate computation of the full frequency spectrum at a rate significantly faster than with the traditional discrete frequency sweeps, and with a reasonably high signal-to-noise ratio, and (ii) the bulk viscoelastic response of the microscopic model can be described in terms of a simple mesoscopic constitutive model. The simulated gel response is in fact well described by a mechanical model corresponding to a fractional Kelvin-Voigt model with a single Scott-Blair (or springpot) element and a spring in parallel. By varying the viscous damping and the particle mass used in the microscopic simulations over a wide range of values, we demonstrate the existence of a single master curve for the frequency dependence of the viscoelastic response of the gel that is fully predicted by the constitutive model. By developing a fast and robust protocol for evaluating the linear viscoelastic spectrum of these soft solids, we open the path toward novel multiscale insight into the rheological response for such complex materials.

Simple Modelling of Undrained Shear Response of Granular Materials

A vast amount of past experimental investigations reported that the internal peak angle of sand was jointly governed by the density and effective stress level. Several relationships were proposed between these elements. The dependence of dilatancy characteristics on the internal state of a granular material was examined and revealed. A simple constitutive model framework was established on a basis of several well-proven and experienced relationships for granular materials to simulate their undrained shear behaviour. A basic hardening law connecting the varying tendency of the stress ratio with shear strain was employed. This model is capable of predicting the undrained monotonic stress-strain relationship of granular materials at different densities and various confining pressures. A series of parametric studies are conducted to investigate the susceptibility of the simulation results to the selected parameters. The simulation results also confirm the influential influences of dilatancy and deformability on the shear characteristics of granular materials at the critical state.

Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. The algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.

Nonlinear Buckling Analysis of H-Type Honeycombed Composite Column with Rectangular Concrete-Filled Steel Tube Flanges

This paper was concerned with the nonlinear analysis on the overall stability of H-type honeycombed composite column with rectangular concrete-filled steel tube flanges (STHCC). The nonlinear analysis was performed using ABAQUS, a commercially available finite element (FE) program. Nonlinear buckling analysis was carried out by inducing the first buckling mode shape of the hinged column to the model as the initial imperfection with imperfection amplitude value of L/1000 and importing the simplified constitutive model of steel and nonlinear constitutive model of concrete considering hoop effect. Close agreement was shown between the experimental results of 17 concrete-filled steel tube (CFST) specimens and 4 I-beams with top flanges of rectangular concrete-filled steel tube (CFSFB) specimens conducted by former researchers and the predicted results, verifying the correctness of the method of FE analysis. Then, the FE models of 30 STHCC columns were established to investigate the influences of the concrete strength grade, the nominal slenderness ratio, the hoop coefficient and the flange width on the nonlinear stability capacity of SHTCC column. It was found that the hoop coefficient and the nominal slenderness ratio affected the nonlinear stability capacity more significantly. Based on the results of parameter analysis, a formula was proposed to predict the nonlinear stability capacity of STHCC column which laid the foundation of the application of STHCC column in practical engineering.