Elastic-perfectly Plastic Model Research Articles

Revamp of the eco-friendly grouting materials by mixing basalt fiber for earthen sites conservation: Compressive performance and constitutive models

Reinforcement techniques, including anchorage and sealing with grout, are frequently employed to protect earthen sites and minimize the impact of fissures, the effectiveness of these approaches relies heavily on the mechanical properties of grout. To enhance the strength and ductility of the conventional grout, an eco-friendly composite grouting material mixture basalt fibers of varying lengths and contents is prepared. The DIC-based UCS tests were conducted to evaluate its compressive performance. Constitutive models of the basalt fiber-reinforced grout, including elastic perfectly-plastic (EPP) and median nonlinear (MNL) constitutive models, were established respectively based on the equal energy rule and cross-sectional data analysis for simplification application and precision evaluation purposes. The results show that the mixture of basalt fibers resulted in a distinct semi-brittle failure mode for the grout, with a significant increase in its compressive strength, ductility, compressive fracture energy, and residual bearing capacity. However, the elastic modulus will be lower when the fibers are relatively longer. Considering the differences in the relations between performance parameters and fiber content, and length, the highest compressive strength was reached at the fiber length of 6 mm and the content of 0.2 wt%, while maximum ductility was achieved at 18 mm and 0.4 wt%. The fracture energy exhibits an approximate positive correlation with fiber content. In addition, the EPP and MNL constitutive models can effectively characterize the compressive mechanical behavior of semi-brittle materials to satisfy different requirements on the precision of engineering analysis. This study contributes valuable insights into the development of high-ductility grouting materials of earthen sites, and the establishment of constitutive models for semi-brittle materials.

An efficient second-order cell-centered Lagrangian discontinuous Galerkin method for two-dimensional elastic-plastic flows

An efficient second-order cell-centered Lagrangian discontinuous Galerkin (DG) method for solving two-dimensional (2D) elastic-plastic flows with the hypo-elastic constitutive model and von Mises yield condition is presented. First, starting from the governing equations of conserved quantities in the Euler framework, the integral weak formulation of them in the Lagrangian framework is derived. Next, the DG method is used for spatial discretization of both the weak formulation of conserved quantities and the evolution equation of deviatoric stress tensor. The Taylor basis functions defined in the reference coordinates provide the piecewise polynomial expansion of the variables, including the conserved quantities and the deviatoric stress tensor. The vertex velocities and Cauchy stress tensor on the edges are computed using a nodal solver equipped with a variant of Li's new Harten-Lax-van Leer-contact approximate Riemann solver [Li et al., “An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model,” J. Comput. Phys. 448, 110675 (2022)], in which the longitudinal wave velocity in the plastic state is modified. Then the vertex velocities and Cauchy stress tensor on the edges are used to compute numerical fluxes. A second-order total variation diminishing Runge–Kutta scheme is used for time discretization of both the governing equations of conserved quantities and the evolution equation of deviatoric stress tensor. After solving the evolution equation of deviatoric stress tensor, a radial return algorithm is performed at the Gauss points of each element according to the von Mises yield condition. And then the coefficients of the DG expansion for the deviatoric stress tensor on each element are modified by a least squares procedure using the deviatoric stress tensors at these Gauss points. To achieve second-order accuracy, the least squares procedure is used for piecewise linear reconstruction of conserved quantities and the deviatoric stress tensor, and the Barth–Jespersen limiter is used to suppress the nonphysical numerical oscillation near the discontinuities. After that, the coefficients of the DG expansion are modified through L2 projection using the reconstructed polynomials. Finally, a second-order cell-centered Lagrangian DG scheme is established. Several tests demonstrate that the new scheme achieves second-order accuracy with good robustness, and that the DG method of updating the deviatoric stress tensor has comparable accuracy and much higher efficiency with mesh refinement compared with previous works.

Application of Clay–rubber Mixtures for the Transportation Geotechnics—the Numerical Analysis

Abstract The use of waste materials (including rubber) in industry is one of the most important issues in terms of environmental protection. One of such applications is the use of soil–rubber mixtures in backfills or lower layers of embankments or road structures. The numerical analyses of the behavior of a clay–rubber mixture layer built into a road embankment are presented in this article. An elastic-perfectly plastic model with a Coulomb–Mohr yield surface was used in the finite element analysis. The parameters of soil–rubber mixtures adopted for the analysis were estimated on the basis of triaxial tests: monotonic (UU—unconsolidated undrained, and CU—consolidated undrained) and cyclic (CU) performed with low frequency (f = 0,001 Hz). The triaxial tests were carried out on mixtures of kaolin (K) and red clay (RC) with the addition of 1–5 mm rubber granulate (G) in the amount of 5–25% by weight. Numerical analyses included a static plate load test (VSS) of a layer made of a rubber–soil mixture built into the embankment and testing the stability of embankments using the c–ϕ strength reduction procedure. The results of laboratory tests confirm the necessity of testing soil–rubber mixtures each time before their use in embankments. The observed overall decrease in shear strength and stiffness of the tested material is variable and depends on the type of soil and the content of rubber waste. Satisfactory results of the analysis were obtained, both in terms of the values of layer stiffness modules and slope safety factors, which allows for the conclusion of the possibility of using soil–rubber mixtures (with the recommended granulate addition up to 30% by weight) in the layers of road embankments and (depending on the road class) in the lower layers of the pavement structure.

Numerical Analysis of a 3D Unit Cell Model for Soft Soil Reinforced with Different Granular Columns

Recycled aggregates have been increasingly considered in recent years, owing to the limited supply of natural aggregates coupled with the corresponding carbon footprint. Recycled aggregates are aggregates prepared from construction and demolition waste. Their use aims to reduce energy consumption and contributes to reducing waste harmful to the environment. This study is based on a number of numerical tests using the finite element method of PLAXIS 3D software with the elastic-perfectly plastic behavior model and the Mohr flow criterion for all materials. A unit cell model of soft soil treated with three types of granular columns was loaded to failure: ordinary stone columns (OSCs), sand-fiber mix (SFM) and recycled aggregate porous concrete pile (RAPP). An extensive parametric study was conducted to investigate the effect of column type, friction angle, elasticity modulus, column length and geotextile effective stiffness on the behavior of soft soils. The results of numerical tests indicated that the bearing capacity of the recycled aggregate columns is three times greater than that of columns of natural aggregates. The findings of this research are given in the form of load-settlement graphs, which made it possible to release recommendations to carry out works using this technique. KEYWORDS: Soft soil, Granular column, Numerical analysis, Unit cell, Bearing capacity, PLAXIS 3D software

Elastic perfect plastic rock mass analysis and equivalent GSI determination considering strain-softening behavior and three-dimensional strength

The elastic perfect plastic model (EPP) fails to accurately capture the strain-softening mechanical behaviors of rock masses, while the post-peak constitutive model of elastic strain softening (ESS) has great application limitations in practical engineering for complex numerical algorithms. In this paper, an EPP constitutive approximation of rock mass considering three-dimensional strength and strain-softening characteristics is proposed. The forward analysis method of the equivalent Geological Strength Index (GSIeq) is given considering the impact of in-situ stress, rock mass properties and engineering excavation. Extensive case studies demonstrate that the radial stress and displacement obtained by the proposed method agree well with those of the ESS model, with only small errors in the Ground Response Curve. The rock mass elastic modulus E and the initial stress level p0 significantly affect GSIeq, while the support pressure ps contributes little to that. As Rp,EPP/R0 > 3.0, usually GSI < 25, the residual strength parameter GSIr can be directly used as the calculation parameter of the EPP model, while for a highly qualified rock mass, such as GSI > 75, the peak strength parameter GSIp can be directly used as an approximate value of GSIeq. Furthermore, with the increase of the in-situ stress level, GSIeq gradually decreases to GSIr, and the difference of plastic stress distribution law based on ESS and EPP models gradually diminishes. Moreover, the proportion of plastic deformation to total deformation increases nonlinearly with buried depth. The proposed method offers a new calculation idea for the simplified analysis of strain-softening rock masses.

Low Temperature Effect on the Mechanical Properties of EH36 with Strain Rates

With the expansion of the Arctic route, the safety of ship crossing the area in light of the low temperature and ice has become of focus, especially with regards to the ship’s structure. The mechanical properties of the material making up the ship’s structure may not be suitable for the Arctic environment. A series of quasi-static and dynamic tests were performed to investigate the behaviour of EH36 steel, which is used to build Arctic ships, at temperatures ranging from 20 °C to −60 °C. The yield and ultimate tensile stress increased more than 10% as the temperature decreased from 20 °C to −60 °C, whereas the toughness decreased as the temperature decreased. A formula was derived to illustrate the relationship between the temperature reduction and the yield strength by fitting the experimental data. Four common constitutive rigid-perfectly plastic, elastic-perfectly plastic, bilinear elastic-plastic, and multi-linear elastic plastic models were fitted to simulate the hull structure under static loading and low temperature. Additionally, the strain rate effect of EH36 steel at low temperatures was illustrated by quasi-static and high-speed impact tests. A constitutive model including the low temperature and strain rate was introduced based on a modified Cowper-Symonds model, in which the coefficients of the constitutive model are fitted by the test results. It is improved by an iterative numerical method used to obtain more accurate coefficients using a series of numerical analyses. Detailed finite element simulations of the experiment conditions revealed that the constitutive model accurately predicts the dynamic response at low temperatures.

Modeling How Interface Geometry and Mechanical Stress Affect Li Metal/Solid Electrolyte Current Distributions

We develop a coupled electrochemical-mechanical model to assess the current distributions at Li/single-ion conducting solid ceramic electrolyte interfaces containing a parameterized interfacial geometric asperity, and carefully distinguish between the thermodynamic and kinetic effects of interfacial mechanics on the current distribution. We find that with an elastic-perfectly plastic model for Li metal, and experimentally relevant mechanical initial and boundary conditions, the stress variations along the interface for experimentally relevant stack pressures and interfacial geometries are small (e.g., <1 MPa), resulting in a small or negligible influence of the interfacial mechanical state on the interfacial current distribution for both plating and stripping. However, we find that the current distribution is sensitive to interface geometry, with sharper (i.e., smaller tip radius of curvature) asperities experiencing greater current focusing. In addition, the effect on the current distribution of an identically sized lithium peak vs valley geometry is not the same. These interfacial geometry effects may lead to void formation on both stripping and plating and at both Li peaks and valleys. The presence of high-curvature interface geometry asperities provides an additional perspective on the superior cycling performance of flat, film-based separators (e.g., sputtered LiPON) versus particle-based separators (e.g., polycrystalline LLZO) in some conditions.

Simulação numérica de ruptura por punção em lajes de concreto com agregado reciclado com reforço de fibra de aço

Abstract The use of construction waste as aggregate in the production of concrete is becoming a more frequent alternative due to the advantages associated with the sustainability aspect. Results obtained in experimental tests with recycled aggregate concrete suggest that mechanical properties such as elastic modulus, compressive, tensile and flexural strength tend to reduce with partial or total replacement of natural aggregate by recycled one. On the other hand, the use of steel fiber reinforcement can minimize the reduction of these properties, since the fibers tend to improve the material strength and ductility. This work proposes a numerical approach, seeking to better predict and understand the structural mechanical behaviors and failure patterns of reinforced recycled aggregate concrete slabs with and without steel fiber. Based on the finite element method, an appropriated constitutive damage model is employed to represent the nonlinear behavior of the conventional/recycled concrete, while an elastic-perfectly plastic model is used to describe the mechanical behavior of the reinforcements. To couple the independent FE meshes and incorporate the mutual interaction between the different components, rigid and non-rigid coupling technique is used to represent the perfect adherence or the bond-slip behavior. Seven concrete slabs were numerically analyzed either with different percentages of recycled aggregate replacement (0, 50 and 100%) or steel fibers content (0.0, 0.5 and 1.0%) and the results were compared with the experimental ones. The results showed that the applied methodology is capable of simulating with good accuracy the punching shear failure mechanism of the slabs. It was observed that the punching ultimate load decreased with increase of recycled aggregate content, as well as that the steel fiber addition can minimize the negative effects of recycled aggregate employment.

Experimental Setup for Measuring p-y Curves of Rigid Walls Supporting Granular Backfill

Abstract In the context of performance-based design, there is interest in quantifying the relationship between the lateral earth pressure and the wall displacement using the concept of p-y curves. Although p-y curves have been extensively used in the analysis of piles, their use in the analysis of rigid walls is still in its early stages. There is a need for realistic and simplified models that could describe the p-y relationship for rigid walls to be used as input in robust soil-structure-interaction analyses. This paper aims at studying the development of lateral stresses behind rigid walls in the context of p-y curves using a laboratory-scale retaining wall prototype that is 0.5 m wide, 1.2 m high, and 2.6 m long. The main objective is to provide insight on the p-y response behind rigid walls under static and cyclic loading conditions for different backfill densities and confinement conditions. Results indicate that the proposed experimental setup yields repeatable and consistent measurements of the p-y response, which was found to be highly nonlinear and not adequately represented by the simple elastic-perfectly plastic model that was adopted in the literature in modeling soil-structure interaction between basement walls and sand backfill. Unique results from the cyclic tests indicated a process of densification that dominated the volumetric tendency of the sand during cyclic loading, with the p-y curves showing a significant increase in stiffness and maximum pressure at the passive side after 10 loading cycles. The gradual increase in stiffness decreased with the number of cycles until convergence in the passive stiffness was observed after 9 to 10 cycles.

Elastic-Plastic Finite Element New Method for Lower Bound Shakedown Analysis

Shakedown analysis methods have been well developed to determine the shakedown limit load of structures under various repeated loading situations. However, to take the limited kinematic hardening, geometric effect, and deformation into account, further research is required. A new numerical method is proposed for the lower bound shakedown analysis that applies the extended static shakedown theorem for limited kinematic hardening. The new method determines the shakedown limit load with two kinds of elastic-plastic finite element (FE) analyses: (1) the elastic-plastic loading and unloading analysis is carried out using the hardening model with the actual material parameters and (2) the elastic-perfectly plastic model with ultimate stress as the yield stress is used for the limit analysis. An incremental FE technique for finite strain plasticity is utilized to take the geometric effect into account. Furthermore, the deformation of the structure is monitored by checking the calculated deformation parameters. The method is applied to a square plate with a small central hole subjected to cyclic tensile load. The corresponding physical shakedown experiment of the above square plate was conducted for verification. The numerical result shows a good agreement with the experimental result. The new method provides a valid method for the structural lower bound shakedown analysis taking into account limited kinematic hardening, geometric effect, and deformation.

Nonlinear Elastic-Perfectly Plastic Model of Soil and its Numerical Implementation and Application

Nonlinear Elastic-Perfectly Plastic Model of Soil and its Numerical Implementation and Application

Implementation of the Non-Associated Elastoplastic MSDPu Model in FLAC3D and Application for Stress Analysis of Backfilled Stopes

The multiaxial Mises-Schleicher and Drucker-Prager unified (MSDPu) criterion has been shown to exhibit several specific features compared to other yield and failure criteria, including a nonlinear mean stress dependency, influence of the Lode angle, use of independent uniaxial compressive and tensile strength values and absence of an apex (singularity) on the envelope surface in the negative stress quadrant. However, MSDPu has been seldom used in practice to solve geotechnical and geomechanical engineering problems mainly because it had not yet been fully implemented into three-dimensional (3D) numerical codes. To fill this gap, a 3D elastoplastic MSDPu formulation is developed and implemented into FLAC3D. The proposed MSDPu elastic-perfectly plastic (EPP) constitutive model is then validated against existing analytical solutions developed for calculating the stress and displacement distributions around cylindrical openings. The FLAC3D MSDPu-EPP model is then applied to evaluate the vertical and horizontal stress distributions in a three-dimensional vertical backfilled stope. The numerical results obtained with the MSDPu-EPP model are compared with those obtained with the Mohr-Coulomb EPP model, to highlight key features of the new formulation.

Critical limit of diameter-to-thickness ratio for inner tubes of DSSTCC columns

To improve the confinement efficiency of steel tubes to the sandwiched concrete, the concept of double skin steel tubes confined concrete (DSSTCC) columns was proposed. This paper aims to theoretically investigate the local stability of inner steel tubes in DSSTCC columns. Firstly, considering that the stress state and failure mode of the inner steel tube are similar to those of the fixed circular arch subjected to a uniform radial load, the arc section of the inner steel tube was simplified into a circular arch for stress analysis. Secondly, the expected value of the in-plane elastic ultimate axial compressive stress of the circular arch was solved by the Monte Carlo method, and the ratio of its value to the yield stress was used to characterize the stable state of the inner tube. Then, the influence of the maximum included angle corresponding to the formed circular arch on the result was discussed, and an empirical formula was given to obtain a reasonable estimation of the critical limit of diameter-to-thickness ratio. Finally, it can be seen from the analysis that the method proposed in this paper is suitable for inner tubes made of the material with an elastic perfectly-plastic model, a bilinear model, or a bilinear plus nonlinear hardening model. These results are a contribution to the buckling analysis of inner tubes.

Modeling of non-ductile RC structure under near-fault ground motions: A nonlinear finite element analysis

The old existing reinforced concrete (RC) structures in Taiwan are susceptible to severe damage under earthquakes because of the soft-story mechanism. Moreover, the effects of near-fault ground motions often contain a long period of velocity pulse and permanent ground displacement. This study is based on the tri-axial shaking table test conducted at the National Center for Research on Earthquake Engineering in Taiwan and a series of seismic performance evaluations of a non-ductile RC structure in Taiwan. Finite element analysis (FEA) will be conducted to simulate the linear and nonlinear behavior of the seven-story building. This accommodates the damage plasticity model for concrete and the elastic-perfectly plastic model for reinforcement. Comparison of the results between the experimental test and numerical model showed that the similarity of the vibration period has a great influence on the simulation results. The findings showed that the data of acceleration and displacement behavior corresponded with the experimental results in a satisfactory margin. Also, the damage mode is very similar to the shaking table test results. The study found that using FEA can satisfactorily simulate the seismic performance of mid-rise buildings under a near-fault earthquake.

Analytical modeling for the load-transfer behavior of stiffened deep cement mixing (SDCM) pile with rigid cap in layer soils

A new composite structure named stiffened deep cement mixing (SDCM) piles has recently been considered and applied in many geotechnical engineering projects. The SDCM pile was formed by inserting a stiffened core into the deep cement mixing (DCM) pile that has just finished construction, thereby combining the advantages of DCM piles and concrete piles. This study developed a load-transfer analytical approach for SDCM pile with rigid cap in layer soils from the theoretical solution view. Herein, the nonlinear mechanical behaviors of the DCM pile–soil and DCM pile–stiffened core interfaces were characterized by a tri-linear bond-slip model, and the action of soil on the pile end was simulated by an elastic-perfectly plastic model. Three-dimensional finite element simulations were conducted for SDCM piles embedded in homogeneous soil and double-layer soils. The reasonable matches between the predictions and the results from FE simulations and physical model tests confirmed the applicability of the theoretical approach. The full-range load-transfer behavior and the bearing performance of SDCM piles were further discussed. Parametric studies were finally conducted, providing insights into the design practice of SDCM piles.

Identification of constitutive equations at very high strain rates using shock wave produced by laser

A method coupling experiments and simulations, is developed to characterize the yield stress and strain hardening of several metals loaded at 106 s−1 and < 25 ns, typically involved during Laser Shock Peening. It was applied to four materials: pure aluminum, 2024-T3 and 7175-T7351 aluminum alloys and Ti6Al4V-ELI titanium alloy. Thin foils have been irradiated with high-power laser to induce high-pressure shock wave. Plastic deformation is activated through the thickness up to the rear free-surface of the foils. These experiments have been simulated using three material constitutive equations: Elastic–Perfectly Plastic model considering static yield stress, Johnson–Cook model without strain hardening and Johnson–Cook model with strain hardening. The material parameters of Johnson–Cook law were identified by comparison of the experimental and calculated velocity profiles of the rear-free surface. Results are shown and discussed.

A numerical study on undrained passive earth pressure

This paper presents a numerical study on passive earth pressure under undrained conditions. First, a simplified problem is investigated in order to evaluate the resulting earth pressure for a parallel movement of a rigid wall. It is shown that for undrained conditions the type of constitutive model employed has an influence on the limiting passive earth pressure. Comparison with limit analysis is provided whenever possible, giving confidence that the finite element results are reliable. In a second study, a simplified deep excavation problem is analysed where the positive effect of negative excess pore water pressures developed during undrained excavation increases the factor of safety against global failure. However, this effect is only temporarily and it is shown that standard strength reduction procedures to calculate factors of safety, as applied frequently in practice, are not well suited for this type of problems. An alternative way is therefore suggested. Again, the influence of the constitutive model is addressed, and it is shown that simple elastic-perfectly plastic models may not be conservative. In addition the influence of geometric effects is highlighted.

An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model

In this work, an elastic-perfectly plastic model in two-dimensional planar geometry is studied and a new HLLC-type approximate Riemann solver (HLLCN) is put forward. The main feature of the new approximate Riemann solver is that it almost includes all stress waves, such as elastic, plastic, longitudinal and shear waves simultaneously in the presence of elastic-plastic phase transition. The analyses of the Jacobian matrix of governing equations are carried out for elasticity and plasticity separately, and the complicate order in the light of magnitude of characteristic speeds is simplified when constructing the approximate Riemann solver. The radial return mapping algorithm originally proposed by Wilkins is not only applied for the plastic correction in the discretization of the constitutive law, but also used to determine the elastic limit state in the approximate Riemann solver. A cell-centered Lagrangian method equipped with this new HLLC-type approximate Riemann solver is developed. Typical and new devised test cases are provided to demonstrate the performance of proposed method.

The elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect

Pressure vessel is a kind of special equipment which is involved in various industries. Once it is damaged, it will cause great loss to people’s life and property. The traditional elastic modulus reduction method for upper bound limit analysis of pressure vessels adopts the elastic-perfectly plastic material model. This method will result in waste of materials without considering the material strain hardening effect. So the material strain hardening effect is introduced into upper bound limit analysis. Firstly, the equivalent yield strength considering material strain hardening effect is established. Then, the formula of limit load multiplier which is expressed by the equivalent yield strength is derived based on the upper bound theorem. Combined with the strategy for elastic modulus adjustment, the elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect is constructed. The limitation of the elastic-perfectly plastic model for the upper bound analysis method is eliminated by the method proposed in this paper. The result calculated by this method is closer to the true limit load of pressure vessels.

Seismic behavior and failure modes of non-ductile three-story reinforced concrete structure: A numerical investigation

Reinforced concrete (RC) buildings in Taiwan have suffered failure from strong earthquakes, which was magnified by the non-ductile detailing frames. Inadequate reinforcement as a consequence of the design philosophy prior to the introduction of current standards resulted in severe damage in the column and beam-column joint (BCJ). This study establishes a finite element analysis (FEA) of the non-ductile detailing RC column, BCJ, and three-story building that was previously tested through a tri-axial shaking table test. The results were then validated to laboratory specimens having the exact same dimensions and properties. FEA simulation integrates the concrete damage plasticity model and the elastic-perfectly plastic model for steel. The load-displacement responses of the column and BCJ specimens obtained from FEA were in a reasonable agreement with the experimental curves. The resulting initial stiffness and maximum base shear were found to be a close approximation to the experimental results. Also, the findings of a dynamic analysis of the three-story building showed that the time-history data of acceleration and displacement correlated well with the shaking table test results. This indicates the FEA implementation can be effectively used to predict the RC frame performance and failure mode under seismic loads.