Prager Model Research Articles

Graphene Oxide-Based Nanocomposites for Stereolithography (SLA) 3D Printing: Comprehensive Mechanical Characterization under Combined Loading Modes.

Additive manufacturing, particularly Stereolithography (SLA), has gained widespread attention thanks to its ability to produce intricate parts with high precision and customization capacity. Nevertheless, the inherent low mechanical properties of SLA-printed parts limit their use in high-value applications. One approach to enhance these properties involves the incorporation of nanomaterials, with graphene oxide (GO) being a widely studied option. However, the characterization of SLA-printed GO nanocomposites under various stress loadings remains underexplored in the literature, despite being essential for evaluating their mechanical performance in applications. This study aimed to address this gap by synthesizing GO and incorporating it into a commercial SLA resin at different concentrations (0.2, 0.5, and 1 wt.%). Printed specimens were subjected to pure tension, combined stresses, and pure shear stress modes for comprehensive mechanical characterization. Additionally, failure criteria were provided using the Drucker--Prager model.

A Modified Drucker–Prager Model Considering Tensile Strength Reduction and Its Applications in Slope Stability Analysis

A Modified Drucker–Prager Model Considering Tensile Strength Reduction and Its Applications in Slope Stability Analysis

Plastic behavior of a film type of epoxy adhesive under a wide range of stress multiaxiality conditions

The yield stress of rubber-modified epoxy adhesives is affected by hydrostatic stress in the adhesive layer. It is necessary to clarify whether hydrostatic stress modeling is essential for highly toughened epoxy adhesives and how hydrostatic stress should be considered under high multiaxial stress conditions. The elastic–plastic stress–strain behavior of a film-type epoxy adhesive AF163-2U was examined using a bulk adhesive tension test and a thick adherend shear test (TAST). The exponent Drucker–Prager model with an appropriate hydrostatic-stress sensitivity parameter (λ-parameter = 1.639) fully described the stress–strain curves both for the bulk adhesive tension test and TAST. The Hill’48 model of hydrostatic-stress-independent plasticity also simulated the bulk adhesive tension test and TAST as a response by determining the appropriate anisotropic parameters. To examine the effect of extremely high hydrostatic stress, a butt-joint tensile test and a finite element (FE) simulation were conducted using the exponent Drucker–Prager and Hill’48 models. The Hill’48 model completely failed in the butt-joint tensile test simulation. The exponent Drucker–Prager model, where a higher λ-parameter (=2.1) was required; consequently, it was concluded that the hydrostatic-stress effect should be considered for the adhesive model and the λ-parameter is not a fixed value but increases with increasing hydrostatic stress.

Experimental Construction and Validation of Revised Drucker–Prager Model Using Finite Element Method for Moisture Condensation Zone in Bentonite-Bonded Silica Sand

For predicting casting deformation by FEM (finite element method) thermal stress analysis, this paper experimentally constructed and validated the Drucker–Prager (DP) model and its revised model (RDP) for the condensation zone of bentonite-bonded sand molds. The condensation zone has been known as a remarkably low-strength region in the mold, and its mechanical response should be dominant to the casting deformation. To construct the models through uniaxial and triaxial compression tests, the test pieces reproducing the condensation zone were prepared by permeating water vapor through a test piece of bentonite-bonded sand. The constructed models were then applied to the FEM stress analysis of the triaxial test to validate them by comparing the analytical stress–strain curves with the experiment. The experimental stress–strain curve after permeating water did not show any distinct yielding point; however, the analytical curve with the original DP model clearly exhibited a yielding point due to the yield criterion of the model. The distinct yielding criterion should be essentially fatal to reproduce the stress–strain relationship of the condensation zone. Contrarily, the RDP model reproduced the experimental curve with less than 10 % error and was found to be advantageous for modeling the smooth stress–strain relationship of the condensation zone.

Mechanical parameter evolutions and deterioration constitutive model for ductile–brittle failure of surrounding rock in high-stress underground engineering

The deep surrounding rock is usually in the true triaxial stress state, and previous constitutive models based on the understanding of uniaxial and conventional triaxial test results have difficulty characterizing the degradation and fracture process of rock ductile–brittle failure under true triaxial stress state. Therefore, this study conducted a series of true triaxial tests to obtain the understanding of the ductile–brittle behaviour of rock, and then combined the test results and the Mogi–Coulomb strength criterion, and proposed calculation methods for the elastic modulus E, cohesion c and internal friction angle φ and the evolution functions of E, c and φ of rock under true triaxial stresses. With the decreasing of the minimum principal stress σ3 or increasing of the intermediate principal stress σ2, the marble post-peak stress drop rate gradually increases, the ductility gradually weakens, and the brittleness significantly strengthens. The calculation method and evolution function of rock E, c and φ under true triaxial stress were proposed. E decreased at first and then tended to remain stable with the increasing of equivalent plastic strain increment dεp. c and φ slowly increased at first and then rapidly decreased. With a method of parameter degradation rate to realize post-peak stress drop rate to reflect the ductile–brittle characteristics, a new three-dimensional ductile–brittle deterioration mechanical model (3DBDM) was established. The proposed model can accurately characterize the influence of σ2 and σ3 on mechanical parameters, the ductile–brittle behaviour of rock under true triaxial stresses, and the asymmetric failure characteristics of surrounding rock after excavation of deep underground engineering. The proposed model can be reduced to elastic–perfectly plastic, elastic–brittle, cohesion weakening friction strengthening (CWFS), Mohr–Coulomb, and Drucker–Prager models.

Parameter Selection for Concrete Constitutive Models in Finite Element Analysis of Composite Columns

Concrete, as a complex and anisotropic material, poses challenges in accurately simulating its behavior in numerical simulations. This paper focuses on selecting an appropriate constitutive model for simulating the behavior of a steel–concrete composite column using finite element analysis under compression and push-out tests. Two models are analyzed and compared, namely, Drucker–Prager and concrete damage plasticity. The results demonstrate that the concrete damage plasticity model outperforms the Drucker–Prager model in all six test cases, indicating its superior accuracy in capturing the composite column’s behavior. This study enhances the reliability of numerical simulations for steel–concrete composite structures by choosing the most suitable constitutive model, parallel with extensive sensitivity analysis and model calibration. The findings emphasize the significance of meticulous model selection and precise parameter definition for achieving accurate predictions of concrete behavior. This research contributes to advancing the understanding and modeling of concrete’s intricate behavior in structural analyses.

Deterministic Seismic Damage Analysis for Concrete Gravity Dams: A Case Study of Oued Fodda Dam

Abstract One of the major dangers for seismic damage of concrete dams is the propagation of cracks in dam concrete. The present study undertakes a numerical investigation of the seismic damage for Oued Fodda concrete gravity dam, located in the northwest of Algeria, considering the impacts of properties of joints along the dam-foundation rock interface and cross-stream earthquake excitation. Three-dimensional transient analyses for coupled dam-foundation rock system are carried out using Ansys software. The hydrodynamic effect of reservoir fluid is modelled using the added mass approach. The smeared crack approach is utilised to present the seismic damage of dam concrete using the Willam and Warnke failure criterion. The dam-foundation rock interface joints are presented with two ways, adhesive joints and frictional joints. The Drucker–Prager model is considered for dam concrete in nonlinear analyses. Consideration of the study results indicates that the frictional joints model can reduce the seismic response and damage hazard of the dam body to a better extent compared with the adhesive joints model. Furthermore, the application of cross-stream earthquake excitation reveals the significant effect on cracking response of the dam in the two models of joints.

Developing Elastic–Plastic Material Models for Pressure Measurement Films in a Steel–Steel Contact for Smooth and Rough Surfaces

AbstractThe contact zone between two steel components can be identified by utilizing a pressure measurement film in the contact between them. To reduce the number of necessary experiments, it is possible to simulate the contact situation using “finite element analysis.” This analysis requires material models for the contact partners and for the pressure measurement films. It is known that the pressure measurement film deforms not only elastically but also plastically. Taking this plastic deformation into account requires an appropriate material model such as the Drucker–Prager model. Based on published data of experiments with pressure measurement films that had been inserted between smooth and rough Hertzian bodies, we developed material models for three pressure measurement films. The roughness of a Hertzian body was studied by determining multiple pressure–clearance curves for three different surface roughnesses and for three different pressure measurement films. These curves were developed with micromodels, which represented a small section of the rough contact surface. An average curve for each material was then implemented in the macromodel for each roughness representing the contact situation. Subsequently, the resulting contact areas were compared with the published experimental data. This comparison showed that the material model for the smooth contact was able to emulate the experimentally determined contact areas. Including the pressure–clearance curves in the material model allowed the simulation of the rough contact situation. However, the deviation between the simulated and the experimental data was slightly larger for the rough surface than for the smooth surface.

Numerical Simulation on Laser Shock Peening of B4C-TiB2 Composite Ceramics.

The introduction of residual stresses using laser shock peening (LSP) is an effective means of improving the mechanical properties of ceramics. Numerical simulations offer greater convenience and efficiency than in-lab experiments when testing the effects of different processing techniques on residual stress distribution. In this work, a B4C-TiB2 ceramic model based on the extended Drucker-Prager model was established to investigate the effects of laser power density, the number of impacts and laser spot overlapping rate on the residual stress distribution, and the reliability of the simulation method was verified by experimental data. The following results are obtained: increasing the laser power density and the number of impacts can increase the surface residual compressive stress and reduce the depth of the residual compressive stress; the presence of multiple impacts will significantly reduce the depth of the residual compressive stress layer; with the increase in the laser spot overlapping rate, the compressive residual stress in the processed area gradually increases and is more uniformly distributed; the best processing effect can be achieved by using a spot overlapping rate of 50%.

Study on Mechanical Failure Behavior of Steel-Wire Wound Reinforced Thermoplastic Pipe under Combined Internal Pressure and Soil Landslide Conditions.

A steel-wire wound reinforced thermoplastic pipe (SWW-RTP) has been widely utilized in many industrial areas, and a soil landslide is an inevitable hazardous extreme condition for the SWW-RTP as it is usually buried underground. It is imperative to study the mechanical failure behavior and the failure criterion of the SWW-RTP under the combination of internal pressure and soil landslide conditions, and this paper is the first study to investigate the topic. In this paper, groups of stress-strain curves of high-density polyethylene (HDPE) and steel wires were obtained by uniaxial tensile tests at different strain rates, with the help of a Digital Image Correlation device (DIC). A rate-dependent constitutive model was employed to represent the mechanical behavior of the HDPE and to help deduce the stress-strain curve of the HDPE under the required strain rate, estimated from the static simplification of the dynamic soil landslide. Afterwards, a finite element model of the SWW-RTP, embedded in a cubic of soil, was established with the software ABAQUS. The SWW-RTP model was composed of HDPE solid elements, embedded with steel-wire truss elements, and the soil was characterized with the extended Drucker-Prager model. A quartic polynomial displacement distribution was applied to the soil model to represent the soil landslide. Then, the mechanical response of the SWW-RTP was analyzed. It was found that the failure criterion of the HDPE yield was more suitable for the pipe subjected to internal pressure and soil landslide conditions, instead of the steel-wire strength failure criterion always used in traditional research on the SWW-RTP. Further, the influence of landslide width, internal pressure and steel-wire number were discussed. The larger the width of the landslide area, the gentler the deformation of the pipeline; this resulted in an increase in the maximum landslide and a decrease in the maximum curvature with the width of the landslide area. The relatively high internal pressure was beneficial to the safety of the SWW-RTP under landslide, because the internal pressure could increase the stiffness of the pipeline. The number of steel wires had a limited influence on the maximum landslide required for the SWW-RTP's failure. This work can be useful for the design and safe assessment of the SWW-RTP under internal pressure and soil landslide conditions.

A new nonlinear spring‐dashpot model of CPRF of NPP structure based on coupled BEM‐FEM approach

AbstractIn this paper, a BEM‐FEM coupled model of combined piled raft foundation (CPRF) is proposed for both the frequency domain and the time domain dynamic analyses of a NPP structure in the linear, equivalent linear and nonlinear soil domain. The piles are modeled using the finite element method as a beam element, while the raft and internal domain of soil are modeled using the eight nodded brick element. It is assumed that the piles are rigidly connected with the raft. The nonlinearity of soil is modeled using the hyperbolic stress–strain relation and Modified Drucker–Prager Model. The boundary of the layered soil domain is modeled using the boundary element method. For simplification, it is assumed that the raft and piles are rigidly connected with the soil that means there are no slip and separation conditions at the interface of pile‐soil and raft‐soil. In order to validate the proposed approach, numerical results, that is, impedances in the horizontal, vertical and rocking directions, are compared with the published literature. Further, dynamic analyses of a lumped structure founded on CPRF is carried out in the time domain and frequency domain using these impedances and results are compared with the FEM. It is found that the spring‐dashpot models give the reasonably good agreement with finite element method for linear, equivalent linear and nonlinear models for both frequency domain and time domain analyses. Moreover, practical application of proposed model is shown for a very large problem of raft‐pile‐soil‐structure interaction such as a NPP structure on the layered soil. It was found that the nonlinearity significantly increases the response of the NPP structure. The proposed model has many advantage over the finite element model, for example, first it is very simple and second it reduced the computation time significantly with the good accuracy.

A closed-form logarithmic spiral method for seismic passive earth pressure in anisotropic sand

The shear strength of soils is always anisotropic due to the compaction and deposition history. A closed-form logarithmic spiral method combined with an anisotropic failure criterion is proposed to estimate the seismic passive earth pressure coefficient and failure surface of anisotropic sand. The seismic condition is implemented by the pseudo-static approach. The results obtained by the proposed method are validated by methods in the literature and by the finite element method based on a proposed anisotropic Drucker–Prager model. The comparisons show that the method is effective and efficient. In addition, the seismic passive earth pressure coefficients considering various backfill slopes and various soil-wall frictions are presented for reference in engineering design.

An elastic‐inelastic model and embedded bounce‐back control for layered printing with cementitious materials

AbstractThis paper presents a finite‐deformation model for extrusion‐based layered printing with cementitious materials. The evolution of mechanical properties as the printed material cures and stiffens results in nonphysical reduction in the magnitude of elastic strains when standard constitutive models are employed. This elastic recovery of the printing induced deformation contradicts the experimentally observed behavior of the printed cementitious materials that harden at a nearly‐frozen deformed state. A thermodynamically motivated constraint on the evolution of elastic strains is imposed on the constitutive model to remedy the nonphysical bounce‐back effect. An algorithm that is based on a strain‐projection technique for the elastic part of deformation is developed that complements the inelastic response given by the Drucker–Prager model. It is then embedded in a finite strain finite element framework for the modeling and simulation of cure hardening and inelastic response of the early age cementitious materials. A ghost mesh method is proposed for continuous layer‐wise printing of the material without the need for intermittent mesh generation technique or adaptive remeshing methods. The model is validated via comparison with experimental data and representative test cases are presented that investigate the mathematical and computational attributes of the proposed model.

Buildability prediction of 3D–printed concrete at early-ages: A numerical study with Drucker–Prager model

3D–Printed concrete (3DPC) at early-ages often collapses during the printing process owing to insufficient buildability, which affects continuous printing. To correctly simulate the buildability of early-age 3DPC, a finite element (FE) model with the Drucker–Prager (D–P) model reflecting the fundamental concrete material properties was proposed. The yield criterion, flow, and hardening rule of the D–P and the Mohr–Coulomb (M–C) models were comparatively analyzed. A nonlinear stress–strain relationship was selected to describe the mechanical behavior of early-age 3DPC. Uniaxial compression tests, hollow cylinder, and straight wall printing tests were used to calibrate and verify the simulation results. The predicted peak stress in uniaxial compression tests and the elastic buckling of straight walls agree with the test results. The predicted error of the plastic collapse of the hollow cylinder with the D–P model decreased by 13.8% compared with that of the M–C model. Finally, the feasibility of the D–P model is demonstrated and discussed.

Coupled Thermo–Mechanical Damage Evolution of Granite under Repeated Heating–Cooling Cycles and the Applications of Mohr–Coulomb and Drucker–Prager Models

Coupled Thermo–Mechanical Damage Evolution of Granite under Repeated Heating–Cooling Cycles and the Applications of Mohr–Coulomb and Drucker–Prager Models

Experimental characterization and micro-modeling of transverse tension behavior for unidirectional glass fibre-reinforced composite

The mechanical behaviour of unidirectional fibre-reinforced polymer composites under transverse tension was studied using micromechanical computation and macroscopic experimentation. The representative volume element (RVE) of a composite with random fibre distribution was built by the proposed algorithm, which can effectively solve the jamming-limit problems for the hard-core-based model. The progressive damage process of the interface and matrix was simulated using the cohesive zone model and the extended Drucker–Prager model. The solutions of the mechanical loading case and the thermal mechanics loading case were compared to illustrate the effect of thermal residual stress. According to parametric studies, the failure models were mainly divided into two categories: interface-dominated and matrix-dominated damage, which rely on the interface strength, interface fracture energy, and matrix plastic deformation.

Characterization and prediction of fracture in 6000- and 7000-series aluminum alloy sheet under various stress states

This study investigates the stress state dependentfracture of several high strength aluminum sheet alloys, AA6013-T6, AA7075-T6 and a developmental AA7xxx-T76 alloy. These alloys are targeted for use in automotive structural applications for which accurate knowledge of the fracture loci are required to support crash safety simulations. A generalized Drucker–Prager (GDP) model to describe the fracture locus was proposed and calibrated to the measured fracture strains under simple shear, uniaxial, plane strain and biaxial tension. Calibration of the fracture loci was undertaken directly using measured fracture strains and direct integration of stress based on the measured strain histories. The calibrated fracture loci using the GDP function exhibited good agreement with the measured data across the range of the stress state conditions. An advantage of the GDP model is the admission of fracture asymmetry in uniaxial and biaxial tension which is not captured using the Hosford–Coulomb model. The experimental fracture loci were then paired with a damage model for non-linear strain paths and used to simulate three-point bend experiments on structural hat channel sections. For each material, the load response and onset of fracture were well predicted.

Numerical simulation of the behavior of kinematically unstable slopes under dynamic influences

Introduction. The concept of estimating the dynamic parameters of the “base — weakened layer — block” system is proposed, taking into account the physical nonlinearity of the material and the kinematic method of excitation of vibrations. In accordance with this approach, the physical nonlinearity of the base and block material is considered using the Drucker- Prager model. The weakened layer is modeled by 3D spring finite elements. The verification procedure of the proposed methodology is carried out on the example of the dynamic calculation of the “base — weakened layer — slope” system.Materials and Methods. The computational experiments were performed using the ANSYS Mechanical software package in combination with a nonlinear solver based on the Newton-Raphson procedure. SOLID45 volumetric finite elements were used to discretize the computational domains. Combined elastic-viscous elements COMBIN14 were used to simulate the displacement of the block relative to the fixed base.Results. An engineering technique for the dynamic analysis of the stress-strain state of the “base — weakened layer — block” spatial system with kinematic method of excitation of vibrations is developed. The accuracy and convergence of the proposed method is investigated using specific numerical examples.Discussion and Conclusion. Based on the mathematic simulation performed, it is shown that the developed technique provides assessing the risks of the occurrence of real landslide processes caused by external non-stationary impacts.

An optimization procedure for the soil behavior identification using pressuremeter results

The soil parameters identification procedure is usually a trade-off between sophisticated soil model behaviour and the large number of parameters to identify. Such procedure that can accomplish both of these objectives is highly desirable, but also difficult. This paper presents a methodology for identifying soil parameters that takes into account different constitutive equations. For identifying the generalized Prager model parameters, associated to the Drucker and Prager failure criterion, using an in-situ pressuremeter curve, we have proposed a procedure that is based on an approach of inverse analysis. This approach involves the minimizing the function representing the area between the experimental curve and the simulated curve, obtained by fit in the model along the in-situ loading path. A comparative study between two optimization processes is proposed. The first is based on the technique of the simplex by Nelder and Mead, while the second is based on the decomposition of the pressuremeter curve in three distinct areas. After a brief description of an existing computer program called Press-Sim, which has been written in Fortran for analyzing a cavity expansion using the finite element method, a short explanation is given about the two optimization procedures considered in this article. Then, for a chosen site where soil strength parameters are measured, the comparative study has been performed for both methods at four different depths. For the determination of the angle of friction, the two procedures yield very close values and are in a good agreement with that given by the triaxial test, while for the cohesion, they both diverge from each other on both sides of the value measured by the trial test.

Combined-loading elastoplastic constitutive model for a unified description of the mechanical behavior of the soil skeleton

This paper proposes a combined-loading elastoplastic constitutive model (CL model) for a unified description of the mechanical behavior of soil materials, including clay, sand, and intermediate soil. This mathematical model combines the super-subloading yield surface Cam-clay model and the non-associated Drucker–Prager (DP) model. The first model introduces the skeleton soil structure concept into the Cam-clay model based on critical-state soil mechanics. It describes the mechanical behavior of naturally deposited clay more accurately than the existing model does. The non-associated DP model considers the frictional properties of granular materials and is widely used to describe the undrained shear behavior, particularly that of sandy soil. The newly proposed model is one in which these two independently existing models simultaneously or independently work in loading states according to the loading criterion, which can be derived as a natural result from plastic multipliers. This framework allows for a unified description of a wide range of soil materials, including naturally deposited clayey soils and sandy soils.