Drucker-Prager Constitutive Model Research Articles

Finite element simulation and experimental investigation of in-situ laser-assisted diamond turning of monocrystalline silicon

While the effectiveness of in-situ laser-assisted diamond turning (In-LAT) for promoting the ductile machinability of monocrystalline silicon has been demonstrated, the underlying cutting mechanisms remain inadequately understood. In this study, we investigate the fundamental mechanisms involved in the In-LAT of monocrystalline silicon by finite element (FE) simulations and experiments. Specifically, a FE model of In-LAT of monocrystalline silicon is developed, which incorporates a Drucker–Prager constitutive model to address the brittle fracture of the material, as well as temperature-dependent materials properties to address the thermal softening effect. Furthermore, experiments of In-LAT of monocrystalline silicon are conducted with the self-developed In-LAT device, including tapering cutting and end face cutting. Simulation results demonstrate that In-LAT significantly increases the critical depth of cut for the brittle-to-ductile transition of monocrystalline silicon in tapering cutting mode by 72.2% compared to conventional cutting, accompanied with significantly reduced cutting forces, continuous chip profile and reduced surface brittle damage. The promotion of ductile machinability of monocrystalline silicon under In-LAT is attributed to the reduction and dispersion of stress in the cutting zone, which is in contrast to the significant stress concentration at the rake face and cutting edge in conventional cutting. And simulation results also provide an optimal temperature field of 900 K for the In-LAT of monocrystalline silicon, above which the excessive plastic flow accompanied by thermal accumulation results into deteriorated surface roughness. These findings provide valuable insights for understanding the cutting mechanisms of In-LAT and the parameter optimization for In-LAT application.

Study on meso‑mechanical properties and failure mechanism of soil-rock mixture based on SPH model

This study adopts the Smoothed Particle Hydrodynamics (SPH) technique to accurately and efficiently replicate and forecast the mesoscopic behavior of soil-rock mixtures (SRM). It introduces a novel approach for generating rock blocks within the SRM, utilizing a method that randomly selects angles and lengths. In addition, this research proposes a method for discretizing any shaped region into free particles with specific material attributes, named the regional medium particle discretization method. It incorporates the Drucker-Prager constitutive model to develop the SPH numerical model for SRM. Furthermore, it examines the effects of different rock sizes and rock contents on the SRM's failure characteristics and mechanical properties. The findings revealed that, for identical rock contents, smaller rock samples exhibit a more dispersed failure surface with numerous secondary shear bands, whereas larger rock samples display a smoother and more concentrated failure surface. As the rock content decreases, shear bands typically form in the sample's center and are relatively straight. However, as the rock content increases, the shear bands' configuration becomes more intricate, often featuring multiple shear bands. This method offers a fresh perspective for exploring the mechanical properties of heterogeneous materials.

Chip formation mechanism in milling metallic glasses based on Drucker-Prager (D-P) constitutive model

In this paper, further in-depth research on chip formation mechanism is conducted on the cutting of metallic glasses. The study of chips contributes to a better understanding of the machining nature of materials, which is of significant importance for improving product quality, reducing energy consumption, and resource utilization. This paper employs a combination of simulation and experimental methods, wihch not only analyzes the mechanism of chip formation in depth, but also investigates the time-varying characteristics of cutting forces. The results indicate that, when comparing simulation with experiments, the average error in cutting forces is 7.62%, and the chip morphology is also quite similar. Observations in the simulation show that as the cutting thickness increases from 7.96 μm to 23.87 μm, the free surface of the chip exhibits serrated features, and the main shear zone of the chip becomes clearer. Cutting forces exhibit periodic variations, with alternating peaks and valleys representing the formation of shear zones in the chip. In the experiment, observed chips displays a wrinkled free surface and a smooth non-free surface, with some chip edges exhibiting a burr phenomenon. By selecting appropriate machining parameters, the generation of secondary shear bands on the free surface was effectively reduced. By observing the chip morphology, it is found that the chip formation is accompanied by the material removal of plasticity and brittleness, which is the result of the combined action of heat, stress, and free volume. It should be considered to lower temperature to reduce the phenomenon of chip adhesion, providing guidance for further optimizing the cutting process of metallic glass. This paper can provide to readers further understanding of the chip formation mechanism in milling metal glass.

A hybrid phase-field method for modeling mixed-mode fractures in elastoplastic rock-like materials

The phase-field method has been proven to be a powerful tool for predicting complex crack patterns and widely utilized in many fields. To effectively characterize and depict the complex cracking behaviors of rock-like materials, however, is still a challenge. In this study, a modified phase field model for mixed-mode fractures in rock-like materials is proposed. The effect of plastic free energy on damage is taken into consideration by developing a new phase field evolution equation. A non-associative Drucker–Prager constitutive model is coupled within the framework to capture more accurate stiffness and plastic strain in rock-like materials. To solve the coupled problem more efficiently, an accelerated monolithic iteration method has been developed. Several numerical results are presented to examine the viability of the established phase field model. Additionally, the investigation of the local stress field is done to identify the main driving forces of the different fracture modes.

Numerical modeling of the damage mechanism of concrete-soil multilayered medium subjected to underground explosion using the GPU-accelerated SPH

The prediction of the damage mechanism of the concrete-soil multilayered medium subjected to underground explosion is a challenging task to address. In this paper, the smoothed particle hydrodynamics methodology is introduced to deal with the soil fragmentation and fracture propagation in concrete which are involved in the physical process of explosion in this double-layered medium. The Drucker–Prager constitutive model and the Holmquist–Johnson–Cook concrete constitutive model are employed to describe the dynamic behavior of the soil and concrete, respectively. Firstly, the numerical model was validated by two cases, namely the high velocity impact of an aluminium sphere on a concrete plate and the fracture propagation of rock medium under blast loading. Subsequently, the explosion in the three-dimensional concrete-soil multilayered medium involving millions of particles was simulated and investigated using GPU-accelerated smoothed particle hydrodynamics methodology. The numerical results obtained using smoothed particle hydrodynamics are compared against the available experimental data, which shows that the present SPH model can reproduce the failure pattern and fracture propagation of the concrete medium with cylindrical hole in the concrete plate and different burial depths of the explosive.

SPH Analysis of Sliding Material Volume and Influence Range of Soil Slope Under Earthquake

The post-failure process of soil slope triggered by earthquake is usually characterized by large deformation, which can be properly addressed by SPH simulation. Meanwhile, it is of engineering significance to evaluate the sliding volume and influence range after the failure of soil slope. The simulation method is based on the Drucker–Prager constitutive model and the SPH method. The fixity boundary and free boundary particles are adopted to realize the application of ground motion and the simulation of free field boundary, and this study proposes a dynamic analysis model for the whole-failure process simulation of soil slope under earthquakes. By comparing the PGA amplification coefficients obtained from the model test and numerical simulation, the accuracy of ground motion input and ground motion response simulation is verified. Then, the proposed dynamic analysis method is used to simulate a shaking table test of soil slope in the literature. The results of the deformation of the soil slope after the test are compared to verify the accuracy of the analysis method in the soil slope displacement and the influence range under the earthquake action. Finally, by comparing the SPH results of slopes under different angles with and without vibration, this study obtains the variation rules of sliding material volume and the influence range of soil slope under seismic vibration. The greater the slope angle is, the greater the displacement of the slope will be with vibration, and the sliding material volume will present different trends under different displacement thresholds. Moreover, the horizontal displacement of the slope under the effect of an earthquake increases nonlinearly with the increase of slope incline angle.

Three-dimensionsal granular flow continuum modeling via material point method with hyperelastic nonlocal granular fluidity

The accurate and efficient modeling of granular flows and their interactions with external bodies is an open research problem. Continuum methods can be used to capture complexities neglected by terramechanics models without the computational expense of discrete element methods. Constitutive models and numerical solvers are the two primary aspects of the continuum methods. The viscoplastic size-dependent nonlocal granular fluidity (NGF) constitutive model has successfully provided a quantitative description of experimental flows in many different configurations in literature. This research develops a numerical approach, within a hyperelasticity framework, for implementing the dynamical form of NGF in three-dimensional material point method (3D MPM, an appropriate numerical solver for granular flow modeling). This approach is thermodynamically consistent to conserve energy, and the dynamical form includes the nonlocal effect of flow cessation. Excavation data, both quantitative measurements and qualitative visualization, are collected experimentally via our robotic equipment to evaluate the model with respect to the flow geometry as well as interaction forces. The results are further compared with the results from a recent modified plastic Drucker–Prager constitutive model, and in other configurations including wheel–soil interactions, a gravity-driven silo, and Taylor–Couette flow.

Analysis of Characteristics of Plastic Zone and Mechanical Properties of Anchor Structure in Hydraulic Tunnels with High Ground Temperature

In order to explore the characteristics of plastic zone and the mechanical properties of anchor structure during the construction of hydraulic tunnels with high ground temperature, the high-temperature section of the diversion tunnel of a hydropower station in Xinjiang was studied. Based on the temperature data and the axial force data of the bolt on-site, the Drucker-Prager constitutive model and the finite element method were adopted to simulate and analyze the temperature-stress coupled field and the initial anchoring support during the construction of the high ground temperature tunnels. The results showed that, after the excavation of the tunnel, a crescent-shaped plastic zone first appeared at the hance, then expanded to the spandrel and vault, and finally formed an irregular ring-shaped plastic zone around the tunnel. The higher the initial temperature of surrounding rocks, the larger the plastic deformation and the range of the plastic zone. When the temperature exceeded 80∘∘C, the plastic zone was more likely to expand to the spandrel and vault; and meanwhile, when the bolt was closer to the hance, the neutral point was closer to the cavity wall. As the stress was released, the neutral point moved from close to the cavity wall to away from the cavity wall. Anchoring support can effectively limit the development of plastic zone in surrounding rocks under high ground temperature. After 10 days of anchoring support at 60∘∘C, 80∘∘C, and 100∘∘C, the range of the plastic zone decreased by 9%, 20%, 24%, respectively, and the maximum axial force of a single bolt was 19.4 kN, 20.1 kN, and 23.8 kN, respectively. The higher the temperature, the higher the strength of the bolt.

Numerical study on rock damage characteristics of multi hole blasting

In this study, a two-dimensional finite element numerical simulation method was used to study the damage characteristics of rock mass under multi-hole blasting load. In the analysis, Drucker-Prager constitutive model was used to characterize the strength of rock mass. The stress acting on the blasting hole was simulated by exponential functions, that the stress could reach the maximum value in a short time and then drop to zero in a relative long time. The damage characteristics of rock under different confining pressures, and the influence of free surface on the damage of rock were examined. The results show that under the same blasting load, increasing the confining pressure of surrounding rock can inhibit the development of rock cracks; The free surface made the explosion stress wave reflect, the rock mass between the blasting hole and the free surface produced a phenomenon of stratification crack which restrained the crack propagation below the blasting hole.

Hydro-mechanical coupled B-spline material point method for large deformation simulation of saturated soils

Numerical simulation for large deformation problems of saturated soil poses an ongoing challenge since it requires the capabilities of modeling large deformations, interactions between solid skeleton and pore water, as well as fluidization behaviors. A hydro-mechanical coupled B-spline material point method is developed to simulate large deformations of saturated soils. Based on Biot's mixture theory, a single set of material particles is adopted to represent saturated soils where Darcy's law is employed to govern the motion of pore water and the momentum conservation of the mixture is used to govern the motion of solid skeleton. The convergence and effectiveness of the proposed method are examined by one-dimensional consolidation tests and quasi-static footing penetration into two-dimensional elastic saturated soils. The capability of simulating practical engineering for the proposed method is demonstrated by reproducing the dynamic process of three-dimensional saturated soil slopes with a strain-softening Drucker-Prager constitutive model. Results show that the coupled BSMPM well reveals the overall dynamic process of saturated soil slope involving evolution of shear bands, formation of graben and horst, and fluidization of progressive failures with improved computational accuracy and enhanced convergence, which demonstrates the proposed method is a promising approach for large deformation problems of saturated soils.

Analysis of Under-Reamed Piles Subjected to Different Types of Load in Clayey Soil

Underreamed piles with one or more bulbs have been widely used in almost all types of soil to support a range of structures. In some cases, in addition to vertical compressive or uplift loads, piles must withstand a considerable lateral load. A 3-D finite element study using ABAQUS software was conducted to examine the behavior of underreamed piles in clay soil under pure lateral, pure uplift, and combined uplift and lateral loads. In this study, pile (L/D) ratios of 11.66, 15, 20, and 25 were considered by adjusting the pile length to simulate the behavior of rigid and flexible piles. The piles were modeled as a linear elastic material, and the soil behavior was simulated using the Drucker-Prager constitutive model. The findings show that the lateral resistance of piles with (L/D) ratios of 11.66 and 15 increased slightly when underreamed piles were used. However, no change in lateral resistance was observed for underreamed piles with (L/D) ratios of 20 and 25 compared with straight piles. The uplift capacity of underreamed piles was significantly greater than that of a straight pile. The lateral capacity was marginally influenced by the prior uplift loading, such that it decreased for a rigid underreamed pile, and increased for a flexible underreamed pile.

The Xinmo rockslide-debris avalanche: An analysis based on the three-dimensional material point method

On June 24, 2017, a catastrophic rock avalanche with a volume of 5.08 × 106 m occurred in Xinmo village, Maoxian County, Sichuan Province, SW China. Several studies focusing on the triggering factors, failure mechanism and dynamic process of the Xinmo landslide have been reported in the literature. However, there are few studies with detailed three-dimensional investigations based on numerical modeling that assess the post-failure stage of the landslide. In the present study, the three-dimensional material point method is used to reproduce the kinematics of the landslide to obtain better insight into the disaster by considering the effects of fragmentation and entrainment. Based on this framework, a velocity-weakening friction law is implemented to describe the basal friction between the moving mass and the substrate, and a strain–softening Drucker–Prager constitutive model is used to describe the internal deformation of the moving mass. The entrainment processes obtained with and without the proposed model are compared, and the simulated results generated with the presented models showing the distribution characteristics of the materials in the deposit area match the observed results fairly well. The implementation of a velocity-weakening friction law and a strain-softening Drucker–Prager constitutive model in the material point method may provide valuable insight for the enforcement of physically based risk assessments of “rockslide-debris avalanches”.

Dynamic modeling of large deformation slope failure using smoothed particle finite element method

In this paper, a novel node-based explicit smoothed particle finite element method (SPFEM), on the basis of the particle finite element method (PFEM) framework, is utilized to evaluate the stability of slopes and to simulate the post-failure behavior of soil. The main advantage of SPFEM in slope stability analysis lies in its capabilities to consider the whole dynamic failure process of slope and to simulate large deformation and post-failure of soils. For the stability analysis of a cohesive soil slope, the shear strength reduction technique with a kinetic energy-based criterion for distinguishing slope failure is adopted to obtain the factor of safety (FOS) of a slope, and the FOS is compared with that obtained by the classical FEM and LEM approaches for further validation. Then, the dynamic failure process of a non-cohesive granular material slope is simulated using Drucker-Prager constitutive model. The influence of friction resistance of granular material, as well as the repose angle of slope after failure, is discussed. Finally, the progressive failure behavior of a long clayey slope is modeled using SPFEM in conjunction with a strain-softening Tresca constitutive model. The retrogressive failure behavior of a long clayey slope is analyzed.

Elastoplastic Cosserat continuum model considering strength anisotropy and its application to the analysis of slope stability

Aiming at solving the problems of strength anisotropy and strain localization of cohesive soil, Pietruszczak’s method, in which the microstructure tensor is combined with stress invariance, is developed to analyze the cohesion anisotropy and is introduced into the Drucker-Prager constitutive model under Cosserat continuum theory. A consistent algorithm of the corresponding constitutive model is derived. The characteristics of strength anisotropy and the reliability of the developed numerical method are verified by the experiments in laboratory. The importance and necessity of developing the numerical model with strength anisotropy under the framework of Cosserat theory are evaluated via simulation of a plane strain compression model. It indicates that the degree of the cohesion anisotropy has an important influence on the bearing capacity, and that the numerical model can overcome the ill-posedness of the mesh sensitivity and maintain the well-posedness of the strain localization problem. Furthermore, the effects of strength anisotropy and strain softening on the safety factor of the slope are analyzed via the gravity increase method. It is demonstrated that the Cosserat continuum model can effectively overcome the problems of mesh-dependence encountered by the classical continuum model and yield a reasonable safety factor with mesh refinement.

A two-field semi-Lagrangian reproducing kernel model for impact and penetration simulation into geo-materials

In this paper, a displacement–pressure (u–p) semi-Lagrangian reproducing kernel (RK) is introduced to study the penetration depth of various projectile types into dry and fully saturated geo-materials. To describe the poromechanics of saturated materials, Biot theory is incorporated into the semi-Lagrangian formulation and a damage model is embedded into Drucker–Prager constitutive model to simulate the soil behavior and separation during the impact and penetration process. The stabilized nodal domain integration is developed in the two-field semi-Lagrangian RK formulation to ensure numerical stability, and the kernel contact algorithm is implemented to model the interaction between soil and projectile bodies. Several examples are studied to validate and assess the proposed method’s performance in predicting the final penetration depth, and the results are compared to those reported in the literature.

Finite element analysis of the effect of tool rake angle on brittle-to-ductile transition in diamond cutting of silicon

Brittle-to-ductile transition plays a crucial role in ultra-precision machining of hard-brittle materials. In the present work, we investigate the brittle-to-ductile transition in diamond grooving of monocrystalline silicon by finite element modeling and simulation based on Drucker-Prager constitutive model. The brittle-to-ductile transition behavior is distinguished by analyzing evolutions of chip profile and cutting force. Corresponding diamond grooving experiment using the same machining configuration with the finite element simulation is also carried out to derive the critical depth of cut for the brittle-to-ductile transition. The comparison of experimental value of the critical depth of cut and predicted one by the finite element simulation demonstrates the high accuracy of as-established finite element model. Subsequent finite element simulations are performed to investigate the influence of rake angle of cutting tool on both diamond grooving and conventional diamond cutting with a constant depth of cut, which demonstrates a prominent dependence of brittle-to-ductile transition of silicon on the rake angle ranging from − 60° to 0°. And a critical rake angle for the most pronounced ductile machinability of silicon is found.

Mechanical characterization of the AlSi9Cu3 cast alloy under distinct stress states and thermal conditions

This paper presents the results of several mechanical tests aiming at characterizing the constitutive behaviour of the AlSi9Cu3 cast alloy, covering different temperatures and stress fields, including tensile and compressive tests of smooth and notched specimens as well as combined shear/tension and shear/compression with special designed specimens. The Johnson-Cook model was able to correlate the flow stress under quasi-static uniaxial compression, including thermal effects. However, under tension the yield stress does not reduces monotonically and gradually with temperature, which impedes the application of Johnson-Cook model for positive triaxialities. At room temperature, the AlSi9Cu3 alloy shows significant asymmetrical tensile and compressive behaviours requiring a plasticity model sensitive to the stress triaxiality such as the Drucker-Prager. As regards the ductility limits of the material, different data was analysed to generate fracture loci for the material where equivalent fracture strains were plotted against the stress triaxialities. The calibrated Drucker-Prager constitutive model together with a damage approach based on the fracture loci generated was successfully verified using test data from specimens loaded under combined shear/tension or shear/compression. The AlSi9Cu3 cast alloy exhibits a sharp reduction in ductility between the negative stress triaxiality cut-off and −0.1, keeping at low levels above this triaxiality value.

Investigation of the tool-rock interaction using Drucker-Prager failure criterion

Mechanical rock breaking in different forms have found wide applications in the mining and civil engineering industry such as drilling, tunnelling and grinding. A detailed understanding of the tool-rock interaction is essential to achieve high efficiency in rock breaking and to optimize the cutting parameters. The finite element simulation of the tool-rock interaction remains a challenging task due to the complexity caused by the physical rock properties, the crack initiation and propagation, as well as the chip generation phenomenon. This study has implemented the Drucker-Prager constitutive model with an isotropic damage model in a finite element analysis to examine the rock failure modes, considering the interaction of cutting tool and the rock. The material parameters for the rock derive from the uniaxial compressive strength (UCS) and Brazilian tensile strength (BTS) tests performed on rock specimens. This study includes an experimental program to examine the crack initiation, crack propagation and the chip generation in rock specimens. The results show the Drucker-Prager failure criterion with the calibrated material parameters and element sizes simulate closely the tool-rock interaction phenomenon. The mesh size imposes a great effect on the parameter selection of the rock model, particularly for the fully damaged plastic strain value. This study leads to an enhanced understanding of rock breaking mechanisms in the mechanical excavation, and provides the basis to improve the rock excavation machine design.

Study of the Bearing Capacity of Closely Spaced Square Foundations on Granular Soils

In the present study, the effect of the interaction between two closely spaced square footings is analyzed through finite element simulations. The numerical analyses were performed through the construction of three-dimensional 3D Boundary Value Problems constructed with the software Abaqus Standard. Several values for the foundation embedment and separation between footings were considered. The behavior of the granular soil was simulated through an extended Drucker–Prager constitutive model. The results were used to calibrate an extended bearing capacity equation through a multiple variable regression analysis, and accounts for the effect of the embedment depth and separation between footings. Finally, the proposed relation was compared with some reported values in the literature, including experimental tests and numerical results, and showed a better agreement with the experimental data than other reported studies.

Simulation of quasi-static axisymmetric collapse of granular columns using smoothed particle hydrodynamics and discrete element methods

Flow of granular materials under different conditions poses significant challenges to engineers as their behavior can vary from solid-like to fluid-like. The quasi-static axisymmetric collapse of granular columns is an interesting case of granular flow relevant to the active deformation of retaining structures. This study aims to shed light on this type of collapse using numerical simulations including the smoothed particle hydrodynamics (SPH) method in the continuum framework and the discrete element method (DEM) in the discrete framework. Three-dimensional SPH and DEM models are developed to investigate the quasi-static axisymmetric collapse of granular columns, which is initiated by slowly expanding the cylindrical wall of the column. The Drucker–Prager constitutive model with non-associated flow rule is implemented into SPH formulations to model elastoplastic behavior of granular material. The linear contact model is used in DEM simulations with calibrated contact stiffness parameters. The effects of particle shape and hysteretic contact behavior in the DEM model are indirectly considered through reducing particle rotational velocities by a calibrated constant factor at every time step. Using the developed models, the final deposit profile (e.g., height, runout distance, repose angle), non-deformed region, collapse pattern and energy dissipation for different initial aspect ratios are investigated. In addition, final height, runout distance and energy dissipation are theoretically derived and are found to be in good agreement with SPH and DEM simulations. Results show that the quasi-static axisymmetric collapse can be modeled using both the continuum and discrete frameworks as long as appropriate constitutive models or contact behaviors are implemented. However, DEM simulations are more capable of capturing particle-level behaviors, such as the sharp edges of the free surface and flow front. Results demonstrate that quasi-static granular collapse is qualitatively similar to the dynamic collapse, but results in smaller runout distances for all aspect ratios.