Contact Constitutive Model Research Articles

Analysis of Short-range Contact Forces in Peridynamics Endowed with an Improved Nonlocal Contact Model

The motion and deformation laws of multi object interactions in computational models depend on contact algorithms. However, research on the peridynamic contact problem is limited. In this paper, in order to effectively prevent non-physical intrusion during contact, the inherent problems of the contact algorithm in peridynamic discrete models are analyzed, and a force boundary contact method using nonlinear contact stiffness is proposed. Through numerical calculations and geometric analysis of the peridynamic discrete model, the characteristics and reasons for the variation of contact force in the peridynamic contact model under fixed contact stiffness are discovered. To address the nonlinear reduction of contact force and potential non-physical intrusion in the peridynamic contact model, a force boundary peridynamic contact method is proposed by introducing a nonlinear changing contact stiffness function. Then the characteristics of contact force variation in different kinds of contact functions are studied and the parameter setting of contact functions is discussed. The results show that this method can effectively prevent non-physical intrusion and the calculation error is acceptable. This paper lays a foundation for further research on contact constitutive model based on Peridynamic framework.

A contact-based constitutive model for the numerical analysis of masonry structures using the distinct element method

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

Three dimensional discrete element modelling of the conventional compression behavior of gas hydrate bearing coal

To analyze the relationship between macro and meso parameters of the gas hydrate bearing coal (GHBC) and to calibrate the meso-parameters, the numerical tests were conducted to simulate the laboratory triaxial compression tests by PFC3D, with the parallel bond model employed as the particle contact constitutive model. First, twenty simulation tests were conducted to quantify the relationship between the macro–meso parameters. Then, nine orthogonal simulation tests were performed using four meso-mechanical parameters in a three-level to evaluate the sensitivity of the meso-mechanical parameters. Furthermore, the calibration method of the meso-parameters were then proposed. Finally, the contact force chain, the contact force and the contact number were examined to investigate the saturation effect on the meso-mechanical behavior of GHBC. The results show that: (1) The elastic modulus linearly increases with the bonding stiffness ratio and the friction coefficient while exponentially increasing with the normal bonding strength and the bonding radius coefficient. The failure strength increases exponentially with the increase of the friction coefficient, the normal bonding strength and the bonding radius coefficient, and remains constant with the increase of bond stiffness ratio; (2) The friction coefficient and the bond radius coefficient are most sensitive to the elastic modulus and the failure strength; (3) The number of the force chains, the contact force, and the bond strength between particles will increase with the increase of the hydrate saturation, which leads to the larger failure strength.

Exploring the Cyclic Behaviour of URM Walls with and without Damp-Proof Course (DPC) Membranes through Discrete Element Method

Unreinforced masonry (URM) walls are common load-bearing structural elements in most existing buildings, consisting of masonry units (bricks) and mortar joints. They indicate a highly nonlinear and complex behaviour when subjected to combined compression–shear loading influenced by different factors, such as pre-compression load and boundary conditions, among many others, which makes predicting their structural response challenging. To this end, the present study offers a discontinuum-based modelling strategy based on the discrete element method (DEM) to investigate the in-plane cyclic response of URM panels under different vertical pressures with and without a damp-proof course (DPC) membrane. The adopted modelling strategy represents URM walls as a group of discrete rigid block systems interacting along their boundaries through the contact points. A novel contact constitutive model addressing the elasto-softening stress–displacement behaviour of unit–mortar interfaces and the associated stiffness degradation in tension–compression regimes is adopted within the implemented discontinuum-based modelling framework. The proposed modelling strategy is validated by comparing a recent experimental campaign where the essential data regarding geometrical features, material properties and loading histories are obtained. The results show that while the proposed computational modelling strategy can accurately capture the hysteric response of URM walls without a DPC membrane, it may underestimate the load-carrying capacity of URM walls with a DPC membrane.

Discrete element modelling of the uniaxial compression behavior of pervious concrete

Pervious concrete (PC) has been widely used in recent years. With increasing attention on PC, it promotes further understanding of its mechanism responsible for the resulted performance. The objective of this study is to propose a 3D discrete element method (DEM) model to simulate the uniaxial compression process and analyze the meso mechanical properties of PC. The user-defined ellipsoid composed of pebble discrete elements was used to simulate aggregate. In the DEM, the mechanical behaviors of materials were simulated with contact constitutive models of discrete elements. The linear contact model and parallel-bond model were employed to simulate the strength properties between two adjacent aggregates, and between cement paste and aggregate. The parallel-bond parameters were calibrated based on the stress-strain curve obtained from the laboratory test. The reliability of the method was verified by comparing the virtual results with the laboratory tests of PC with 6 groups of different aggregate sizes. It was proved that the DEM model established can be used to simulate the rising section of the stress-strain curve of PC accurately. The maximum absolute error of uniaxial compressive strength is 0.67 MPa, and the relative error is within 5%. By analyzing the number of contact points, the contribution rate of different sizes of aggregates to the contact force and the distribution of the force chain, it can be concluded that the coarse aggregate plays a major role in resisting compression load in PC, while fine aggregate mainly increases the number of contact points to achieve force transmission.

Research on creep modeling and simulation of cotton fiber assembly based on the three-dimensional discrete element

In order to analyze the mesoscopic contact characteristics of cotton fiber creep, this paper uses the meso-particle discrete element method to establish a cotton fiber assembly creep microscopic model based on the existing cotton fiber creep experiment. The microscopic parameters of the Particle Flow Code contact constitutive model are calibrated according to the macroscopic mechanical indexes of cotton fiber creep obtained from experiments, and the creep strain of the cotton fiber in the instantaneous creep stage under different compressive stresses and the contact force between particles are analyzed. According to the time–temperature equivalence principle, the calculation efficiency of the viscoelastic discrete element model is optimized, which improves the time scale of the simulation test. The results show that the numerical simulation results accord with the variation characteristics of the experimental creep variables, which verifies the feasibility of the method in this paper. The research results can provide a certain reference for the deeper study of cotton fiber creep characteristics and its mechanism.

Research on rock triaxial cyclic loading and unloading characteristics based on PFC3D

Numerical methods provide a new way for solving complex geotechnical engineering problems. Firstly, we review the emergence and development of numerical methods, and introduce the basic principles of particle flow discrete element and its application in geotechnical engineering. After that, a method of servo combination of cylinder and loading plate is used, the numerical simulation of the three-dimensional rock in triaxial loading and unloading test is carried out by PFC3D software, and the loading and unloading mechanical characteristics of rock mass under the linear elastic contact constitutive model and parallel bonded contact constitutive model are studied respectively, and we obtain the triaxial loading and unloading stressstrain curves of rock under the elastic constitutive model and elastoplastic constitutive model. The residual strains and hysteresis phenomena of the rock under the two constitutive models are analysed, and the feasibility of the particle flow discrete element method in studying the mechanical characteristics of rocks is demonstrated.

Contact acoustic nonlinearity effect on the vibro-acoustic modulation of delaminated composite structures

In recent years, Vibro-Acoustic Modulation (VAM) techniques for structural health monitoringhave received increasing attention. For such techniques, the sidebands and higher-order harmonics generated by double/single sinusoidal excitations are utilized to identify a series of damages. Currently, most VAM investigations are experimental, mainly involving signal processing, while few studies have paid attention to the mechanics of VAM generation. This paper presents a comprehensive investigation which studies the effects of Contact Acoustic Nonlinearity (CAN) on VAM for delaminated composite structures. The paper includes theoretical analysis, simulations, and experiments. Considering both a nonlinear contact constitutive model and the clapping/rubbing discontinuity, an approximate solution for nonlinear motional equation was established by using Fourier series expansion. A modified Greenwood-Williamson (GW) model for physical contact was implemented into the commercial finite element software ABAQUS by a UINTER subroutine, which described the contact behaviors between rough surfaces. The calculated signal responses from the delaminated composite plates were compared to experimental results. A good agreement was qualitatively and quantitatively achieved with acceptable error. Particularly, some specific features of higher-order sidebands existing in the experiment were identified. Results showed that the combined effect of the nonlinear contact constitutive model and the clapping/rubbing mechanism caused odd–even order differences. The asymmetry between the sidebands indicates the existence of amplitude and frequency modulations, which can be used to extract nonlinear damage indexes. These indexes are capable of characterizing the degree and range of damage.

In-plane structural performance of dry-joint stone masonry Walls: A spatial and non-spatial stochastic discontinuum analysis

In this study, the in-plane structural behavior, capacity, and performance of dry-joint stone masonry walls (DJ-SMWs) and the effects of the vertical stress level on these factors are investigated via a stochastic discontinuum analysis that considers the material uncertainty. A discontinuum type of analysis is performed based on the discrete element method (DEM), where each stone masonry unit is explicitly represented in the computational model. To better simulate the cracking and shear failure modes within the stone units, a coupled fracture energy-based contact constitutive model is implemented into a commercial discrete element code, 3DEC. First, the proposed modeling approach is validated by comparing to experimental findings in literature. Then, the approach is used to explore the failure mechanism and the force–displacement behavior of DJ-SMWs, considering different vertical stress levels and material properties. The results of the novel modeling strategy provide a better understanding of the progressive collapse mechanism of DJ-SMWs and the influence of the vertical stress level. Furthermore, the outcomes of this research indicate the major role of the frictional resistance at the joints in the safety and performance assessment of the dry-joint load-bearing masonry walls. Finally, important inferences are made regarding the non-spatial and spatial stochastic discontinuum analysis.

Stochastic discontinuum analysis of unreinforced masonry walls: Lateral capacity and performance assessments

In this study, lateral capacity and load-deflection behavior of unreinforced stone masonry walls are analyzed based on the discrete element method considering the uncertainties in the material properties. Through this research, discontinuum-based computational models are used to simulate the composite and low-bond strength characteristics of masonry. The unreinforced masonry walls are replicated via the system of deformable rectangular blocks interacting along their boundaries. Local failure modes of masonry (cracking, sliding, and crushing) are taken into consideration at the joints, in which the contact stresses are calculated and updated based on the relative displacement among the adjacent blocks and contact constitutive models, respectively. First, the numerical approach is experimentally validated using previous test results. The same models are then used to determine the influence of uncertainties in the material properties on the macro behavior of the URM walls. The importance of considering the inherent variability in the material and modeling parameters is highlighted. Results clearly show the informative outcomes of the stochastic analysis and provide a deeper understanding of the structural behavior of URM walls in terms of the governing failure mechanisms, displacements, and load-carrying capacities. These results also underline the importance of the variability in the force and displacement capacities, which should be considered when defining performance limits for stone masonry in the future, as they are currently unavailable in national standards for Turkey and the US.

Variational multiscale method for fully coupled thermomechanical interface contact and debonding problems

In this study, a computational framework is proposed for thermomechanical contact and debonding problems with proper thermal resistance at the interface. Using the Variational Multiscale (VMS) framework, we present a fully coupled thermomechanical formulation with an explicit expression of the pressure at the contact interface. The formulation considers the quasi-static balance of the momentum and the transient heat transfer problem in a fully coupled fashion. At the interface, two different contact constitutive models are utilized for tension and compression. For tensile problems, in the mechanical phase, a tensile debonding model is employed, whereas in the thermal phase, the displacement-dependent model is employed. For compressive problems, in the mechanical phase, a Coulomb frictional model is employed while in the thermal phase, a pressure-dependent model is embedded. Because of the naturally derived interface stability terms that possess area- and stress-weighting, the proposed VMS formulation accommodates contact/debonding and contact/frictional sliding at the interface due to both thermal and mechanical loading without losing numerical stability. The proposed method is applied to a class of numerical test problems with discontinuity at the interfaces, and good agreement with analytical and numerical data is achieved.

Tensile Fracture Mechanism of Masonry Wallettes Parallel to Bed Joints: A Stochastic Discontinuum Analysis

Nonhomogeneous material characteristics of masonry lead to complex fracture mechanisms, which require substantial analysis regarding the influence of masonry constituents. In this context, this study presents a discontinuum modeling strategy, based on the discrete element method, developed to investigate the tensile fracture mechanism of masonry wallettes parallel to the bed joints considering the inherent variation in the material properties. The applied numerical approach utilizes polyhedral blocks to represent masonry and integrate the equations of motion explicitly to compute nodal velocities for each block in the system. The mechanical interaction between the adjacent blocks is computed at the active contact points, where the contact stresses are calculated and updated based on the implemented contact constitutive models. In this research, different fracture mechanisms of masonry wallettes under tension are explored developing at the unit–mortar interface and/or within the units. The contact properties are determined based on certain statistical variations. Emphasis is given to the influence of the material properties on the fracture mechanism and capacity of the masonry assemblages. The results of the analysis reveal and quantify the importance of the contact properties for unit and unit–mortar interfaces (e.g., tensile strength, cohesion, and friction coefficient) in terms of capacity and corresponding fracture mechanism for masonry wallettes.

A meso-scale discrete element method framework to simulate thermo-mechanical failure of concrete subjected to elevated temperatures

This paper presents mesoscale thermo-mechanical analyses of plain (unreinforced) concrete based on the discrete element method (DEM). The proposed discontinuum modelling strategy represents the aggregates and matrix as a system of deformable polyhedral blocks, interacting along their boundaries. The nodal velocities of each block are calculated via the explicit integration scheme of DEM, and contact stresses are computed based on the relative contact displacements of the adjacent blocks. To better predict the thermo-mechanical behaviour of concrete, fracture energy-based contact constitutive models are implemented by considering temperature dependency at the zone and contact properties. First, the discrete meso models are tested under uniaxial compression loading at room temperature. Then, transient thermo-mechanical tests are performed considering different load levels. The results of the computational models are compared with the macroscopic response quantities of concrete obtained from the available experimental studies in the literature. The results indicate that the developed DEM framework predicts the complex mesoscale thermo-mechanical response history and the typical damage progression observed in concrete. Furthermore, the fracture patterns, crack propagation with temperature, and the differential thermal expansion phenomena are studied in detail.

Crack nucleation in the adhesive wear of an elastic-plastic half-space

The detachment of material in an adhesive wear process is driven by a fracture mechanism which is controlled by a critical length-scale. Previous efforts in multi-asperity wear modeling have applied this microscopic process to rough elastic contact. However, experimental data shows that the assumption of purely elastic deformation at rough contact interfaces is unrealistic, and that asperities in contact must deform plastically to accommodate the large contact stresses. We therefore investigate the consequences of plastic deformation on the macro-scale wear response using novel elastoplastic contact simulations. The crack nucleation process at a rough contact interface is analyzed in a comparative study with a classical J2 plasticity approach and a saturation plasticity model. We show that plastic residual deformations in the J2 model heighten the surface tensile stresses, leading to a higher crack nucleation likelihood for contacts. This effect is shown to be stronger when the material is more ductile. We also show that elastic interactions between contacts can increase the likelihood of individual contacts nucleating cracks, irrespective of the contact constitutive model. This is supported by a statistical approach we develop based on a Greenwood–Williamson model modified to take into account the elastic interactions between contacts and the shear strength of the contact junction.

Simulation of the in-plane structural behavior of unreinforced masonry walls and buildings using DEM

In this study, a novel computational modeling strategy is proposed to estimate the lateral load capacity and behavior of unreinforced masonry (URM) structures. All commonly noted failure mechanisms are captured via the proposed modeling strategy using the discrete element method (DEM) in three-dimensions (3D). Masonry walls are represented as a system of elastic discrete blocks, where the nodal velocities are evaluated by integrating the equations of motion using the central difference method. Then, the mechanical interactions among adjacent blocks are examined utilizing the relative contact displacements and employed in the contact stress calculation. Through this research, a new stress-displacement contact constitutive model is considered and implemented in the commercial software 3DEC, which includes softening stress-displacement behavior for tension, shear, and compression along with the fracture energy concept. The results of the discontinuum models are validated on small- and large-scale experimental studies available in the literature with good agreement. Furthermore, important inferences are made regarding the effect of block size, the number of contact points, and contact stiffness values for robust and accurate simulations of masonry walls.

A cohesive discrete element based approach to characterizing the shear behavior of cohesive soil and clay-infilled rock joints

The mechanical behaviour of the infilled rock joints is highly concerned in rock joint studies due to its involvement in a wide range of mining collapses. In this study, a new cohesive constitutive model was employed and used in discrete element method (DEM) simulation to analyse the failure mechanism of infilled rock joints numerically. The exponential softening responses of the model in mixed mode loading conditions allow more realistic modelling of clay-infilled rock joints, which is more phenomenologically promising than the use of the current constitutive models in PFC2D such as the parallel bond model (PBM). The proposed model is implemented in DEM commercial codes (PFC2D) as a user-defined contact constitutive model. In parallel with this theoretical development, experimental works on shear behaviour of infilled materials and infilled rock joints under different normal loads are also carried out for the calibration of the cohesive model, and validation of the DEM based approach, respectively. Simulation results show excellent agreement with experimental counterparts demonstrating the effectiveness of the proposed cohesive model in reproducing the shear properties of clay-infilled rock joint. The proposed cohesive DEM framework, therefore, will facilitate better understanding of the shear mechanism of cohesive infilled rock joints.

Simulation of uniaxial tensile behavior of quasi-brittle materials using softening contact models in DEM

This study proposes new contact models to be incorporated into discrete element method (DEM) to more accurately simulate the tensile softening in quasi-brittle materials, such as plain concrete and masonry with emphasis on fracture mechanism and post-peak response. For this purpose, a plain concrete specimen (double notched) and stack bonded masonry prism under direct tensile test are modeled. Furthermore, mixed mode crack propagation is investigated in concrete and brickwork assemblages. Two modeling approaches are proposed, the simplified and detailed meso modeling, both based on DEM. In the simplified meso-model, a smooth contact surface is considered between two separate blocks, whereas the internal structure of the material is explicitly represented as a tessellation into random polyhedral blocks in the detailed meso-model. Furthermore, recently developed tensile softening contact constitutive models implemented into a commercial discrete element code (3DEC) are used to simulate the softening behavior of concrete and masonry. As an important novel contribution, it is indicated that the proposed computational models successfully capture the complete (pre- and post-peak) material behavior and realistically replicate the cracking mechanism. Additionally, a sensitivity analysis demonstrates the influence of the various micro-contact parameters on the overall response of the examined materials.

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method (DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil (e.g. cavity expansion), DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response. Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model, and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation (i.e. cavity expansion), a minimum distance of 11a (a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.

Studying On The Parameters Of Bond-model In DEM For Asphalt Mixture

The discrete element method used to simulate asphalt mixture’s performance can fully consider the effect of interaction between particles, but the key to use discrete element method is to select reasonable parameters of contact constitutive model. Using 2D and 3D discrete element method to establish asphalt mixture splitting test model which adopting contact-bond method between particles, the influence of particle stiffness and bond strength on the simulation results are analyzed. It is found that the straight slope of the load-deformation curve is mainly determined by the stiffness parameter and the peak load is determined by the bond strength. Asphalt mixture laboratory splitting test of AC-20 and AC-13 at -10°C, 0°C, 10°C and 20°C are accomplished, then according to the load-deformation curve’s initial slope and peak load, discrete element model parameters are determined. The relationship between load-deformation curve’s initial straight slope and stiffness, peak load and bond strength are concluded on the basis of splitting test results curve.

Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints

In this paper, a simple and effective numerical approach is presented on the basis of the Member Discrete Element Method (MDEM) to investigate static and dynamic responses of steel frames with semi-rigid joints. In the MDEM, structures are discretized into a set of finite rigid particles. The motion equation of each particle is solved by the central difference method and two adjacent arbitrarily particles are connected by the contact constitutive model. The above characteristics means that the MDEM is able to naturally handle structural geometric nonlinearity and fracture. Meanwhile, the computational framework of static analysis is consistent with that of dynamic analysis, except the determination of damping. A virtual spring element with two particles but without actual mass and length is used to simulate the mechanical behaviors of semi-rigid joints. The spring element is not directly involved in the calculation, but is employed only to modify the stiffness coefficients of contact elements at the semi-rigid connections. Based on the above-mentioned concept, the modified formula of the contact element stiffness with consideration of semi-rigid connections is deduced. The Richard-Abbort four-parameter model and independent hardening model are further introduced accordingly to accurately capture the nonlinearity and hysteresis performance of semi-rigid connections. Finally, the numerical approach proposed is verified by complex behaviors of steel frames with semi-rigid connections such as geometric nonlinearity, snap-through buckling, dynamic responses and fracture. The comparison of static and dynamic responses obtained using the modified MDEM and those of the published studies illustrates that the modified MDEM can simulate the mechanical behaviors of semi-rigid connections simply and directly, and can accurately effectively capture the linear and nonlinear behaviors of semi-rigid connections under static and dynamic loading. Some conclusions, as expected, are drawn that structural bearing capacity under static loading will be overestimated if semi-rigid connections are ignored; when the frequency of dynamic load applied is close to structural fundamental frequency, hysteresis damping of nonlinear semi-rigid connections can cause energy dissipation compared to rigid and linear semi-rigid connections, thus avoiding the occurrence of resonance. Additionally, fracture analysis also indicates that semi-rigid steel frames possess more anti-collapse capacity than that with rigid steel frames.