Contact Law Research Articles

Restating the Acquis Communautaire? A Critical Examination of the 'Principles of the Existing EC Contact Law'

Restating the Acquis Communautaire? A Critical Examination of the 'Principles of the Existing EC Contact Law'

Effect of the backfill material in the seismic response of multi-span masonry arch bridges under seismic loading

The present study deals with numerical modelling of multi-span masonry arch bridges under seismic loading. Based on the evidence coming from an experimental program reported in the literature, a reference 3D nonlinear Finite Element model is calibrated. The numerical model is realized in Abaqus software by adopting a macro-modelling strategy for simulating the masonry behavior. To this purpose the Concrete Damage Plasticity material model is used. The backfill material follows a Drucker-Prager behavior, while the interaction between the two materials is simulated by means of an appropriate contact constitutive law. After calibration, the response of the bridge under longitudinal seismic loads is thus investigated. In particular, a mass proportional load distribution is adopted. Then, the effects of the mechanical parameters of the backfill material on the global response of the bridge are investigated by means of a parametric analysis, which is carried out by varying: i. elastic modulus, ii. cohesion, iii. backfill-masonry contact law, and iv. backfill friction angle. The obtained results provide preliminary indications about reliable retrofitting techniques for cases similar to the one under consideration.

Assessing the Effects of Material Properties on Load Behavior in Dry Ball Mills Using DEM

Understanding how the mill load behaves is crucial for enhancing ball mill effectiveness. This study aimed to create a discrete element method (DEM) model to simulate the motion charge in ball mills and to analyze how the simulation material properties affected the load behavior. The steel balls were modelled as a collection of distinct particles, each of which was subject to Newton’s laws of motion and tracked in a Lagrangian manner. Hertzian contact law was used to describe inter-particle collisions. Then, this numerical model was coded using the open-source C++ program LAMMPS Improved for General Granular and Granular Heat Transfer Simulation (LIGGGHTS) to mimic laboratory and pilot-scale ball mills. The load positions measured from the DEM simulations were compared to the published experimental data and empirical models of comparable laboratory and pilot-scale experiments to validate the findings. The angular shoulder position ranged between 137° to 154° for the range of Young’s modulus of 0.5 to 1000 MN/mm2. Angular shoulder and toe positions had a variation of less than 10% from the laboratory and pilot-scale experimental data. The outcomes demonstrated a significant relationship between load position and material characteristics such as Young's modulus in DEM simulation. This preliminary model can be used for choosing the appropriate material parameters for ball mills both with DEM and coupled CFD–DEM multiphase simulations. This assessment concluded that material properties affect the load behavior in computer simulations of ball mills.

A study of impact induced stress due low velocity impact on laminated composite skewed hypar shell roof

The doubly ruled hypar shell, being one of the most feasible shell roof configurations, enjoys industrial preference for covering large column free areas. This class of shells is unique as the only curvature here is the cross curvature and these do not admit easy closed form solution particularly when the boundary conditions are complicated. Laminated composite, an innate choice to different industrial sectors for its huge specific strength and stiffness, good weathering resistance, is now being extensively employed in civil engineering. However the low transverse shear strength of the composite shell impelled the researchers to study the response of the same under the action of impact loads. In the present study, a finite element code is functioned to investigate the impact induced stress history generated in simply supported laminated composite hypar shell for different impact velocities of a spherical solid striker. Contact behavior is described by modified Hertzian contact law where as time dependent equations are solved using Newmark’s time integration algorithm in present analysis. A practicing engineer often has to select a particular shell option consisting stacking sequence among a number of possibilities. The present paper discusses the behaviour of composite hypars under low velocity impact and different stresses induced due to the same from engineering standpoint to propose a selection guide line among the available options and to proposes values of practical parameters like the equivalent static loads and dynamic magnification factors for designing such shells through static simplification of the problems.

Transient response of pre-twisted FG-GRC sandwich conical shell subjected to low-velocity impact in thermal environment

A finite element method-based dynamic analysis of pre-twisted sandwich conical shell panel having functionally graded graphene-reinforced composite (FG-GRC) facings and homogenous core without or with pores under low-velocity impact in thermal environments is performed utilizing a higher-order shear deformation theory (HSDT). In each facing, the graphene sheets are either uniformly dispersed or layer-wise functionally graded across its thickness. The extended Halpin-Tsai model is employed to estimate the temperature-dependent elastic properties of the nanocomposite facings. The contact force induced between the impactor and target panel is computed through the modified Hertzian contact law. The equations of motion of the FG-GRC sandwich conical shell panel are formulated based on Lagrange’s equation. The solutions of the resulting equations of motion are obtained employing Newmark’s time integration scheme. After verifying the consistency and accurateness of the present method, the effects of some critical parameters like graphene grading profile, temperature, core-to-facings thickness ratio, pre-twist angle, span-to-cone length ratio, impactor’s initial velocity, impactor’s size, and porosity coefficient on the impact response of the pre-twisted FG-GRC sandwich conical shell panel in uniform thermal environments are scrutinized.

Detection of near-surface defects using a coin-tap approach based on the equivalent impact stiffness of Hertzian contact theory

In this paper, a novel method to analyze the mechanical behavior of the coin-tap test using the principle of pounding mechanics is proposed. Based on the Hertzian contact theory, the linearized contact law is applied to simplify the mathematical model of the coin-tap test. By modeling the stiffness of the defect as an equivalent spring in a serial connection with the contact stiffness, the impact force and impact time can be theoretically derived. The derived expressions show that, the closer the defect is to the surface of the structure, the longer the impact duration time and the smaller the impact force will be. In addition, with the increase of defect radii, the peak force and duration of the impact will decrease and increase, respectively. Another innovation of this paper is that an equivalent impact stiffness (EIS)-based damage index (DI) is proposed to reveal the severity and location of the near-surface damages. Two validation experiments were carried out to validate the influences of the damage’s radii and under-surface depths. In the first experiment, the impact force and time of the central point for eight plates are measured to validate the accuracy of the proposed model. In the second experiment, 18 points on the horizontal centerline of eight specimens were tapped at an interval of 1 cm. The recorded pounding force and time were processed by EIS-based DI. Experimental results show that the EIS-based DI can effectively predict the position and severity of the defects and it holds the potential for practical application.

A coupled SPH-DEM approach for modeling of free-surface debris flows

A Lagrangian mesh-less model is proposed to simulate fluid–solid flows with multiple-sized solids, i.e., millimeter-sized particle and larger-sized debris. Considering the difference in the size of solid phases, a hybrid resolved and unresolved model is established based on the coupling method of smoothed particle hydrodynamics (SPH) and discrete element method (DEM). SPH is used to model fluid, and the locally averaged Navier–Stokes equations are adopted as governing equations. DEM is used to model the particle–particle interactions, and the unresolved description of hydrodynamic forces including drag and buoyancy is established. The large-sized debris is modeled as the rigid body, which is discretized by particle elements having both SPH and DEM characteristics, where SPH particle elements are involved in the closure of the SPH fluids, and DEM particle elements interact with the solid particles following the contact law. The numerical model is validated and verified by several examples, including single-particle sedimentation, collapse of cylinder columns, and debris dam break. Results show that the present model reproduces general features of the complex fluid–solid flow with free surfaces. The advantage of the hybrid model is that it can deal with the fluid–solid flow problem with both small particles and large objects at a suitable resolution, and it is especially good at dealing with the free surface flow problem. A discretization for the modeling of debris flows is proposed based on the coupled SPH-DEM method. The novelty of the work is a coupled resolved–unresolved scheme for the free surface flow with multi-sized solids. The present scheme allows using a uniform resolution by bridging the size difference between small-scale solid particles and large-scale debris. The unresolved model of fluid-particle flow is efficient because the fluid resolution can be configured comparably to the particle size. The unified nature of the model allows the combination of resolved and unresolved simulations in the same computational domain.

Combining discrete and continuum mechanics to investigate local wear processes induced by an abrasive particle flow

Wear caused by hard debris or abrasive slurries trapped between moving surfaces is a major industrial problem concerning engineering and agriculture machine components, causing abrasion and reducing their service life. In this context, the wear of diamond tools used to cut stones represents an interesting case study due to the particular tribological interactions involved. Diamond tools are characterised by diamonds (the cutting edge) and the metal matrix (the retaining binder). While several attempts have been made to analyse diamond wear, the wear process involving the matrix is not yet well understood. In particular, the phenomena responsible for wear at the local scale have not yet been fully investigated as they are difficult to quantify experimentally and the existing numerical models, to the authors' knowledge, greatly simplify the physical behaviour and interactions between the different materials in contact. A new code is therefore used in this work. It is able to treat the metal matrix as a deformable polycrystalline material and the debris flow by controlling the shape and size of the grains. Furthermore, the wear of the metal matrix will be described as a loss of intergranular cohesion caused by the continuous passage of debris through a cohesive contact law that also takes fatigue into account. The model will show, albeit qualitatively, that the wear of the metal surface is caused by the asperities of the debris grains, thus validating one of the fundamental assumptions behind the model defined by the same authors at a larger scale. Another aspect investigated is the relationship between the temporal evolution of wear and the roughness of the metal surface. Again, it will be shown how the temporal evolution of the metal surface is consistent with what has been observed in the literature. Moreover, due to the complexity of the model, a sensitivity study will be necessary to understand the physical significance of the parameters and how to adapt them to the specific case study. It will then be shown how these parameters can change the physics of the problem being analysed and must therefore be chosen carefully.

Relative motion relationship and collision mechanism of slipper-retainer assembly of axial piston machines

Under high-speed rotation, the retainer-slipper assembly has serious collision interference, which affects the performance of the key friction pair of the piston pump. And abnormal wear of the retainer and slipper is observed in the faulty piston pump, even with fracture of the retainer and severe wear of the slipper neck. Based on the master-slave principle of the slipper and the retainer, a mathematical model of the relative motion relationship between the slipper-retainer is established. And the collision law between the slipper and the retainer is obtained by combining the relative motion velocity equation of the slipper. The effects of swashplate angle and pump shaft speed on the relative motion trajectory and collision strength of the slipper-retainer assembly are analyzed. The coordinates of all contact points between the slipper and the retainer during one piston cycle are calculated. These results clearly show the friction area of the retainer hole. Researches show that the rotation angle of the power slipper at the transition point is reduced with increasing swashplate angle. The increase of pump shaft speed has no influence on the contact law of the assembly. The collision strength of the assembly increases with the swashplate angle and pump shaft speed. A parametric investigation of the contact and collision between the slipper and the retainer is realized, providing a design method for analyzing the wearing character and mechanical properties of the axial piston pump.

Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body.

We consider dynamic motion of a linearized elastic body with a crack subject to a modified contact law, which we call the Signorini contact condition of dynamic type, and to the Tresca friction condition. Whereas the modified contact law involves both displacement and velocity, it formally includes the usual non-penetration condition as a special case. We prove that there exists a unique strong solution to this model. It is remarkable that not only existence but also uniqueness is obtained and that no viscosity term that serves as a parabolic regularization is added in our model.This article is part of the theme issue ‘Non-smooth variational problems and applications’.

Dynamic modeling and analysis of maritime alongside replenishment system using multibody dynamics method

Alongside replenishment at sea is essential for the sustainable operation of ocean-going ships. Current researches mainly focus on hydrodnamics, control methods and simple static analysis, however, the dynamic modeling and analysis of the system are hardly investigated. In this paper, an new dynamic model of the alongside replenishment system is presented using the multibody dynamics method. The corotational cable element and the contact law are employed to formulate the cable-pulley interactions. To improve the computational efficiency, a simplified dynamic model is proposed, in which the effect of the cable is modeled as a force element using the constant tension characteristic while the cable's mass is taken into account. The validity of the simplified method is verified by the detailed model. The mechanical behaviors of the replenishment system are studied. We find that the dynamic analysis is necessary in rough sea conditions while the static equilibrium analysis doesn't work well. The influence of several model parameters is investigated. It shows that the cargo safety can be improved by increasing the height difference and tension force while decreasing the transmission distance. Moreover, the resonance of the cargo can be excited if the ship motion frequency is near the natural frequency of the system.

Functionally graded porous plate reinforced by carbon nanotubes subjected to low-velocity impact: an analytical and numerical analysis

PurposeThe purpose of this study is a numerical simulation and an analytical analysis about the low-velocity impact on a functionally graded porous plate with porosity distribution in the thickness direction. In this article, polymethyl methacrylate is used for matrix, and single-walled carbon nanotube (CNTs) (10,10) with consideration agglomeration sizes and lumping of CNT inside the agglomerations is applied for reinforcement.Design/methodology/approachIn analytical formulation, the non-linear Hertz contact law is applied for interaction between projectile and plate surface. High-order shear deformation plate theory is developed, and energy of the system for impactor and plate is written. The governing equations are derived using Ritz method and Lagrange equations and are solved using the fourth-order Runge–Kutta method. Also, ABAQUS finite element model of functionally graded porous plate with all edges simply supported and reinforced by CNT under low-velocity impact is simulated and is compared with those is achieved in the present analytical approach.FindingsIn parametric studies, the influence of porosity distribution patterns include uniform, non-uniform symmetric and non-uniform asymmetric on the histories of contact force and impactor displacement of simply supported plate reinforced by CNT are presented. Eventually, the effects of porosity coefficient, impactor initial velocity, impactor radius and CNTs lumping inside agglomerations for non-uniform symmetric distribution patterns are discussed in impact event in detail.Originality/valueIn this paper, the effect of combination of polymethyl methacrylate and CNTs with consideration agglomeration sizes and lumping of CNTs inside the agglomerations in the form of a functionally graded porous plate is studied in the problem of low-velocity impact analysis.

Efficient DEM simulations of railway ballast using simple particle shapes

For complex shaped materials, computational efficiency and accuracy of DEM models are usually opposing requirements. In the literature, DEM models of railway ballast often use very complex and computationally demanding particle shapes in combination with very simple contact laws. In contrast, this study suggests efficient DEM models for railway ballast using simple particle shapes together with a contact law including more physical effects. In previous works of the authors, shape descriptors, calculated in a shape analysis of two types of ballast, were used to construct simple particle shapes (clumps of three spheres). Using such a shape in DEM simulations of compression and direct shear tests, accurate results were achieved only when the contact law included additional physical effects e.g. edge breakage. A parametrisation strategy was developed for this contact law comparing DEM simulations with the measurements. Now, all the constructed simple particle shapes are parametrised allowing to study their suitability and relating their shape descriptors to those of railway ballast. The most suitable particle shapes consist of non-overlapping spheres, thus have a high interlocking potential, and have lowest sphericity and highest convexity values. In a micromechanical analysis of the four best performing shapes, three shapes show similar behaviour on the bulk and the micro-scale, while one shape differs clearly on the micro-scale. This analysis shows, which shapes can be expected to produce similar results in DEM simulations of other tests/load cases. The presented approach is a step towards both efficient and accurate DEM modelling of railway ballast.Graphic abstract

A developed multibody knee model for unloading knee with cartilage penetration depth control.

Unloader knee braces could relieve pain by decreasing the medial knee loading. Particularly for knee osteoarthritis (KOA) patients, this study investigates the relevance of the knee model after identifying the most influential parameter. Since KOA causes the cartilage in a joint to lose its elasticity and thickness, the lack of normal bone-to-bone separation can be painful. We believe that cartilage penetration depth control is an impactful strategy in this research. Moreover, the knee contact force in KOA is fewer than in healthy knees, confirming that the contact force control cannot be a straight factor. Therefore, a biomechanical human knee model is developed, and a generic procedure for dynamic analysis of contact problems in combination with the musculoskeletal model is introduced. The developed model includes the geometric expression of collision curves and an algorithm for determining collision points. This presentation addresses cartilage penetration depth and contact force calculation through nonlinear discontinuous contact law. In view of this, femur and tibia's relative motion is analyzed through the combined collision reactions of cartilage and bone in the knee. In the simulation, maximum penetration depth in a healthy knee is reported to be 0.795 mm, while in a 75% KOA is 0.521 mm, including 0.5 mm cartilage-cartilage contact and 0.021 mm bone-bone contact. The top unloading 852 N is achieved, reducing penetration depth to 0.45 mm, avoiding bone-bone contact. This proposed procedure with low computation gives us a suitable analysis method for designing knee assistive devices.

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Identifying parameters of a discrete numerical model of soil from a geotechnical field test

A discrete numerical model of a pressuremeter test was developed in this paper. The model is constituted of spherical particles with a contact law involving an inter-particle rolling resistance in addition to the classical Coulomb friction model. The model is calibrated from a pressuremeter test performed in the Hostun sand. An adaptive size of discretization of the soil domain is considered to limit the computational cost. Different parameter sets are defined to identify the initial density of the numerical granular assembly. Then, each parameter set leads to a different calibration of the mechanical parameters of the model in order to reproduce the pressuremeter test results. Simulations show that experimental data from a pressuremeter test alone are not enough to fully calibrate the discrete model. Other laboratory test results need to be considered in the calibration methodology. Eventually, the prediction capability of the model is assessed by comparing the simulated constitutive responses to those measured experimentally on different triaxial loading paths.

Friction-dependent rheology of dry granular systems

Understanding the rheology of granular assemblies is important for natural and engineering systems, but the relationship between inter-particle friction (or microscopic friction) and macroscopic friction is still not well understood. In this study, using the discrete element method (DEM) with spherical particles and realistic contact laws, we investigate the mechanics of granular systems with a wide range of inter-particle frictional coefficients and aim to establish a friction-dependent rheology for dry granular flows. The corresponding results show that increasing inter-particle friction dramatically increases the effective frictional coefficient, μeff, while decreasing the solid fraction of the system and increasing the transitional inertial number that marks the division of quasi-static regimes and intermediate flow regimes. We further propose a new dimensionless number, $${\cal M}$$ , as a ratio between the inertial effect and frictional effect, which is similar to the effective aspect ratio in granular column collapses, and unifies the influence of inter-particle friction with the inertial number. We then establish a relationship between $${\cal M}$$ and the dimensionless granular temperature, Θ, to further universalize the influence of inter-particle frictions. Such study can broaden the application of the μ(I) rheology in natural and engineering systems and help establish a more general constitutive model for complex granular systems.

A novel form of imperfect contact laws in flexoelectricity

Flexoelectric materials exhibit coupling between electric polarization and mechanical strain gradient. At the nano-scale and micro-scale, these materials offer a promising potential for the development of mechanical transducers and energy harvesters. This work proposes a new imperfect interface model simulating the behavior of a thin flexoelectric layer (adhesive) of vanishing thickness, embedded between two flexoelectric media (adherents). The adhesive is assumed to be mechanically compliant and electrically lowly-conducting. The interface model is obtained by using the asymptotic analysis. The contact laws, expressed in terms of the jumps and means values of the displacements, normal derivatives of the displacements, and electric potential across the interface, represent a formal generalization of the soft elastic and piezoelectric interface conditions. A simple application, considering a one-dimensional three-layer composite micro-bar subject to electro-mechanical loads, is developed in order to analytically/numerically assess the asymptotic model. Nonlocal phenomena and end-effects, related to a flexoelectric length-scale parameter, are highlighted. The example illustrates the usefulness of the proposed approach toward the design of thin nano- and microscale devices exploiting the flexoelectric effect.

Theoretical modeling of low-velocity impact behavior of sandwich-structured composites reinforced with weft-knitted spacer fabric

The aim of this paper is to develop an analytical model to predict indentations of the impactor on the composites reinforced with weft-knitted spacer fabric using Hertz contact law. For this purpose, simply supported rectangular plate with partially load developed by Timoshenko was applied to analyze the deflection of top face, and the concepts of the buckling of initially curved struts were used to find the buckling of Z-fibers. To evaluate the accuracy of the model, the effect of the number of Z-fiber per unit area and elastic modulus of Z-fiber were investigated. The results showed that in the outside the contact area, the impact force bends the layer and causes the Z-fibers to buckle, but no indentation occurs. Inside the contact zone, the indentation has occurred, in addition to the layer deflection and Z-fiber buckling. Also, indentations in both X and Y directions decrease by increasing the Z-fiber density. In addition, the higher the z-fiber modulus leads to fewer indentations. Decreasing the angle coefficient of Z-fibers leads to increase their buckling resistance. Moreover, a reasonable agreement was observed between theoretical and experimental results; so that the maximum error of prediction was less than 20%. Furthermore, the proposed model can give the indentation of different points of sandwich-structured composites according to their coordinates.

Low-Velocity Impact Behavior of Sandwich Plates with FG-CNTRC Face Sheets and Negative Poisson’s Ratio Auxetic Honeycombs Core

The combination of auxetic honeycomb and CNT reinforcement composite is expected to further improve the impact protection performance of sandwich structures. This paper studies the low-velocity impact response of sandwich plates with functionally graded carbon nanotubes reinforced composite (FG-CNTRC) face sheets and negative Poisson’s ratio (NPR) auxetic honeycomb core. The material properties of FG-CNTRC were obtained by the rule of mixture theory. The auxetic honeycomb core is made of Ti-6Al-4V. The governing equations are derived based on the first-order shear deformation theory and Hamilton’s principle. The nonlinear Hertz contact law is used to calculate the impact parameters. The Ritz method with Newmark’s time integration schemes is used to solve the response of the sandwich plates. The (20/−20/20)s, (45/−45/45)s and (70/−70/70)s stacking sequences of FG-CNTRC are considered. The effects of the gradient forms of FG-CNTRC surfaces, volume fractions of CNTs, impact velocities, temperatures, ratio of plate length, width and thickness of surface layers on the value of the plate center displacement, the recovery time of deformation, contact force and contact time of low-velocity impact were analyzed in detail.