Non-Smooth Contact Dynamics Method Research Articles

Bayesian interface based calibration of a novel rockfall protection structure modelled in the non-smooth contact dynamics framework

This article presents the development and calibration of a numerical model simulating the response of a novel rockfall protection structure subjected to localized dynamic loading. This structure is made of piled-up concrete blocks interconnected via metallic components whose dynamics response under projectile impact is examined via real-scale experiments. The corresponding numerical model is developed in a python based open source software Siconos which implements the Non-Smooth Contact Dynamics (NSCD) method. The geometrical features and mechanical properties are incorporated in the model via specific developments pertinent to the modelling requirements in Siconos. Some parameters peculiar to the numerical model are calibrated against the spatial–temporal measurements from two full-scale impact experiments. The Bayesian interface statistical learning method aided by the polynomial chaos expansion based meta-model of the NSCD model is deployed for the calibration. The additional understanding of the model dynamics through the byproducts of the meta-model is highlighted. In the end, the NSCD model is successfully calibrated against the spatial–temporal response of the experimental structure with more than 90% accuracy for impact energies up to 1 MJ.

Modelling of earthquake-induced pounding between adjacent structures with a non-smooth contact dynamics method

This article presents the kinematic analysis of two adjacent structures with pounding using the framework of finite element dynamic analysis and a non-smooth contact dynamics (NSCD) method for treating contact-impact. The latter consists of a Moreau-Jean implicit integration scheme that uses Moreau’s sweeping process and Newton’s impact law. Test cases are carried out to prove the efficiency of the implementation and accuracy of the results relative to the widely used penalty method (PM). Furthermore, finite element simulations are compared with shaking table results of two structures susceptible to pounding. Models are steel frames 2.5 m to 5 m high, 3 m in span, have reinforced-concrete slabs, and distant 0 to 5 cm. Floor displacements, number and time of occurrence of impacts, as well as shape of the response spectra are in good agreement with experimental observations. Moreover, using the building pounding frame and the NSCD method, an estimation of a constant value for the coefficient of restitution was carried out. It is concluded that the NSCD method is a very numerically efficient tool in terms of reduction of CPU time and description of the impact physics. Consequently, this approach is amenable for fragility analysis of the dynamic response of structures involving a contact-impact phenomenon.

FE vs. DE Modeling for the Nonlinear Dynamics of a Historic Church in Central Italy

The present research paper properly focuses on the dynamics and failure mechanisms of the masonry “Apennine Church” of Santissimo Crocifisso in Pretare, municipality of Arquata del Tronto in the province of Ascoli Piceno (Marche region, Central Italy). Such a peculiar structural type traditionally characterizes the intense seismic area of Central Italy, unfortunately almost totally damaged by the recent shock sequence of 2016. Advanced numerical modeling through discontinuous and continuous approaches were here utilized to have an insight into the dynamic properties and behavior of the structure under strong nonlinear dynamic excitations. In the discrete element approach, the non-smooth contact dynamics method, implemented in LMGC90©, was applied, adopting a full 3D detailed discretization. The church was schematized as an arrangement of rigid blocks, subjected to sliding by friction and perfect plastic collisions, with a null restitution coefficient. In the finite element approach, the concrete damaged plasticity model available in Midas FEA NX© was involved. This model allows reproducing the tensile cracking, the compressive crushing, and the degradation of the material under cyclic loads. Finally, the numerical analyses provided a valuable picture of the actual behavior of the church, thus giving useful hints for future strengthening interventions.

Discontinuous approaches for nonlinear dynamic analyses of an ancient masonry tower

The aim of this paper is to present the development of discontinuous approaches to simulate the nonlinear dynamic behaviour of the civic clock tower of Rotella, in the province of Ascoli Piceno (Italy). The study involves the use of the Non-Smooth Contact Dynamics method implemented in the LMGC90© code, where sliding motions are governed by Signorini's impenetrability condition and dry-friction Coulomb's law, and the Discrete Element Method with cohesive and tensional behaviours at the joints in the 3DEC© code. The tower was represented using three different geometric models ranged from the most complex one, including the full geometry and multi-leaf masonry walls, to the simplest one, including the single-leaf walls as a simplification of the real masonry. The numerical results highlighted the modes of failure depending on the shape, size and texture of the masonry and the modalities of progressive damage under dynamic actions. Moreover, both numerical approaches have proven to be capable of simulating large displacements and complete block separations, reproducing complex mechanical behaviours and making predictions on the vulnerability assessment of the historical masonry buildings.

Cohesive GTN model for ductile fracture simulation

The present work addresses the micromechanical modeling and the simulation of crack initiation and propagation in ductile materials failing by void nucleation, growth and coalescence. A cohesive–volumetric approach is used and the overall material behavior is characterized both by a hardening bulk constitutive law and a softening surface traction–separation law embedded between each mesh of a finite element discretization. The traction–separation law sums up across a surface all the ductile damage processes occurring in a narrow strain localization band, while the bulk behavior concerns the other elasto-plastic effects. The proposed cohesive zone model is based on a micromechanical approach where the Gurson–Tvergaard–Needleman ductile damage model is adapted to the reduced kinematics of a surface while ensuring the complete effect of the strain rate or stress triaxiality both on the local plasticity and on the void growth. The corresponding cohesive model is implemented in the XPER computer code using the Non-Smooth Contact Dynamics method where cohesive models are introduced as mixed boundary conditions between each volumetric finite element. The present approach is applied to the simulation of crack growth in a standard ferritic steel. Results are compared with available experimental data. The efficiency of the proposed cohesive-GTN model is underlined since the shape of the cohesive law and its mechanical parameters arise directly from the micromechanical approach without any ad hoc fitting parameter.

Multiscale modeling of continuous crushing of granular media: the role of grain microstructure

Natural granular materials such as sands often possess complex microstructural features including cleavage and minerals interfaces. Those features bring apparent mechanical anisotropy to particles and are known to have pronounced influence on particle crushing characteristics. This paper presents a multiscale simulation of continuous crushing of granular sand under one-dimensional compression in consideration of particle-scale anisotropy through modeling planes of weakness inside individual particles, with reference to granular materials rich in minerals and containing cleavages. The multiscale modeling is based on a coupled peridynamics and non-smooth contact dynamics method where peridynamics is used to model crushing of individual particles and non-smooth contact dynamics is employed to simulate discrete granular system. Weak microstructural planes are simulated by breaking a fraction of peridynamic bonds as an initial condition. Simulation results show that anisotropic particles containing weak planes result in larger number of fragments and exhibit relatively higher fractal dimension with respect to particle size. Particle shape is found to approach a steady state profile with continuous crushing. Anisotropic particles generally bear smaller sphericity, aspect ratio, elongation and flatness than those isotropic particles. The anisotropy in particles seems to mitigate shape effect on particle strength and crushing energy. Macromechanical yield stress of the sample is related to single particle strength monotonically, but the relationship appears to be nonlinear when different microstructural features are involved.

Simulation of air invasion in immersed granular beds with an unresolved FEM–DEM model

This paper is devoted to an unresolved model for the simulation of air invasion in immersed granular flows without interface reconstruction between the liquid and the gas. Experiments of air invading a granular bed immersed in ethanol were achieved in a Hele-Shaw cell to observe the gas invasion paths and to calibrate the numerical multiscale model. The grains movements are computed at a fine scale using the non-smooth contact dynamics method, a time-stepping method considering impenetrable grains. The fluid flow is modelled by equations averaged using the volume fraction of fluid and computed at a coarse scale with the finite element method. A phase indicator function is used to dissociate the gas and the liquid constituting the fluid and to compute the density and viscosity of the fluid at each position. It is moved using a convection equation at each time step. The fluid, solid and phase indicator function computations are validated on simple cases before being used to reproduce experiments of air invasion in immersed granular flows. The experiments are supported by simulations in two dimensions to refine the study and the understanding of the invasion dynamics at short times.

Numerical Modeling of the Motion of an Underwater Body with Positive Buoyancy by the Method of Nonsmooth Contact Dynamics

A numerical method based on the nonsmooth contact dynamics method is proposed for calculating the dynamics of an underwater solid body with positive buoyancy, which is attached to the operational surface (bottom of the reservoir) by flexible cables. A hemisphere-shaped body with three cables is considered as an example. The results of numerical calculations confirming the efficiency of the method are presented.

Finite element steady state solution of a beam on a frictionally damped foundation under a moving load

The application of beams on foundation models subjected to moving loads in the engineering analysis of high-speed railway tracks requires a realistic characterization of the foundation behavior. In particular, the dissipative frictional character of the substructure of a railway track should be taken into account. In this paper, the steady state responses of a Euler–Bernoulli beam under a moving load on a foundation composed of a continuous distribution of linear elastic springs associated in parallel with a continuous distribution of Coulomb frictional dampers are computed. The steady state of the beam is governed by a partial differential inclusion that is semi-discretized in space, using a Discontinuous Least-Squares Finite Element Method (DLSFEM), as a system of ordinary differential inclusions, and integrated using a special implementation of the Non-Smooth Contact Dynamics method (NSCD) adapted to distributed Coulomb friction. The steady state solutions are then obtained for different values of the maximum force per unit length of the frictional dampers and for different values of the load velocity at both subcritical and supercritical regimes. It is found that the NSCD-DLSFEM produces consistent and accurate numerical outcomes in a wide range of the mechanical parameters that may be of interest in high-speed railway tracks engineering.

Advanced Seismic Analyses of “Apennine Churches” Stroked by the Central Italy Earthquakes of 2016 by the Non-Smooth Contact Dynamics Method

The dynamic behaviour and the seismic vulnerability of different masonry “Apennine Churches”, dramatically damaged by the last shocks sequence of 2016 that occurred in Central Italy, have been studied in this paper by means of advanced 3D numerical analyses with the Discrete Element Method (DEM). Thus, a discontinuous approach has been used to assess the dynamic properties and the vulnerability of the masonry structure, through large deformations regulated by the Signorini’s law, concerning the impenetrability between the rigid bodies, and by the Coulomb’s law, regarding the dry-friction model. The major purpose of this study is to highlight that relevant data on the real structural behaviour of historical masonry can be provided through advanced numerical analyses. The comparison between the results of the numerical simulation and the survey of the existing crack pattern of the churches permitted to validate the used approach. Finally, from the results and conclusions of these cases study, it is possible to affirm that the used methodology can be applied to a wide variety of historical masonry structure in Europe.

Effect of micro and macro parameters in 3D modeling of grain crushing

Coarse granular materials exhibit important grain breakage in civil engineering structures, making it more complicated to predict the settlement and collapse of structures. A three-dimensional numerical model is presented using the discrete element method (Non-Smooth Contact Dynamics method). Polyhedral grains are generated, divided into tetrahedral subgrains and glued together using a cohesive law. Samples of breakable grains are subjected to oedometric compression where grains interact via contact and friction processes. Multiple geometrical and physical parameters are tested to analyze the response on the macroscopic and microscopic scales. The tendencies found show the ability of the model to represent the real material’s behavior.

Behavior of confined granular beds under cyclic thermal loading

We investigate the mechanical behavior of a confined granular packing of irregular polyhedral particles under repeated heating and cooling cycles by means of numerical simulations with the non-smooth contact dynamics method. Assuming a homogeneous temperature distribution as well as constant temperature rate, we study the effect of the container shape, and coefficients of thermal expansions on the pressure buildup at the confining walls and the density evolution. We observe that small changes in the opening angle of the confinement can lead to a drastic peak pressure reduction. Furthermore, the displacement fields over several thermal cycles are obtained and we discover the formation of toroidal convection cells inside the granular material. The root mean square of the vorticity is then calculated from the displacement fields and a quadratic dependency on the ratio of thermal expansion coefficients is established.

Damage assessment of ancient masonry churches stroked by the Central Italy earthquakes of 2016 by the non-smooth contact dynamics method

The non-smooth contact dynamics method was selected to investigate the damage occurred to typical masonry churches (namely Apennine churches) belonging to Central Italy areas affected by the seismic activity started in 2016. The investigated buildings show discontinuous dynamics since the optioned method gave the chance to properly model the temples as multi rigid body systems using the Signorini’s impenetrability condition and the dry-friction Coulomb’s law, achieving a thoughtful response to ground seismic solicitations. The results provided by the assessment grant an overview of the most common damages and failure mechanisms, giving the guidelines to restoration projects that fully respond to structural needs.

Digital Study of the Thermo-Mechanical Behavior of a Dry Granular Media in a Cell of Annular Shear

In the aim to understand the thermo-mechanical phenomenology of the dry granular media due to the grains’ flow nature of (rheology) or particles that constitute this medium. We will illustrate in this present article a numerical study by the discrete elements (MED) method on the thermo-mechanical behavior of a set of rigid particles sheared in an annular cell. This study is focused on the modeling of local friction between particles, from the generation of heat and its diffusion by conduction. We realized out a two-dimensional (2D) numerical model of type Couette geometry to simulate the different thermo-mechanical quantities such as: flow velocity and media temperature. This modeling is implemented within the platform used LMGC90, which is based on the NSCD (Non-Smooth Contact Dynamics Method) approach. In the First time, we’ll study the various realistic physical quantities of the contact’s rheology (type of particles material, the applied pressure and the shear velocity). Then we will continue by the analytical analysis and interpretation of the obtained results. DOI: http://dx.doi.org/10.5755/j01.mech.24.6.22461

Modal parameters identification with environmental tests and advanced numerical analyses for masonry bell towers: a meaningful case study

In the first part, a dynamic monitoring for non-destructive evaluation of heritage structures is discussed with reference to a case study, namely the Pomposa Abbey belfry, located in the Ferrara Province (Italy). The main dynamic parameters constitute an important reference to define an advanced numerical model, discussed in the second part, based on Non-Smooth Contact Dynamics (NSCD) method. Schematised as a system of rigid blocks undergoing frictional sliding and plastic impacts, the tower has exhibited complex dynamics, because of both geometrical nonlinearity and the non-smooth nature of the contact laws. First, harmonic oscillations have been applied to the basement of the tower and a systematic parametric study has been conducted, aimed at correlating the system vulnerability to the values of amplitude and frequency of the assigned excitation corroborated by the dynamic identification results. In addition, numerical analyses have been done to highlight the effects of the friction coefficient and of the blocks geometries on the dynamics, in particular on the collapse modes. Finally, a study of the tower stability against seismic excitations has been addressed and 3D simulations have been performed with a real earthquake.

Moving loads on beams on Winkler foundations with passive frictional damping devices

This paper analyses the dynamic behavior of Euler-Bernoulli beams on elastic foundations of the Winkler type submitted to moving loads. In particular, the usefulness of passive frictional damping devices, that present ecological and economic advantages with respect to viscous ones, in the context of minimizing the consequences of resonance phenomena is studied.A program in Matlab environment based on the finite element method (FEM) that simulates the dynamic behavior of the beam, foundation and frictional damping devices driven by a moving load, is developed and used to study the effect of the frictional dissipation on the values of the critical velocities and dynamic amplifications. The time integration of the global equations of the motion is performed using the nonsmooth contact dynamics method (NSCD) with persistent contact, especially conceived for friction problems which are governed by a nonsmooth constitutive law.

Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation

This article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a 42 degree-of-freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modeled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb’s friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time-stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Furthermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time-stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event-detecting time-stepping schemes, the event-capturing scheme enables us to perform the time-integration with a large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite-time accumulations with a reasonable time-step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical method deals with more than 70 contact points without any problems. Furthermore, the number of contact parameters is small—one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency, allows us to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data, showing a very good correlation.

Stem cell mechanical behaviour modelling: substrate\u2019s curvature influence during adhesion

Recent experiments hint that adherent cells are sensitive to their substrate curvature. It is already well known that cells behaviour can be regulated by the mechanical properties of their environment. However, no mechanisms have been established regarding the influence of cell-scale curvature of the substrate. Using a numerical cell model, based on tensegrity structures theory and the non-smooth contact dynamics method, we propose to investigate the mechanical state of adherent cells on concave and convex hemispheres. Our mechanical cell model features a geometrical description of intracellular components, including the cell membrane, the focal adhesions, the cytoskeleton filament networks, the stress fibres, the microtubules, the nucleus membrane and the nucleoskeleton. The cell model has enabled us to analyse the evolution of the mechanical behaviour of intracellular components with varying curvature radii and with the removal of part of these components. We have observed the influence of the convexity of the substrate on the cell shape, the cytoskeletal force networks as well as on the nucleus strains. The more convex the substrate, the more tensed the stress fibres and the cell membrane, the more compressed the cytosol and the microtubules, leading to a stiffer cell. Furthermore, the more concave the substrate, the more stable and rounder the nucleus. These findings achieved using a verified virtual testing methodology, in particular regarding the nucleus stability, might be of significant importance with respect to the division and differentiation of mesenchymal stem cells. These results can also bring some hindsights on cell migration on curved substrates.

Dense flow around a sphere moving into a cloud of grains

A bidimensional simulation of a sphere moving at constant velocity into a cloud of smaller spherical grains without gravity is presented with a non-smooth contact dynamics method. A dense granular “cluster” zone of about constant solid fraction builds progressively around the moving sphere until a stationary regime appears with a constant upstream cluster size that increases with the initial solid fraction ϕ 0 of the cloud. A detailed analysis of the local strain rate and local stress fields inside the cluster reveals that, despite different spatial variations of strain and stresses, the local friction coeffcient μ appears to depend only on the local inertial number I as well as the local solid fraction ϕ , which means that a local rheology does exist in the present non parallel flow. The key point is that the spatial variations of I inside the cluster does not depend on the sphere velocity and explore only a small range between about 10−2 and 10−1 . The influence of sidewalls is then investigated on the flow and the forces.

Nonsmooth Contact Dynamics for the large-scale simulation of granular material

For the large-scale simulation of granular material, the Nonsmooth Contact Dynamics Method (NSCD) is examined. First, the equations of motion of nonsmooth mechanical systems are introduced and classified as a Differential Variational Inequality (DVI) that has a structure similar to Differential–Algebraic Equations (DAEs). Using a Galerkin projection in time, we derive nonsmooth extensions of the SHAKE and RATTLE schemes. A matrix-free Interior Point Method (IPM) is used for the complementarity problems that need to be solved in each time step. We demonstrate that in this way, the NSCD approach yields highly accurate results and is competitive compared to the Discrete Element Method (DEM).