Non-smooth Contact Dynamics Research Articles

A variational-based non-smooth contact dynamics approach for the seismic analysis of historical masonry structures

A variational formulation of the non-smooth contact dynamics method is proposed to address the dynamic response of historical masonry structures modeled as systems of 3D rigid blocks and subjected to ground excitation. Upon assuming a unilateral-frictional contact law between the blocks, the equations of motions are formulated in a time-discrete impulse theorem format in the unknown block velocities and contact impulses. The variational structure of the problem to be solved at each time step is proven. On that basis, the numerical method requires at each time step to perform a collision detection that identifies antagonist contact points based on the given structural configuration, to solve a second-order conic programming problem that outputs block velocities and contact impulses, and to update the structural configuration for the solution to advance in time. As a merit of the formulation, large-scale problems can be robustly and efficiently addressed thanks to the convex setting of the time-step optimization problem. Numerical results are presented to test the computational performances of the proposed approach. Benchmark problems provide numerical evidence that the formulation is consistent with event-driven solutions based on the classical Housner impact model. The dynamic response, failure domains, and fragility functions of real-size masonry structures are then explored under ground impulse or earthquake excitation. The obtained results prove the reliability of the present computational method for the dynamic analysis and seismic assessment of historical masonry constructions of engineering interest.

Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics

Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics

Simulation of impacts between spherical rigid bodies with frictional effects

AbstractThis work studies the impact between spherical rigid bodies in the frame of nonsmooth contact dynamics considering friction effects. A new impact element formulation based on the classical instantaneous local Newton impact law is presented. The kinematics properties of the spheres are described by a rigid body formulation with translational and rotational degrees of freedom referred to an inertial frame. In addition, an extension of the nonsmooth generalized‐ time integration scheme applied to collisions with multiple impacts including Coulomb's friction law is given. Six numerical examples are presented to evaluate the robustness and the performance of the proposed methodology.

An improved normal compliance method for non-smooth contact dynamics

An improved normal compliance method for non-smooth contact dynamics

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.

Numerical investigation of the effects of symmetric and eccentric earthquake-induced pounding on accelerations and response spectra for two-storey structures

This paper examines the effect of symmetric and eccentric earthquake-induced pounding between adjacent two-storey structures on acceleration times histories and response spectra. The numerical investigation benefits from experimental data issued from an extensive shake table campaign involving two-storey steel–concrete composite structures and slab-to-slab contacts. It is shown that the high frequency branch of the floor response spectra is only related to the maximum impulse acceleration spike during time, characterized by its impulse value, contact duration and time-history shape. In order to numerically reproduce such characteristics, three-dimensional detailed models are set up by modeling the slab with shell elements or hexahedral elements. Previously developed explicit time integrator, the CD-Lagrange scheme, based on non-smooth contact dynamics approach, is employed for ensuring the contact conditions expressed in terms of velocity and impulse, without requiring any contact parameters such as contact stiffness, local damping and restitution coefficient. The eccentric pounding between slabs is simulated by introducing a small defect in the parallelism of the colliding slabs, as measured in experience. The results of eccentric and symmetric pounding, assuming elastic behavior for the steel and concrete materials, are compared with the experimental data in terms of acceleration time-histories and pseudo-acceleration response spectra. It is concluded that symmetric pounding predicts an acceleration spike with a more abrupt increase to the peak and a shorter contact duration in comparison to experimental data, leading to an overestimation of the high frequency branch of the response spectra. On the contrary, eccentric pounding achieves to reproduce the experimental acceleration time histories as well as response spectra up to 400 Hz. Finally, the robustness of the proposed numerical approach is underlined by changing the time step size of the CD-Lagrange scheme as well as by prospecting different relevant choices concerning the Rayleigh damping.

Multi-scale analysis of shear behaviour of crushable granular sand under general stress conditions

Grain crushing underpins key mechanical behaviours of granular materials. A variety of factors, including grading, particle shapes and loading conditions, have been recognised to affect the crushability of grains and the overall behaviour of a granular material. Among them, the role of intermediate principal stress in a general stress condition on the shear behaviour of crushable granular sand remains less understood, owing to the scarcity of experimental data and analytical tools available. In this paper, a multi-scale computational approach is employed to investigate the shear behaviour of crushable granular sand under general stress conditions with varying intermediate principal stresses and confining pressures. The computational approach features multi-scale coupling between non-smooth contact dynamics and peridynamics, and offers a rigorous way to consider the intertwined evolution of particle size and shape during the process of grain crushing. The numerical study helps to quantify comprehensively and analyse the grain crushing-induced changes of macro- and micro-scale material behaviours including strength, deformability, particle size and shape evolution, particle-scale forces and contact conditions, and the development of anisotropy. The competition between a void-filling mechanism due to grain size change and enhanced friction and interlocking due to grain shape change in dictating the deformation of crushable sand is further discussed. The findings offer insights into the complex behaviours of crushable granular materials under general stress conditions and facilitate future development of physics-based constitutive theories on crushable sand.

A nonsmooth method for spatial frictional contact dynamics of flexible multibody systems with large deformation

AbstractA nonsmooth contact dynamics computation methodology for spatial frictional contact dynamics of flexible multibody systems with large deformation is presented. The contact and friction conditions between contact bodies are formulated as a cone complementary problem (CCP). Based on the mortar discretization method, nonsmooth frictional contact formulations for surface‐to‐surface and beam‐to‐beam contact problems are derived. These formulations can be used to study a wide range of contact problems between three‐dimensional bodies, thin plates and beams. The nonsmooth multibody dynamics equations are solved by using the generalized‐ method. The CCP is solved by using the accelerated projected gradient descend (APGD) algorithm in each Newton's iteration. Finally, six numerical examples are provided to validate the proposed computation methodology.

Bundled Gradients Through Contact Via Randomized Smoothing

The empirical success of derivative-free methods in reinforcement learning for planning through contact seems at odds with the perceived fragility of classical gradient-based optimization methods in these domains. What is causing this gap, and how might we use the answer to improve gradient-based methods? We believe a stochastic formulation of dynamics is one crucial ingredient. We use tools from randomized smoothing to analyze sampling-based approximations of the gradient, and formalize such approximations through the bundled gradient. We show that using the bundled gradient in lieu of the gradient mitigates fast-changing gradients of non-smooth contact dynamics modeled by the implicit time-stepping, or the penalty method. Finally, we apply the bundled gradient to optimal control using iterative MPC, introducing a novel algorithm which improves convergence over using exact gradients. Combining our algorithm with a convex implicit time-stepping formulation of contact, we show that we can tractably tackle planning-through-contact problems in manipulation.

Influence of Stereotomy on Discrete Approaches Applied to an Ancient Church in Muccia, Italy

This work evaluated the remarkable influence of stereotomy on discrete methods adopted for the dynamic response of an ancient masonry structure. The historic building used as a case study is the Church of Santa Maria of Varano in Muccia, in the province of Macerata, Italy, which was exposed to the severe seismic sequence that hit Central Italy in 2016, namely the major events of Accumoli, Visso, and Norcia. The structure was modeled using the actual stereotomy of blocks and three hypothetical arrangements of blocks of the masonry walls to investigate the existing crack pattern and vulnerabilities of the church. Sensitivity analyses were performed using the nonsmooth contact dynamics and discrete-element methods. These novel approaches suitably reproduced complex behaviors, considering large displacements and complete block separations, which is useful for upcoming retrofitting works.

Physics engine based simulation of shear behavior of granular soils using hard and soft contact models

Physics engines have been widely used to simulate physical and mechanical processes in modern video games to create an immersive and realistic gaming experience. This study explores the feasibility of using an open-source physics engine, Chrono, as a discrete element method (DEM) platform to simulate shear behavior of granular soils. This study develops a series of pre-processing, servo-controlling, and post-processing functions to improve the Chrono platform, so that Chrono can generate soil specimens with designed packing densities, perform laboratory test simulations such as direct shear tests, and output stress-strain, fabric, and force chains. Traditional DEM codes use soft contact models (e.g., Hertzian contact model) to determine inter-particle contact forces, while most physics engines use a hard contact model (e.g., non-smooth contact dynamics) to determine inter-particle contact forces. The hard contact model enables physics engines to use large time steps in iterations without affecting the numerical stability and simulation accuracy, which remarkably accelerate simulation speeds compared with traditional DEM codes. Based on systematical comparisons between simulation results of two contact models and experimental results, this study demonstrates that the hard contact model can yield the shear behavior of granular soils observed in soft contact model simulations and laboratory tests.

A semi-smooth Newton and Primal–Dual Active Set method for Non-Smooth Contact Dynamics

Multi-rigid-body dynamic contact systems, in other words Non Smooth Contact Dynamics (NSCD) problems, generate some inherent difficulties to multivocal laws, which results in non-linearities and non-smoothness associated to frictional contact models. Recently, Primal–Dual Active Set strategies (PDAS) have emerged as a promising method for solving contact problems. These methods are based on the following principle: the frictional contact conditions are restated as non-linear complementary functions for which the solution is provided by the iterative semi-smooth Newton method. Based on these prerequisites, this contribution aims to provide a generalization of the NSCD-PDAS for dynamic frictional contact problems. Several numerical experiments are reported for algorithm validation purposes and also to assess the efficiency and performances of PDAS methods with respect to the Newton/Augmented Lagrangian and the Bi-Potential methods.

Numerical investigation of the density sorting of grains using water jigging

This paper is devoted to the investigation of the density sorting of grains using water jigging. Experiments achieved in a laboratory scale water jig for two initial binary bed configurations are studied and compared to numerical results. The vertical composition of the deposit is estimated after different number of water pulses to represent the sorting evolution in time. Simulations are based on a multiscale model in which the fluid is solved at a larger scale than the grain diameter using the finite element method, while the grains are considered as rigid bodies and solved using the nonsmooth contact dynamics. Key parameters are numerically varied and observed to determine the sensitivity of the process.

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.

Effects of Brick Pattern on the Static Behavior of Masonry Vaults

ABSTRACT The design of brick masonry vaults has frequently been one of the main topics of historical construction handbooks, where also the orientation of the blocks was an examined issue. However, the influence of brick-texture has not yet been thoroughly investigated computationally. In the present paper the static behavior of masonry vaults of different shapes (barrel, pavilion, and cross vaults), was studied by analyzing and integrating two points of view: one historical and the other computational. First, the instructions provided by ancient documents were described. Then, a Non-Smooth Contact Dynamics Software was used to model vaults with different brick patterns suggested in the past. The vaults were studied with self-weight to observe load descent. Then, a concentrated force was added up to collapse. The analyses show how the load descent and load-bearing capacity are influenced by the brick pattern. Finally, the results of the various analyses were compared with the insights of the past.

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.

Oedometric compression of a granular material: computation of energies involved during breakage with a discrete element modelling

A numerical model able to simulate the grain breakage with the discrete element method, using the “Non-Smooth Contact Dynamics” is presented. The model reproduces 3D grains having complex shapes and is tested in single grain and in oedometric compressions. Numerical simulations are then carried out to evaluate the different energies active during breakage (surface creation and redistribution energies). The surface creation energy is estimated. Results are closed to the ones found in the literature.

A micro-mechanical compaction model for granular mix of soft and rigid particles

We use bi-dimensional non-smooth contact dynamics simulations to analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles. Deformable particles are modeled using the finite-element method and following a hyper-elastic neo-Hookean constitutive law. The evolution of the packing fraction, bulk modulus and particle connectivity, beyond the jamming point, are characterized as a function of the applied stresses for different proportion of rigid/soft particles and two values of friction coefficient. Based on the granular stress tensor, a micro-mechanical expression for the evolution of the packing fraction and the bulk modulus are proposed. This expression is based on the evolution of the particle connectivity together with the bulk behaviour of a single representative deformable particle. A constitutive compaction equation is then introduced, set by well-defined physical quantities, given a direct prediction of the maximum packing fractionφmaxas a function of the proportion of rigid/soft particles.

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.