Smooth Contact Dynamics Research Articles

3D hybrid modeling approach combining the finite and discrete element methods: Validation based on masonry shear wall tests

The masonry structures represent a remarkable portion of the world’s built heritage. The preservation of these buildings requires a multidisciplinary diagnostic approach that includes a structural assessment to estimate their stability. However, this task remains difficult because of the high nonlinearity behavior of the masonry material and the complexity of the geometries of this type of building. For this reason, several robust modeling strategies have been developed. Among these strategies, block-based models (BBM) based on the discrete element method and more specifically the NSCD “Non Smooth Contact Dynamics” allows to take into account the actual geometrical texture of masonry. However, in this type of approach, blocks are generally rigid or elastic and nonlinearity appears only at the interfaces between blocks governed by cohesive frictional laws. In this study, a new hybrid approach is proposed. It consists of integrating a model combining (i) a frictional cohesive zone model “FCZM” describing the block-mortar interface and (ii) a quasi-brittle damage model associated with the block while (iii) the elasticity of mortar joints is explicitly taken into account in the FCZM model by adding a linear spring in both normal and tangential directions. Thus, avoiding the use of extended blocks and corresponding homogeneous properties. The validation of this numerical approach is carried out on the basis of an experimental campaign on masonry shear wall test subjected to compression.

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.

Non Smooth Contact Dynamics Approach for Mechanical Systems Subjected to Friction-Induced Vibration

The modeling of contact is one of the main features of contact dynamics in the context of friction-induced vibrations. It can have a strong impact on the numerical results and consequently on the design choices during the optimization or specification of industrial mechanical systems. This is particularly the case for scientific studies interested in brake squeal. The objective of the paper is to recall and to promote developments concerning the use of non smooth contact dynamics approach for numerical simulations based on finite element method. The specific problem of the prediction of self-excited vibration in the context of brake squeal is discussed. In order to illustrate the potential benefit for the mechanical community of using formulations and theoretical developments from the mathematical community, the stability analysis and the estimation of nonlinear vibrations of a brake system with multiple frictional interface is investigated.

Topological contact dynamics I: symplectization and applications of the energy-capacity inequality

Abstract We introduce topological contact dynamics of a smooth manifold carrying a cooriented contact structure, generalizing previous work in the case of a symplectic structure [27] or a contact form [5]. A topological contact isotopy is not generated by a vector field; nevertheless, the group identities, the transformation law, and classical uniqueness results in the smooth case extend to topological contact isotopies and homeomorphisms, giving rise to an extension of smooth contact dynamics to topological dynamics. Our approach is via symplectization of a contact manifold, and our main tools are an energy-capacity inequality we prove for contact diffeomorphisms, combined with techniques from measure theory on oriented manifolds. We establish non-degeneracy of a Hofer-like bi-invariant pseudo-metric on the group of strictly contact diffeomorphisms constructed in [4]. The topological automorphism group of the contact structure exhibits rigidity properties analogous to those of symplectic diffeomorphisms, including C0-rigidity of contact and strictly contact diffeomorphisms.

An implicit numerical method for wear modeling applied to a hip joint prosthesis problem

Some phenomenological wear models exist, but they are most of the time used to post-process numerical simulations. In certain situations however, material loss may be sufficient to change the contact area, contact stresses. In such cases, coupling the wear loss estimation to the mechanical contact modelling becomes essential. It can be done, and is done most of the time, by updating geometry between time-steps, introducing no further non-linearity. The option chosen here is on the contrary a fully coupled model where the wear displacement field is added to the unknowns of the frictional contact problem and requires one more equation. This equation is an adaptation of the Archard’s wear law to a local formulation in the context of dynamic and large displacements applications. This method allows simulation of the entire wear process in only a few loading cycles. We even quite accurately simulate the process in a single cycle. This is made possible via our fully coupled approach and an adaptation of the wear factor. The wear factor is artificially increased in order to decrease the number of cycles. A detailed description of the resolution of discrete equations is presented. The solver is a non linear Gauss Seidel algorithm adapted to wear conditions which derives from the ‘Non Smooth Contact Dynamics’ method. The wear model is validated on a total hip arthroplasty problem. Numerical observations are based on previously published experimental results.

Discontinuous modelling of cohesive-frictional blocky materials

ABSTRACT There are many similarities and unifying aspects between the seemingly different discontinuous modelling frameworks and formulations (Discrete Element Method DEM, Combined DEM/FEM, MDEM Modified Distinct Element Method, Discontinuous Deformation Analysis DDA, Non Smooth Contact Dynamics NSCD, Stress Based DEM). This is reflected in the manner they deal with the characterisation of bodies geometry and the contact detection, with the imposition of contact constraints and boundary conditions, with the definition and description of bodies deformability, fracturing and fragmentation, the transition from continua to discontinua as well as the associated time stepping algorithms… Some modelling aspects and illustrative applications of three specific discontinuous computational frameworks will be considered—rigid body spring method (RBSM), discontinuous deformation analysis (DDA) and non-smooth contact dynamics (NSCD)—applicable for analyses of solids and structures with both existing and/or emerging dis...

Discontinuous modeling of cohesive-frictional blocky materials

ABSTRACT There are many similarities and unifying aspects between the seemingly different discontinuous modelling frameworks and formulations (Discrete Element Method DEM, Combined DEM/FEM, MDEM Modified Distinct Element Method, Discontinuous Deformation Analysis DDA, Non Smooth Contact Dynamics NSCD, Stress Based DEM). This is reflected in the manner they deal with the characterisation of bodies geometry and the contact detection, with the imposition of contact constraints and boundary conditions, with the definition and description of bodies deformability, fracturing and fragmentation, the transition from continua to discontinua as well as the associated time stepping algorithms… Some modelling aspects and illustrative applications of three specific discontinuous computational frameworks will be considered—rigid body spring method (RBSM), discontinuous deformation analysis (DDA) and non-smooth contact dynamics (NSCD)—applicable for analyses of solids and structures with both existing and/or emerging discontinuities, where the contact interfaces follow a cohesive-frictional constitutive law.

Discrete element investigations of wire-reinforced geomaterial in a three-dimensional modeling

The aim of the study is to build discrete numerical models of a wire-reinforcement for geomaterials to perform multi-scale investigations. Non Smooth Contact Dynamics is used to carry out large or small strain mechanical tests on a granular sample. Different numerical experiments distinguish the main reinforcement micro-mechanisms and their consequences for macroscopic behavior.

Modélisation par éléments discrets d'ouvrages 3D en génie civil

ABSTRACT After a presentation of the difficulties attached to the masonries modelling and the references concerning the Non Smooth Contact Dynamics method, two real civil engineering structures are presented. They have the peculiar features of a post-stressing use, and the modelling of a Roman bridge, with thousands of three-dimensional blocks, representing the original stone course.

A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media

The NSCD method has shown its efficiency in the simulation of granular media. Since the number of particles and contact increases, the shape of the discrete elements becomes more complicated and the simulated problems becomes more complex, the numerical tools need to be improved in order to preserve reasonable elapsed CPU time. In this paper we present a parallelization approach of the NSCD algorithm and we investigate its influence on the numerical behaviour of the method. We illustrate the efficiency on an example made of hard disks: a free surface compaction.