Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction

International audienceThe aim of the present work is to analyze the modified mass method for the dynamic Signorini problem with Coulomb friction. We prove that the space semi-discrete problem is equivalent to an upper semi-continuous one-sided Lipschitz differential inclusion and is, therefore, well-posed. We derive an energy balance. Next, considering an implicit time-integration scheme, we prove that, under a certain condition on the discretization parameters, the fully discrete problem is well-posed. For a fixed discretization in space, we prove also that the fully discrete solutions converge to the space semi-discrete solution when the time step tends to zero

A novel approach to modelling and simulating the contact behaviour between a human hand model and a deformable object

A deeper understanding of biomechanical behaviour of human hands becomes fundamental for any human hand-operated Q2 activities. The integration of biomechanical knowledge of human hands into product design process starts to play an increasingly important role in developing an ergonomic product-to-user interface for products and systems requiring high level of comfortable and responsive interactions. Generation of such precise and dynamic models can provide scientific evaluation tools to support product and system development through simulation. This type of support is urgently required in many applications such as hand skill training for surgical operations, ergonomic study of a product or system developed and so forth. The aim of this work is to study the contact behaviour between the operators’ hand and a hand-held tool or other similar contacts, by developing a novel and precise nonlinear 3D finite element model of the hand and by investigating the contact behaviour through simulation. The contact behaviour is externalised by solving the problem using the bi-potential method. The human body’s biomechanical characteristics, such as hand deformity and structural behaviour, have been fully modelled by implementing anisotropic hyperelastic laws. A case study is given to illustrate the effectiveness of the approac

The non-smooth contact dynamics method

International audienceThe main features of the Non-Smooth Contact Dynamics method are presented in this paper, the use of the dynamical equation, the non-smooth modelling of unilateral contact and Coulomb's law, fully implicit algorithms to solve the dynamical frictional contact problem for systems with numerous contacting points, in particular large collections of rigid or deformable bodies. Emphasis is put on contact between deformable bodies. Illustrating numerical simulation examples are given for granular materials, deep drawing and buildings made of stone blocks

Time/frequency analysis of contact-friction instabilities. Application to automotive brake squeal.

Robust design of silent brakes is a current industrial challenge. Braking systems enter in the more general context of unstable systems featuring contact friction interaction. Their simulation requires time integra- tion schemes usually not adapted to combination of large industrial models (over 600,000 DOF) and long simulations (over 150,000 time steps). The paper first discusses selection of the contact/friction model and adaptations of the integration scheme. The relation between the nominal steady state tangent modes and the system evolution over time is then evaluated. The time response shows a nearly periodic response that is analyzed as a limit cycle. It is shown that instantaneous dynamic stability predictions show stable/unstable transitions due to changes in the contact/friction state. These transitions are thought to give an understanding of the mechanism that limits levels for these self sustained vibrations. The concept is exploited to suggest novel ways to analyze complex modes

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Rheology, force transmission, and shear instabilities in frictional granular media from biaxial numerical tests using the contact dynamics method

International audienceBy means of the contact dynamics discrete element method, we investigate the quasi-static behavior of granular media composed of rigid frictional particles. Eluding specific modeling of the contact rheology, this method is suitable for numerical simulation of the plastic deformations of granular materials. We studied the macroscopic stress-strain and volume-change behavior, as well as force transmission and shear instabilities, in a two-dimensional biaxial geometry for dense samples composed of 5000 rigid disks. The peak and residual strengths and shear bands were analyzed by varying the confining pressure and the coefficient of friction between particles. The results are consistent with well-known features of the plasticity of noncohesive granular media. The mechanical behavior is rigid-plastic governed by a Mohr-Coulomb yield criterion and showing strain hardening and softening. Conjugated shear bands characterize plastic failure. The volumetric strain is globally dilatant with considerable expansion observed along shear bands. The macroscopic coefficient of friction, determined from peak and residual strengths, increases nonlinearly and saturates to a constant value as a function of contact friction. The strong force chains are mostly parallel to the major principal stress axis, yet deviations are observed near the shear bands. These chains are often composed of particles that are larger than the average. The deviatoric stress shows small fluctuations often in the form of rapid falls that are correlated with tiny contractional events. This behavior is interpreted in terms of the propagation of dynamic shear instabilities along the shear bands, in close analogy with stick-slip behavior

Adaptive numerical simulation of contact problems : Resolving local effects at the contact boundary in space and time

This thesis is concerned with the space discretization of static and the space and time discretization of dynamic contact problems. In particular, we derive a new efficient and reliable residual-type a posteriori error estimator for static contact problems and a new space-time connecting discretization scheme for dynamic contact problems in linear elasticity. The methods enable the efficient resolution of local effects at the contact boundary in space and time. Firstly, we prove efficiency and reliability of the new residual-type a posteriori error estimator for the case of simplicial meshes. Several numerical examples in the two- and three-dimensional case show the performance of the residual-type a posteriori error estimator for simplicial and even for non-simplicial meshes. Secondly, for the discretization in time, we present a new method which allows to implicitly compute the local impact times of each node without decreasing the time step size. As it turns out this method gives rise to a generalization of the Newmark scheme which takes into account the local impact times without additional computational effort

DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact

Cloth simulation has wide applications in computer animation, garment design, and robot-assisted dressing. This work presents a differentiable cloth simulator whose additional gradient information facilitates cloth-related applications. Our differentiable simulator extends a state-of-the-art cloth simulator based on Projective Dynamics (PD) and with dry frictional contact. We draw inspiration from previous work to propose a fast and novel method for deriving gradients in PD-based cloth simulation with dry frictional contact. Furthermore, we conduct a comprehensive analysis and evaluation of the usefulness of gradients in contact-rich cloth simulation. Finally, we demonstrate the efficacy of our simulator in a number of downstream applications, including system identification, trajectory optimization for assisted dressing, closed-loop control, inverse design, and real-to-sim transfer. We observe a substantial speedup obtained from using our gradient information in solving most of these applications

Time/frequency analysis of contact-friction instabilities. Application to automotive brake squeal.

Robust design of silent brakes is a current industrial challenge. Braking systems enter in the more general context of unstable systems featuring contact friction interaction. Their simulation requires time integra- tion schemes usually not adapted to combination of large industrial models (over 600,000 DOF) and long simulations (over 150,000 time steps). The paper first discusses selection of the contact/friction model and adaptations of the integration scheme. The relation between the nominal steady state tangent modes and the system evolution over time is then evaluated. The time response shows a nearly periodic response that is analyzed as a limit cycle. It is shown that instantaneous dynamic stability predictions show stable/unstable transitions due to changes in the contact/friction state. These transitions are thought to give an understanding of the mechanism that limits levels for these self sustained vibrations. The concept is exploited to suggest novel ways to analyze complex modes

Effect of micro-particle addition on frictional energy dissipation and strength of concrete: experiments and modelling

In this thesis, a two-degrees-of-freedom, non-linear model is introduced aiming to describe internal friction phenomena which have been observed in some modified concrete specimens undergoing slow dynamic compression loads and having various amplitudes but never inducing large strains. The motivation for the theoretical effort presented here arose because of the experimental evidence described in some papers in which dissipation loops for concrete-type materials are shown to have peculiar characteristics. Since viscoelastic models –linear or non-linear– do not seem suitable to describe either qualitatively or quantitatively the measured dissipation loops, it is proposed to introduce a micro-mechanism of Coulomb-type internal dissipation associated to the relative motion of the faces of the micro-cracks present in the material. In addition, numerical simulations, showing that the proposed model is suitable to describe some of the available experimental evidences, is presented. These numerical simulations motivate further developments of the considered model and supply a tool for the design of subsequent experimental campaigns. Furthermore, the effect of micro-particle additives such as calcium carbonate on internal dissipation of concrete was experimentally investigated. The damping performance of concrete can be improved by adding to the mixture different kinds of micro-particles with suitable size which fill the pores of the matrix and change the contact interaction between internal surfaces of voids. It was determined that the energy dissipation of the concrete increases with the increasing content of micro particles at least when the concrete matrix is “soft” enough to allow microscopic motions. On the other hand, the increasing percentage of micro-particles addition can affect the mechanical strength of the material. Thus, there is a reasonable compromise in incorporating these micro-particles to obtain higher damping with- out weakening the mechanical properties. Several concrete mixes were prepared by mixing cement powder with different percentages of micro-fillers. A concrete mix without addition of micro-particles was molded as a reference material for the sake of comparison. All these specimens were tested under cyclic loading in order to evaluate energy dissipation starting from the area of a dissipation loop detected in the diagram relative to a representative cycle. The experimental determination of the dissipated energy shows a significant increase in the damping capability of the cement-based materials with micro-filler compared to the standard concrete. The experimental results presented seem to indicate that the proposed model is suitable to describe the mechanical behavior of modified and unmodified concrete, provided that the introduced parameters are suitably tuned in order to best fit the available experimental data