To improve the numerical simulation of rockfall protection barriers, this work addresses an extension of a one-dimensional model for elastoplasticity using a friction element and a spring in series, to include isotropic hardening and unilateral behavior. We reformulate the resulting system of differential inclusions in primal form and develop a timestepping scheme via an extended version of Moreau's midpoint rule. The scheme handles nonsmooth dynamics consistently, allowing to include frictional contact and impacts. The results provide a rigorous and implementable framework for simulating coupled elastoplastic frictional contact systems, contributing to the analysis and computation of nonsmooth rate-independent processes.
This paper aims to illustrate the interest of so-called intrinsic or coordinate-free or geometric approaches in mechanics and to start a discussion about their positions with respect to the opposite aspects carried by computational mechanics. Due to recent developments of pure computational approaches using IA that could finally suggest that equations and formal developments are not necessarily so important in mechanics, it could obviously lead to philosophical and epistemological issues. Our main point of view can be summarized by the well-known sentence of René Thom: "To predict is not to explain". Even if we consider that stressing these questions in the community of mechanics should be fundamental and essential, it will not be however the theme of the present work. On the contrary, we will remain technic in order to defend the idea that intrinsic approaches are actually complementary to computational approaches in mechanics and that, even if these approaches may involve more abstract objects and less usual mathematical concepts, they can lead in fact to practically more efficient developments in applications. This thesis then defends the unity of mechanics and the non-sense to hermetically separate theoretical, computational and applied aspects in mechanics.
The paper deals with the passive control of resonant systems using nonlinear energy sink (NES). The objective is to highlight the benefits of adding nonlinear geometrical damping to the cubic stiffness nonlinearity. The behaviour of the system is investigated theoretically by using the mixed harmonic balance multiple scales method. Based on the obtained slow ow equations, a design procedure that maximizes the dynamic range of the NES is presented. Singularity theory is used to express conditions for the birth of detached resonance cure independently of the forcing frequency. It is shown that the presence of a detached resonance curve is not necessarily detrimental to the performance of the NES. Moreover, the detached resonance curve can be completely suppressed by adding nonlinear damping. The results of the design procedure are then compared to numerical simulations, confirming the beneficial role of nonlinear damping in increasing the dynamic range of NES.
A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.
A growing, albeit not predominant, way to contribute to the climate transition in the field of fracture mechanics is to refine predictions from damage tolerance approaches used to assess the durability and reliability of sensitive components such as those found in railway, aeronautics, aerospace or nuclear industries. If it can be certified that the reduced safety margins remain acceptable, the intervals between maintenance operations could be extended, and the replacement of defective parts delayed, thereby reducing the environmental footprint. The aim of Damage Tolerance Approaches is to ensure that the existence of unavoidable defects does not compromise safety. This involves considering the most unfavorable case of brittle fracture and determining the propagation of a preexisting crack under cyclic loading until the Griffith energy fracture threshold is reached. Currently, this is done using simplified, smoothed-out crack geometries, relying either on tabulated values or Finite Element Methods. Since meshing of the entire structure is required, the lattercurrently struggles to accurately account for the small-scale tortuosity of the crack geometry. This paper aims to show that asymptotic approaches are efficient alternatives to address this challenge.Various aspects of these approaches, along with selected applications, will be reviewed. In addition to supporting the reduction of safety margins, these approaches also help to ensure that small geometrical perturbations do not lead to unexpected catastrophic failure. Asymptotic methods aim to provide analytical formulas for the variation of stress intensity factors caused by small-scale crack shape perturbations. Several applications are presented including crack shape evolution, the influence of heterogeneities, and propagation in general mixed-mode I+II+III condition.
