A new arc-length control method based on the rates of the internal and the dissipated energy

Purpose - The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach - In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings - The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value - A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

Recently, phase-field approaches have gained popularity as a versatile tool for simulating fracture in a smeared manner. In this paper we give a numerical assessment of two types of phase-field models. For the case of brittle fracture we focus on the question whether the functional that describes the smeared crack surface approaches the functional for the discrete crack in the limiting case that the internal length scale parameter vanishes. By a one-dimensional example we will show that Γ-convergence is not necessarily attained numerically. Next, we turn attention to cohesive fracture. The necessity to have the crack opening explicitly available as input for the cohesive traction-relative displacement relation requires the independent interpolation of this quantity. The resulting three-field problem can be solved accurately on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crack opening. A simple patch test shows that this observation does not necessarily extend to unstructured meshes

Strongly coupled finite element framework for a thin fluid flow in contact interfaces

International audienceWe developed a monolithic finite-element framework, which includes robust contact resolution algorithms, fluid-flow elements for solving Reynolds equation for the incompressible viscous flow and fluid-structure interface elements to apply fluid pressure on the solid. Additionally, we take into account the possibility of fluid entrapment in the contact interface and its pressurization using non-linearly compressible constitutive laws and formulate a novel trapped-fluid element

Contact of rough surfaces in presence of interfacial fluid flow

International audienceWe present recent results on interplay of surface roughness, mechanical contact and interfacial flow of incompressible fluids. First, we present a technique to determine accurately the true contact area in the framework of a spectral boundary element method used to solve the contact between two rough surfaces. This technique enables us to uncover a subtle link between the so-called Nayak parameter and the rate of the contact area growth with the applied squeezing pressure. Apart from studying the growth of the true contact area, we study how the presence of a fluid (compressible and incompressible) in the contact interface affects the contact characteristics. Moreover, an interplay of solid contact and fluid flow as well as an entrapment of the latter are considered. Two different approaches are used to handle this problem. The first one assumes a one-way weak coupling between the solid deformation and the fluid flow. This approach uses the already mentioned spectral-based boundary element method to solve the non-linear contact problem in the context of infinitesimal deformations, a separate finite element solver is used to solve a viscous laminar fluid flow through the opening in the contact interface, which is governed by Reynolds equation. A self-consistent homogenization technique is adapted and used to link the effective transmissivity with the probability distribution of the gap function. A second approach, assumes a strong coupling between fluid and solid equations. Within this approach both equations are solved simultaneously within a monolithic and strongly coupled framework implemented using the finite element method. Some model problems of fluid entrapment and flow through a wavy channel assuming strong coupling of equations are presented. An engineering study of a fluid flow in contact interface between elasto-plastic solids at roughness scale will be also discussed

Nouvelles matrices pour materiaux composites a hautes performances a base de polymeres interpenetres: systeme polyepoxyde-polyurethane

CNRS-CDST / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc