Node-to-segment and node-to-surface interface finite elements for fracture mechanics

The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modelling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.Comment: 37 pages, 17 figure

Multiscale hydro-thermo-chemo-mechanical coupling: Application to alkali-silica reaction

Cataloged from PDF version of article.Alkali-Silica Reaction (ASR) is a complex chemical process that affects concrete structures and so far various mechanisms to account for the reaction at the material level have already been proposed. The present work adopts a simple mechanism, in which the reaction takes place at the micropores of concrete, with the aim of establishing a multiscale framework to analyze the ASR induced failure in the concrete. For this purpose, 3D micro-CT scans of hardened cement paste (HCP) and aggregates with a random distribution embedded in a homogenized cement paste matrix represent, respectively, the microscale and mesoscale of concrete. The analysis of the deterioration induced by ASR with the extent of the chemical reaction is initialized at the microscale of HCP. The temperature and the relative humidity influence the chemical extent. The correlation between the effective damage due to ASR and the chemical extent is obtained through a computational homogenization approach, enabling to build the bridge between microscale damage and macroscale failure. A 3D hydro-thermo-chemo-mechanical model based on a staggered method is developed at the mesoscale of concrete, which is able to reflect the deterioration at the microscale due to ASR. (C) 2013 Elsevier B. V. All rights reserved

Computational and theoretical aspects of a grain-boundary model at finite deformations

A model to describe the role of grain boundaries in the overall response of a polycrystalline material at small length scales subject to finite deformations is presented. Three alternative thermodynamically consistent plastic flow relations on the grain boundary are derived and compared using a series of numerical experiments. The numerical model is obtained by approximating the governing relations using the finite element method. In addition, the infinitesimal and finite deformation theories are compared, and the limitations of the former made clear

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Cataloged from PDF version of article.A three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume. (C) 2011 Elsevier B.V. All rights reserved

Computational thermal homogenization of concrete

Cataloged from PDF version of article.Computational thermal homogenization is applied to the microscale and mesoscale of concrete sequentially. Microscale homogenization is based on a 3D micro-CT scan of hardened cement paste (HCP). Mesoscale homogenization is carried out through the analysis of aggregates which are randomly distributed in a homogenized matrix. The thermal conductivity of this matrix is delivered by the homogenization of HCP, thereby establishing the link between micro-mesoscale of concrete. This link is critical to capture the dependence of the overall conductivity of concrete on the internal relative humidity. Therefore, special emphasis is given to the effect of relative humidity changes in micropores on the thermal conductivity of HCP and concrete. Each step of homogenization is compared with available experimental data. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved

On the optimality of the window method in computational homogenization

Cataloged from PDF version of article.The window method, where the microstructural sample is embedded into a frame of a homogeneous material, offers an alternative to classical boundary conditions in computational homogenization. Experience with the window method, which is essentially the self-consistent scheme but with a finite surrounding medium instead of an infinite one, indicates that it delivers faster convergence of the macroscopic response with respect to boundary conditions of pure essential or natural type as the microstructural sample size is increased to ensure statistical representativeness. In this work, the variational background for this observed optimal convergence behavior of the homogenization results with the window method is provided and the method is compared with periodic boundary conditions that it closely resembles. (C) 2013 Elsevier Ltd. All rights reserved

A computational homogenization framework for soft elastohydrodynamic lubrication

Cataloged from PDF version of article.The interaction between microscopically rough surfaces and hydrodynamic thin film lubrication is investigated under the assumption of finite deformations. Within a coupled micro–macro analysis setting, the influence of roughness onto the macroscopic scale is determined using F E2-type homogenization techniques to reduce the overall computational cost. Exact to within a separation of scales assumption, a computationally efficient two-phase micromechanical test is proposed to identify the macroscopic interface fluid flux from a lubrication analysis performed on the deformed configuration of a representative surface element. Parameter studies show a strong influence of both roughness and surface deformation on the macroscopic response for isotropic and anisotropic surfacial microstructures

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory

On a space-time implementation of the wave equation using virtual elements

The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton’s principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way