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

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

11/07/1994 - Balanced Man Scholarship Joshua Renken.pdf

this paper, a method is proposed to define the geometrical contact constraints. Within this treatment one has the possibility to define locally the contact parameters for an accurate treatment of contact constraints. Local values of the geometrical variables can be determined at the integration points, hence the method permits to integrate contact constitutive laws along contact segments. The weak form for this new formulation is developed. Furthermore, also the consistent linearization is carried out. Finally a technique is proposed to reduce the large number of terms involved. In this case, an almost consistent tangent stiffness is determined. @ 1998 Elsevier Science Ltd. All rights reserved

Homogenisation of Microheterogeneous Materials Considering Interfacial Delamination at Finite Strains

In modern engineering, composite materials gained importance because of their specific properties requested by the individual application. They consist of inclusions such as particles or fibres which are introduced into a binding matrix material in order to “design” special material behaviour. In case of particle inclusions, typical materials are concrete, aluminum-boron or rubber filled with carbon. Fibre reinforced composites are typically stiffened by glass-, carbon- or aramid fibres. Recently, fibre reinforced metals are also subject to detailed investigation and application. In all cases the mechanical behaviour on the micro level defines the resulting material behaviour on the macro scale, which is needed from an engineering point of view in an arbitrary design process. The effective properties of the overall material depend on the geometry of the microstructure and the material properties of the constituents. In case of finite strains one can observe interfacial degradation in a cohesive zone between the matrix material and the inclusions. In this paper we focus on the homogenisation process of such materials with interfacial delamination. Here the difficulties arise from the geometrical and material nonlinearities. Even for linear elasticity this homogenisation can hardly be done analytically. Therefore we apply the finite element method to get a numerical approximation for the mechanical behaviour of a representative volume element (RVE). The homogenisation then is done with a statistically representative set of RVEs. In order to increase the efficiency and accuracy of the computations the finite element meshes are refined adaptively using non-conforming elements

On the Calculation of Finite Plastic Strains in Shell Intersections with Finite Elements

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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 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