Infinitesimal strain theory | EPFL Graph Search

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in the

Modèle numérique du comportement non-linéaire d'ouvrages massifs en béton non armé

Patrice Droz

Linear Elastic Fracture Mechanics (LEFM) are used to study crack propagation in unreinforced concrete of massive structures. This approach is well suited to the nonlinear analysis of structures of large dimensions, taking into account the size effect, i.e., the influence of the dimension of the structure on its behaviour at rupture. The Finite Element method is used to calculate the structure and the hypothesis of plane strain is made. The use of a criterion of crack propagation, based on LEFM requires the calculation of stress intensity factors. The evaluation of the latter is performed by the mean of a surface integral defined around the tip of the crack studied. It has been shown in this work that this integral is derived from the path integral J. The use of the surface integral has also been extended to the cases where body forces (gravity, inertie) act, or when the edges of the crack are subjected to pressure. This method is precise and numerically efficient. A smeared crack model is used in order to avoid continuous remeshing during crack propagation. But, as it has been shown in this research, classical smeared crack elements do not give satisfactory results when the crack is submitted to shear loading, a new finite element, using smeared cracking but with discontinuous shape functions has been developed. The model which combines LEFM and the smeared crack approach has been applied to different classical problems of fracture mechanics. It leads to good results under static or dynamic loading. As an example, the nonlinear behaviour of the vertical cross section of a gravity dam during an earthquake has been calculated and the crack pattern identified. Many further developments could be done starting from this original approach, in order to simulate more closely the real behaviour of structures, taking into account friction in the cracks and the three-dimensional development of then.

EPFL1987

Finite element analysis of strain distribution in a bone scaffold used with revision knee prosthesis

Line Aschwanden

The goal of this study is to analyze mechanical behavior of a new scaffold composed of PLA/bTCP in revision knee arhtroplasty (RKA). For this purpose, finite element models of RKA was developed to study the importance of the geometry of bones, the fixation length of the stem, height of the scaffold, and the type of defect (segmental and cavitary). The results of this study indicate that the height of the scaffold is the most important of all and the fixation length of stem is the least important parameter for failure of scaffold. This numerical model also gives a range of average volumetric strain. Volumetric strain of the scaffold is important for bone formation inside the scaffold since it represents the amount of fluid flow. The results obtained using this model will be used later in in vivo experiments.

2008

Strain hardening in 2D discrete dislocation dynamics simulations: A new '2.5D' algorithm

William Curtin, Shyam Mohan Keralavarma

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.

Pergamon-Elsevier Science Ltd2016

Modèle numérique du comportement non-linéaire d'ouvrages massifs en béton non armé

Patrice Droz

EPFL1987