The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

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Phase-field models in materials science

This paper presents a modified regularized formulation of the Ambrosio–Tortorelli type to introduce the crack non-interpenetration condition in the variational approach to fracture mechanics proposed by Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319–1342]. We focus on the linear elastic case where the contact condition appears as a local unilateral constraint on the displacement jump at the crack surfaces. The regularized model is obtained by splitting the strain energy in a spherical and a deviatoric parts and accounting for the sign of the local volume change. The numerical implementation is based on a standard finite element discretization and on the adaptation of an alternate minimization algorithm used in previous works. The new regularization avoids crack interpenetration and predicts asymmetric results in traction and in compression. Even though we do not exhibit any gamma-convergence proof toward the desired limit behavior, we illustrate through several numerical case studies the pertinence of the new model in comparison to other approaches.

Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

Uncertainties and dynamic problems of bolted joints and other fasteners

Introduction -- What are Smart Structures and Materials? Smart Structures -- The Instrumented Materials. Structural and Mesoscopic Materials. Molecular Materials -- An Engineering View. Nuclear Materials. Applications Examples. Scenario Building and the Future.

Smart Structures and Materials

A review of the investigations that have been made on the stress and strength analysis of mechanically fastened joints in fibre-reinforced plastics (FRP) is presented. The experimental observations of the effects of joint geometry, ply-orientation, lay-up and through-thickness pressure on the joint behaviour are described briefly for both single and multi-fastener joints. The analytical and numerical methods of stress analysis required before trying to predict failure are discussed. The numerical approaches cover both two and three-dimensional models and the effects of clearance, friction and geometry are assessed. The several methods that have been used to predict failure in single or multi-fastener joints are described. It is concluded that there are some issues that require further investigation. There is no general agreement about the method that should be used to predict failure, but progressive damage models are quite promising since important aspects of the joint's behaviour can be modelled using this approach. In order to take into consideration several factors related to joint strength the use of three-dimensional models is suggested. These models require a three-dimensional failure criterion and an appropriate property degradation law.

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Stress analysis and strength prediction of mechanically fastened joints in FRP: A review

A method of producing transparent model materials for photo-orthotropic-elastic studies is presented. This material fabricated from glass fibers and a modified polyester matrix exhibits continuous relatively smooth fringe patterns which are linearly related to the state of stress. As such, the heterogenous material can be treated as a homogenous medium with orthotropic properties.

Photo-orthotropic-elasticity

Damage assessment through electrical resistance measurement in graphite fiber-reinforced composites

The application of glass fiber-reinforced polymeric matrix composites in civil engineering structures has been increasing rapidly in recent years. Pultruded composites are attractive for structural applications because of their continuous production and excellent mechanical properties. The present study is intended to be a step in understanding bolted joints in pultruded composites. Specifically, bolted connections in pultruded plates are investigated for their block shear and net tension failure modes. Configurations and dimensions have been selected to highlight the block shear and net tension failure phenomena and to compare the behavior of composites to the standard practice in the case of steel connections. Specimens with single and multiple holes have been tested in tension under bolt-loading conditions. Some of the specimens were instrumented with strain gages and the load-strain responses were monitored. The failed specimens were examined for the cracks and fracture patterns. The results have been analyzed using the strength calculations similar to those used in the load and resistance factor design (LRFD) procedures for steel structures. Two LRFD-type formulae for block shear and net tension failure for pultruded composites are proposed in the present paper. It was found that the failures in the bolt-loaded pultruded specimens could be predicted reasonably well with the proposed formulae. The use of these formulae is also demonstrated by means of examples. The proposed resistance factors are checked with additional test results.

Load and resistance factor design (LRFD) approach for bolted joints in pultruded composites

The transient response of composite plates, with and without central circular holes, to blast loading is studied. The modal-analysis approach has been used in the computation of numerical results, which have been obtained for isotropic and orthotropic plates, with and without holes. In order to verify the theoretical results, experiments have been conducted on aluminum and unidirectionally reinforced E-glassepoxy plates, using a shock tube as the loading device. The experimental peak dynamic strains (normalized with respect to the pressure) are compared with the theoretical values. The strain-time history is also shown for a particular gage location in the composite plate. Finally, a comparison of dynamic-amplification factors, defined as the ratio of the peak dynamic strains to the static strains, has been made between the isotropic and the composite plates.

R. Prabhakaran

Papers

Photo-orthotropic-elasticity

Damage assessment through electrical resistance measurement in graphite fiber-reinforced composites

Load and resistance factor design (LRFD) approach for bolted joints in pultruded composites

Response of composite plates to blast loading

Tensile fracture of composites with circular holes