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A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.

The latest release of the stress analysis finite element system BERSAFE contains a new general substructuring facility for use in either elastic or non‐linear analysis. The technique allows a considerable extension to the available facilities in that parts of the structure can be stored on datafiles for current or subsequent use. In the latter case, repeated computations are avoided for components with identical geometric and material properties, so effectively larger problems can be solved without a proportional increase in cost and effort. For non‐linear analysis, the technique is well suited to cases where non‐linear behaviour is confined to certain parts of the structure, such as in the vicinity of stress concentrations and crack tips. The elastic areas can be replaced by a substructure boundary, thereby concentrating the analysis on the higher‐stressed portions of the structure and so reducing the extent and cost of each iteration. The non‐linear substructuring technique is described in detail and illustrated by examples.

Finite element meshes can today be used to represent very complex structures because of high performance hardware and software. Although a very successful contributor to modern engineering analysis, such techniques are prone to certain classes of numerical analysis errors which have been long recognized and widely investigated. A more recently recognized source of error has, however, received the attention of analysts, being due to the shape distortion effects of popular types of element, such as isoparametric elements. A mesh scanning program, BERQUAL, part of the BERSAFE system, highlights such potential sources of error, but a more precise assessment is only possible from the final results since element performance depends on the stress gradients in each element. Hence additional error checking using certain stress error measures has been devised and implemented in the post‐processing program PLOTTER, part of the BERSAFE system, to enable rapid, interactive, screen diagnosis. The error measures and implementation details are described and illustrated with suitable examples of progressive shape distortion effects.

Theoretical investigations have been performed on slowly propagating cracks in T‐junctions and cross bars using computer procedures developed to analyse the amount and direction of crack growth using automatic mesh modification and the finite element stress analysis program, BERSAFE. The procedures may be used in a linear or non‐linear material. The crack growth for the linear elastic case is calculated to be in the direction of the maximum energy release rate. For the non‐linear case, the direction is taken to be that of Jwi. These procedures have been applied to fatigue crack growth calculations in this paper.

Aims to propose a new dynamic model for the solution of the three‐dimensional structural analysis problem of a non‐linear (non‐symmetrical) structure which is subjected under seismic forces.

This problem is reduced to the solution of a system of ordinary differential equations of the second kind and such a system is numerically solved by using a special kind of finite elements and by solving the corresponding eigenvalues‐eigenvectors problem.

The proposed finite element method is much smaller in degree of freedom size than commercial software, as classical linear stiffness matrices of three‐dimensional beam element have six degrees of freedom per node.

Future research should concentrate on the application of the new dynamic model to solve more complicated forms of non‐symmetrical structures.

Practical implications are given to structural analysis problems to the determination of the eigenvalues‐eigenvectors. As an example, an application is given to the determination of the eigenvalues and eigenvectors of a 15‐floor building consisting of reinforced concrete and subjected to an horizontal seismic vibration.

The new dynamic model which is proposed is addressed to researchers of dynamic analysis and civil engineers.

Exact solutions for Mohr Coulomb elastoplasticity are developed. Using these solutions an exact stress increment for a given finite strain increment can be computed. The developed solutions are valid for perfect and linear hardening/softening plasticity using isotropic work hardening hypotheses. The solutions can be used to check computer codes and assess their ability to handle multiple active yield surfaces. Illustrative examples are included.

The main purpose of this paper is to present and use the particle simulation method to explicitly simulate the spontaneous crack initiation phenomenon in brittle materials, and to compare the particle simulation results with experimental ones on the laboratory scale.

Using the particle simulation method, the brittle material is simulated as an assembly of particles so that the microscopic mechanism of inter‐ and intra‐particle crack initiation can be straightforwardly considered on the microscopic scale. A laboratory test has been conducted using a gypsum sample model to validate the particle simulation method for explicitly simulating the spontaneous crack initiation phenomenon.

The paper finds that in terms of simulating the macroscopic sliding surface along or around the contact plane between a block and its foundation, both the laboratory test and the particle simulation have produced consistent results. This indicated that the particle simulation method is capable of simulating macroscopic cracks through simulating conglomerations and accumulations of microscopic crack initiation within the brittle material. Compared with other numerical methods, the particle simulation method is more suitable for explicitly and effectively simulating spontaneous crack initiation problems on the microscopic scale in brittle materials.

The particle simulation method can be used to explicitly and effectively simulate the spontaneous crack initiation on the microscopic scale in brittle materials. It can be also used to simulate the macroscopic sliding surface along or around the contact plane between a block and its foundation. The experimental results of simulating the spontaneous crack initiation on the laboratory scale in brittle materials are very valuable for validating the numerical simulation results obtained not only from the particle simulation method, but also from other numerical simulation methods.

The finite element analysis of deformation of viscoplastic material involves contact between the tool and the workpiece. Here unilateral contact condition with the possibility of nodes originally in contact, losing contact subsequently, is analysed in non‐steady state forming processes. Friction has been taken into consideration through a potential function. Node to node contact is analysed and contact forces at the node are used to decide if the node is to be released. Two different algorithms are presented for treating the nodal contact condition. The one step explicit method with projections on the surface of contact was already implemented in the FORGE2^® software. An implicit scheme is proposed and compared with the existing scheme. The advantages of this scheme are numerically shown by solving some examples. It is observed that the volume losses are reduced. This makes it possible to use larger time steps or increase the computational accuracy.

Plane strain constitutive behaviour of von Mises and isotropic Hoffman materials is examined using single element tests. Two kinds of tests are conducted – (a) prescribed displacement tests; and (b) tests with a mixture of displacements and boundary tractions prescribed. While (a) are used to understand the manner of stress traversal on the yield surface in principal stress space, (b) are employed to study the load displacement response and the possibility of ensuing localization. Associated plasticity is assumed throughout. The tests are conducted using perfect and strain softening plasticity. It is found that for the von Mises criterion limited exact solutions can be evolved even under softening (or hardening) conditions. For isotropic Hoffman materials the nature of the stress traversal, load deflection response and the satisfaction of the localization conditions are strongly influenced by the ratio and difference of uniaxial yield strengths, in tension and compression, as well as by the softening parameters.

Healthy food sales have increased in recent decades. Retailers are widening their marketing management approach, including the use of social media to communicate with consumers and to promote healthy food. The purpose of this paper is to investigate European retailers’ social media communication content used to promote healthy food products, by analysing retailers’ Twitter messages and accounts characteristics, retailers’ Twitter messages content on healthy food and retailers’ Twitter accounts orientation on healthy food.

Data include approximately 74,000 tweets sent in 2016 from 90 corporate and brand accounts. The tweets were sent by the top 36 European retailers. Data elaboration includes quantitative content analysis of Twitter messages, which is used to identify healthy food categories’ occurrences and co-occurrences. Then, multiple multivariate-linear regression analyses explore the relation between retailers’ characteristics and healthy food messaging and between the overall content of retailer accounts and a healthy food focus.

The vast majority of retailers’ tweets on healthy food issues mainly address general health and sustainability issues. Tweets about food health and nutrition refer to food types, meals or consumer segments. Tweets about food sustainability refer to general issues. Analysis of retailer accounts shows that the larger the retailer is, the lower the relevance of healthy food. Retailers with high numbers of tweets and followers tend to decrease their attention to healthy food promotion. Compared to retailers with lower revenues, retailers with higher revenues tend to send a higher number of tweets that focus on healthy food but the incidence is lower compared to the overall accounts’ messaging.

As the study focuses on a single category of food products, further research into other categories of retail products may contribute to a wider perspective. Future research may include graphical content/emoticons and extend the analysis to other social media platforms. Finally, social media data allow studies to cover a wide geographical area. However, in order to also value non-English written messaging, this research introduces some approximations in language interpretation.

The research provides insights into how retailers use social media and provides an overview of how retailers manage their social media communication in one of the most promising food product categories. Retailers manage social media communication content cautiously to minimise controversial issues. This study provides insights into the need to more effectively target the increasing number of social media users.

The research approach and findings of this study extend prior research on retailers’ communication management by improving the understanding of retailers’ use of social media and marketing communication content for their key products, focusing on healthy food.