Stefanos-Aldo Papanicolopulos

Discretization of Gradient Elasticity Problems Using C 1 Finite Elements

Strain-gradient theories have been used to model a variety of problems (such as elastic deformation, fracture behavior and plasticity) where size effect is of importance. Their use with the finite element method, however, has the drawback that specially designed elements are needed to obtain correct results.

Continua with microstructure: second-gradient theory: Theory, examples and computational issues

ABSTRACT Second-gradient theories represent a frequently used subset of theories of continua with microstructure. This paper presents an extended overview of second-gradient theories, starting from a simple one-dimensional example, proceeding with a thorough description of gradient elasticity and additionally briefly describing some other theories of this kind. A series of characteristic examples is presented to demonstrate the main aspects and applications of second-gradient theories. Finally, the complications in the finite-element implementation of second-gradient theories are presented, along with a review of the finite elements that have been developed for this purpose.

Computation of moderate-degree fully-symmetric cubature rules on the triangle using symmetric polynomials and algebraic solving

A novel method is presented for expressing the moment equations involved in computing fully symmetric cubature rules on the triangle, by using symmetric polynomials to represent the two kinds of invariance inherent in these rules. This method results in a system of polynomial equations that is amenable to solution using algebraic solving techniques; using Grobner bases, rules of degree up to 15 are computed and presented, some of them new and with all their points inside the triangle.Since all solutions to the polynomial system are computed, it is for the first time possible to prove whether a given rule type results in specific rules of a given quality; it is thus proved that for degrees up to 14 there are no non-fortuitous rules that can improve on the presented results. For degree 10, an example is also provided showing how the proposed method can be used to exclude the existence of better fortuitous rules as well.

Efficient computation of cubature rules with application to new asymmetric rules on the triangle

This paper presents a new, efficient method for computing cubature rules, based on least-squares minimisation and the use of orthogonal bases. The method, which can be applied for any integration domain, is tested here for the case of asymmetric cubature rules on the triangle showing how the computation of the necessary basis, and its derivatives, can be optimised. The numerical results presented include three new cubature rules with fewer points than known rules of the same degree.

New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases

Cubature rules on the triangle have been extensively studied, as they are of great practical interest in numerical analysis. In most cases, the process by which new rules are obtained does not preclude the existence of similar rules with better characteristics. There is therefore clear interest in searching for better cubature rules.Here we present a number of new cubature rules on the triangle, exhibiting full or rotational symmetry, that improve on those available in the literature either in terms of number of points or in terms of quality. These rules were obtained by determining and implementing minimal orthonormal polynomial bases that can express the symmetries of the cubature rules. As shown in specific benchmark examples, this results in significantly better performance of the employed algorithm.

Finite element analysis of stresses in a flexible bulk solid container

Current theories and design codes pertaining to storage structures for bulk solids have been developed in the context of rigid-walled silos and may not be applicable for smaller and highly flexible containers that are often used for industrial packaging and intermediate storage. The focus of this study is to investigate the effect of wall flexibility on the bulk stresses and wall pressures during storage using finite element analysis. The results show that when the wall stiffness is low, the computed bulk stresses in the vertical bin section are dominated by plasticity, while the stresses in the hopper section remain in the elastic state. In this situation, the wall pressure in the bin section is heavily influenced by the strength of the stored solid, which controls the extent of plastic flow. Overall, the normal wall pressure in the bin section is found to decrease with wall flexibility leading to a corresponding increase in vertical stress in the stored solid. As a consequence, the stresses in the hopper also increase leading to increasing loads on the hopper walls and potential exacerbation of handling issues for cohesive materials in highly flexible containers.

Review and Comparison of Numerical Implementations for Cosserat Plasticity

The seminal paper of Muhlhaus and Vardoulakis (1987) led to an extensive study of generalised continuum plasticity models for numerical modelling of localisation of deformation. While different models and numerical implementations have been proposed in the literature, all capable of capturing the initial development of localisation, there is a lack of comparative studies to highlight the differences between models and their numerical implementations. In this work we present a review of existing numerical implementations of Cosserat plasticity models. We then implement a number of these models and finite elements within a commercial code to provide a comparison of the localisation behaviour based on numerical results of a simple test.

Restoring Marble Fragments: the Pull-Out Problem

Joining together fragmented structural elements is perhaps the most challenging task during a restoration project. For the monuments of the Acropolis of Athens a pioneering method has been developed already from the early eighties requiring the use of threaded titanium bars and suitable cement mortar [1]. For the complete assessment of the method and the development of innovative connections for the structural integrity of ancient stone temples, in general, it is imperative, among others, to understand the mechanisms leading to the pull-out phenomenon, namely the gradual or abrupt removal of the reinforcing bars from the body of the member. Although the problem is studied by structural engineers long ago, an analytic solution is not yet available and many questions remain still unanswered due to the great number of parameters involved [2]. In this context a combined experimental and numerical analysis is presented here in an effort to study parametrically the various factors affecting the phenomenon.

The Mechanical Strength of Intestinal Anastomoses in Hypothyroid Rats

Intestinal wound healing is an essential process for surgical reconstruction of the digestive tract. Compromised healing - a multifactorial process — is considered a life-threatening complication, leading to prolonged hospitalization, decreased quality of life and increased medical costs [1]. Parameters for anastomotic repair and adhesion formation are mechanical, biochemical or histological, with the measurement of choice being mostly mechanical, biochemical or both.