One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.

Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces

/pdf/feap-a-finite-element-analysis-program-qvz36simr5.pdf

FEAP - - A Finite Element Analysis Program

Crust at many divergent plate boundaries forms primarily by the injection of vertical sheet-like dykes, some tens of kilometres long1. Previous models of rifting events indicate either lateral dyke growth away from a feeding source, with propagation rates decreasing as the dyke lengthens2, 3, 4, or magma flowing vertically into dykes from an underlying source5, 6, with the role of topography on the evolution of lateral dykes not clear. Here we show how a recent segmented dyke intrusion in the Barðarbunga volcanic system grew laterally for more than 45 kilometres at a variable rate, with topography influencing the direction of propagation. Barriers at the ends of each segment were overcome by the build-up of pressure in the dyke end; then a new segment formed and dyke lengthening temporarily peaked. The dyke evolution, which occurred primarily over 14 days, was revealed by propagating seismicity, ground deformation mapped by Global Positioning System (GPS), interferometric analysis of satellite radar images (InSAR), and graben formation. The strike of the dyke segments varies from an initially radial direction away from the Barðarbunga caldera, towards alignment with that expected from regional stress at the distal end. A model minimizing the combined strain and gravitational potential energy explains the propagation path. Dyke opening and seismicity focused at the most distal segment at any given time, and were simultaneous with magma source deflation and slow collapse at the Barðarbunga caldera, accompanied by a series of magnitude M > 5 earthquakes. Dyke growth was slowed down by an effusive fissure eruption near the end of the dyke. Lateral dyke growth with segment barrier breaking by pressure build-up in the dyke distal end explains how focused upwelling of magma under central volcanoes is effectively redistributed over long distances to create new upper crust at divergent plate boundaries.

/pdf/segmented-lateral-dyke-growth-in-a-rifting-event-at-5bg334vaou.pdf

Segmented lateral dyke growth in a rifting event at Bárðarbunga volcanic system, Iceland

The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such mate- rials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg-Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress-strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Origami, the ancient art of paper folding, has inspired the design of engineering devices and structures for decades. The underlying principles of origami are very general, which has led to applications ranging from cardboard containers to deployable space structures. More recently, researchers have become interested in the use of active materials (i.e., those that convert various forms of energy into mechanical work) to effect the desired folding behavior. When used in a suitable geometry, active materials allow engineers to create self-folding structures. Such structures are capable of performing folding and/or unfolding operations without being kinematically manipulated by external forces or moments. This is advantageous for many applications including space systems, underwater robotics, small scale devices, and self-assembling systems. This article is a survey and analysis of prior work on active self-folding structures as well as methods and tools available for the design of folding structures in general and self-folding structures in particular. The goal is to provide researchers and practitioners with a systematic view of the state-of-the-art in this important and evolving area. Unifying structural principles for active self-folding structures are identified and used as a basis for a quantitative and qualitative comparison of numerous classes of active materials. Design considerations specific to folded structures are examined, including the issues of crease pattern identification and fold kinematics. Although few tools have been created with active materials in mind, many of them are useful in the overall design process for active self-folding structures. Finally, the article concludes with a discussion of open questions for the field of origami-inspired engineering.

https://iopscience.iop.org/article/10.1088/0964-1726/23/9/094001/pdf

Origami-inspired active structures: a synthesis and review

Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject. It offers significantly expanded coverage of elasticity in Chapter 5, including solutions of some 3-D problems based on the fundamental potential functions approach. It includes a new section at the end of Chapter 4 devoted to the integral formulation of the field equations. Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained. This book contains expanded and improved problem sets providing both intellectual challenges and engineering applications.

Introduction to continuum mechanics

8 – Non-Newtonian Fluids

In the present edition the illustrations of the Picture Book appear in full color. The scope of the book was extended again. There is now a chapter on hybridization and sections on bound states and on scattering in piecewise linear potentials in one dimension. From the web page www.extras.springer.com all illustrations can be downloaded for easy use in lectures and seminars. The inclusion of a CDROM with with that material (as in the third edition) is no longer necessary. To generate the computer graphics of the first edition of the Picture Book, we developed an interactive program on quantum mechanics. A modernized version, which we call INTERQUANTA (abbreviated IQ), together with an accompanying text has been published by Springer in various editions. The most recent one 1 can be regarded as companion to this Picture Book .I t allows interactive manipulation of of a host of physics and graphics parameters and produces output in the form of static and moving pictures. The program runs under Windows, Linux and Mac OS X. It is a pleasure to acknowledge the generous help provided by IBM Germany in the development of IQ .I n particular, we want to thank Dr. U. Groh for his competent help in the early phase of the work. All computer-drawn figures in the present edition were produced using the published version of IQ or extensions realized with the help of Mr. Anli Shundi, Dr. Sergei Boris, and Dr. Tilo Stroh.

W. Michael Lai

Papers

Introduction to continuum mechanics

8 – Non-Newtonian Fluids

Preface to the Fourth Edition

5 – The Elastic Solid

CHAPTER 3 – Kinematics of a Continuum