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The proposed research is essentially concerned on numerical simulation of materials and structures commonly used in the aerospace industry. The work is primarily focused on the study of the fracture mechanics with emphasis to composite materials, which are widely employed in the aerospace and automotive industry. Since human lives are involved, it is highly important to know how such structures react in case of failure and, possibly, how to prevent them with an adequate design. It has become of primary importance to simulate the material response in composite, especially considering that even a crack, which could be invisible from the outside, can propagate throughout the structure with small external loads and lead to unrecoverable fracture of the structure. In addition, structures made in composite often present a complex behaviour, due to their unconventional elastic properties. A numerical simulation is then a starting point of an innovative and safe design. Conventional techniques (nite elements for example) are not su-cient or simply not ecient in providing a satisfactory description of these phenomena. In fact, being based on the continuum assumption, mesh-based techniques suer of a native incapacity of simulating discontinuities. Novel numerical methods, known as Meshless Methods or Meshfree Methods (MM) and, in a wider perspective, Partition of Unity Methods (PUM), promise to overcome all the disadvantages of the traditional finite element techniques. The absence of a mesh makes MM very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, MM still have signicant limitations that prevent their acceptance among researchers and engineers. Because of the infancy of these methods, more efforts should be made in order to improve their performances, with particular attention to the computational time. In summary, the proposed research will look at the attractive possibilities offered by these methods for the study of failure in composite materials and the subsequent propagation of cracks.

"The last fifteen years have seen much success in the analysis of quasi-static evolution for Griffith fracture, which is the mathematically natural starting point for studying fracture. At the same time, attempts have been made to show existence for similar models based on cohesive fracture rather than Griffith. These models are generally viewed as physically more realistic than Griffith, in that they are better models for crack nucleation. These attempts at existence proofs have been unsuccessful without very strong additional assumptions, for example, specifying the crack path a priori. The main purpose of this thesis is to characterize as well as possible the mathematical difficulties in cohesive fracture, and to make progress toward an existence result without the prescribed crack path assumption. So far, the most powerful method for existence proofs is to build a sequence of approximate solutions, based on time discretization, and take the limit as the time steps go to zero. We show that there are mainly two complications on the cracks of these approximate solutions that we need to rule out in order to show existence. The first one is due to the potential oscillation of the crack path. The second is due to the potential splitting of a crack into two or more nearby cracks, with the same total jump in displacement. We begin by first constructing an example illustrating how oscillations described above can affect the minimality of the limit. Then we prove that the splitting described above can be ruled out for any sequence of unilateral minimizers. With this result, we show how exactly oscillation affect the minimality on the limit of the sequence. We then move to the evolution problem and show the convergence of energy for almost every t. Based on this result we develop a method that allows us to analyze the problem using only a finite set of times. An application of this method is a proof of absolute continuity. Future work will be aimed at using the tools we developed to rule out oscillation and finally to prove existence results under more general assumptions."

This thesis contains a study which has been conducted using fracture mechanics parameters to describe crack and craze growth behaviour in PMMA under the influence of liquid environment. The text of this work is divided into two main parts: Part I has two component chapters; Chapter 1 contains a general introduction to environmental fracture in polymers. Chapter 2 outlines the basis of fracture mechanics concepts used in the analysis of results, and contains a literature review on the failure behaviour of PMMA in dry and wet environment. The survey includes results from dead load tests and monotonically increasing displacement conditions. Part II contains the work which has been undertaken to investigate the environmental fracture of PMMA. This part is subdivided into four phases. Phase I describes an effective method which is successfully used to monitor craze growth in PMMA under the influence of dead load and methanol environment. In the same chapter (3) the results together with the discussion are given. Phase II gives results obtained from crack propagation tests in PMMA in air and liquid environments. These tests are performed under monotonically increasing load-point displacement conditions using the double torsion technique which is described in Chapter 4. Chapter 5 contains the experimental results and shows that in dry tests, crack propagation is stable with characteristic KC and crack speed values. To the contrary, tests performed in methanol have developed unstable cracking which is identified with a sequence of rapid jumps. Phase III follows here where the mechanism which constitutes these jumps is determined. This is done with the aid of the K/v relationship obtained during a crack jump. The linear compliance analysis for the test piece geometry in Chapter 6, together with an experimental technique developed to measure rapid load drops, given in Chapter 7, provide the basis for the measurement of the K/v values. In Phase IV a mathematical model is proposed in Chapter 8, which successfully identifies the various stages which occur during the fracture of PMMA both dry and in methanol. A thorough fractographic study is carried out in Chapter 9 in support and completion of the model, with further evidence given from acoustic emission results, shown in Chapter 10. As an alternative environmental condition, fracture tests are performed in distilled water and crack propagation results are given in Chapter 11. These have shown similar crack jumping mechanism to that in methanol.

A survey has been made of the history of fatigue since the time of Woehler and this revealed the ever-increasing number of problems caused by fatigue, ranging from complex aircraft to everyday products. Consideration of fatigue is now an essential part of design. The possibility of a fatigue failure in mechanical or structural components is usually solved by either 'ad hoc' fatigue tests or by a safety margin. Both solutions are expensive and can only be avoided by making available suitable design data based on carefully planned tests. In this research a large number of tension bolts and screwed bar specimens were tested under constant amplitude loading over a wide range of the variables. Planning of the tests made possible an analysis which allowed statistical values to be quoted for the resulting curves. The theoretical representation of fatigue data has been studied and methods are presented which allow computer production of comprehensive fatigue design S-N curves. The required data to produce the curves is limited to the tensile strength and two constants which can be determined from a small number of fatigue tests. The principles have been demonstrated for tension bolt joints and can be extended to other types of joints. The designer normally obtains data from 'Standards' which provide the statistically safe strength for materials and components. This research demonstrates that fatigue data can be presented to the designer in a similar manner by the introduction of two additional constants.

Fracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate (ξησ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Vasantha Mohan Narendran. / M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Gerald Frank Zamiski. / M.S.

Ductile and brittle failure of solids are closely related to their plastic and fracture behavior, respectively. The two most common energy dissipation mechanisms in solids possess distinct kinematic characteristics, i.e. large strain and discontinuous displacement, both of which pose challenges to reliable, efficient numerical simulation of material failure in engineering structures. This dissertation addresses the reliability and efficiency issues associated with the kinematic characteristics of plasticity and fracture. At first, studies are conducted to understand the relation between two well recognized large strain plasticity models that enjoy widespread popularity in numerical simulation of plastic behavior of solids. These two models, termed the additive hypo-elasto-plasticity and multiplicative hyper-elasto-plasticity models, respectively, are regarded as two distinct strategies for extending the classical infinitesimal deformation plasticity theory into the large strain regime. One of the most recent variants of the additive models, which features the logarithmic stress rate, is shown to give rise to nonphysical energy dissipation during elastic unloading. A simple modification to the logarithmic stress rate is accordingly made to resolve such a physical inconsistency. This results in the additive hypo-elasto-plasticity models based on the kinetic logarithmic stress rate in which energy dissipation-free elastic response is produced whenever plastic flow is absent. It is then proved that for isotropic materials the multiplicative hyper-elasto-plasticity models coincide with the additive ones if a newly discovered objective stress rate is adopted. Such an objective stress rate, termed the modified kinetic logarithmic rate, reduces to the kinetic logarithmic rate in the absence of strain-induced anisotropy which is characterized as kinematic hardening in the present dissertation. In the second part of the dissertation, the computational complexity of finite element analysis of the onset and propagation of interface cracks in layered materials is addressed. The study is conducted in the context of laminated composites in which interface fracture (delamination) is a dominant failure mode. In order to eliminate the complexities of remeshing for constant initiation and propagation of delamination, two hierarchical approaches, the extended finite element method (XFEM) and the s-version of the finite element method (s-method) are studied in terms of their effectiveness in representing displacement discontinuity across delaminated interfaces. With one single layer of 20-node serendipity solid elements resolving delamination-free response of the layered materials, it is proved that the delamination representations based on the s-method and the XFEM result in the same discretization space as the conventional non-hierarchical ply-by-ply approach which employs one layer of solid elements for each ply as well as double nodes on delaminated interfaces. Delamination indicators based on the s-method representation of delamination are then proposed to detect the onset and propagation of delamination. An adaptive methodology is accordingly developed in which the s-method displacement field enrichment for delamination is adaptively added to interface areas with high likelihood of delamination. Numerical examples show that the computational cost of the adaptive s-method is significantly lower than that incurred by the conventional ply-by-ply approach despite the fact that the two approaches produce practically identical results.