An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$\alpha$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.Comment: In this version, typos were fixed, Fig. 16 is added, the literature review is extended and clarifying explanations and remarks are added at several places. Supplementary movies are available at https://av.tib.eu/series/641/supplemental+videos+of+the+paper+an+adaptive+space+time+phase+field+formulation+for+dynamic+fracture+of+brittle+shells+based+on+lr+nurb

Regime analysis of the rheology of spherical and non-spherical particles

In the early stages of granular rheology, the majority of analytical studies were based on granular assembly consisting of spherical particles. This was due to geometric simplicity and feasibility when calculating dynamic variables. Furthermore system limitation emerged as a problem when investigating more complex and realistic considerations. However, in the contemporary research field, with the steadily increasing ability to perform more complex computations and with available resources, attention has focused on non-spherical particles because of their deeper relevance to practical applications. In this work, a 3D shear cell model is developed based on the Discrete Element Method using the commercial software platform “PFC” to study non-spherical particles’ flow characteristics. A comparison is made with those of spherical assemblies. Firstly, the simulation model of annular shear cell consisting of spherical particles is tested with PFC and this agreed well with previous results, thus justifying the use of this tool to analyse the nonspherical level. Then the effect of platen roughness is investigated on spherical particle assembly from the microdynamic perspective, in order to establish a correlation between platen roughness and granular flow dynamics. This is undertaken in terms of particle size that is used to construct the platens. It is found that linearity and non-linearity of gradient profile across several important parameters are distinguishing features affected by variations in platen texture. The externally applied load is the most important aspect that bridges studies where gravity is considered and yet often overlooked. This point is established through in-depth investigation of granular flow in presence and absence of gravity where comparison of an number of flow characteristics is presented. Following this, the effects of particle shape are microdynamically investigated with reference to aspect ratio of non-spherical (ellipsoidal) particles and compared with spherical particles. The following key properties - particle linear velocity, angular velocity, contact normal force, contact shear force, total contact force, total contact moment and porosity - are 4 analysed to explain the effect of variation of the above-mentioned geometric properties on each of these parameters. Then, macrodynamic analysis is performed in a comparative study between spherical particles and ellipsoidal particles of varying aspect ratios with focus on the variables that are important in general constitutive model such as velocity, density and stress tensors. Physics underlying the observation is discussed to highlight effect of particle aspect ratio. Finally and most importantly, regime transition of ellipsoidal particle assembly is contrasted with the findings for spherical particles. In this study, the techniques that are generally used to identify regime transition for granular rheology of spherical particles are tested on flow of non-spherical (ellipsoidal) particles of varying shapes (aspect ratios). This includes correlation between elastically scaled force, kinetically scaled force, coordination number, apparent coefficient of friction and porosity. Some observations are found to be similar and useful for non-spherical particles while others found not suitable for nonspherical particles

Mechanochemical Reactions and Strengthening in Epoxy-Cast Aluminum Iron-Oxide Mixtures

This investigation is focused on the understanding of mechanical and chemical reaction behaviors of stoichiometric mixtures of nano- and micro-scale aluminum and hematite (Fe2O3) powders dispersed in epoxy. Epoxy-cast Al+Fe2O3 thermite composites are an example of a structural energetic material that can simultaneously release energy while providing structural strength. The structural and energetic response of this material system is investigated by characterizing the mechanical behavior under high-strain rate and shock loading conditions. The mechanical response and reaction behavior are closely interlinked through deformation characteristics. It is, therefore, desirable to understand the deformation behavior up to and beyond failure and establish the necessary stress and strain states required for initiating chemical reactions. The composite s behavior has been altered by changing two main processing parameters; the reactants particle size and the relative volume fraction of the epoxy matrix. This study also establishes processing techniques necessary for incorporating nanometric-scale reactants into energetic material systems. The mechanochemical behavior of epoxy-cast Al+Fe2O3 composites and the influence of epoxy volume fraction have been evaluated for a variety of loading conditions over a broad range of strain rates, which include low-strain rate or quasistatic loading experiments (10-4 to 10-2 1/s), medium-strain rate Charpy and Taylor impacts (103 to 104 1/s), and high-strain rate parallel-plate impacts (105 to 106 1/s). In general, structural strength and toughness have been observed to improve as the volume fraction of epoxy decreases, regardless of the loading strain rate regime explored. Hugoniot experiments show damage occurring at approximately the same critical impact stress for compositions prepared with significantly different volume fractions of the epoxy binder phase. Additionally, Taylor impact experiments have indicated evidence for strain-induced chemical reactions, which subject the composite to large shear accompanied by temperature increase and associated softening, preceding these reactions. Overall, the work aims to establish an understanding of the microstructural influence on mechanical behavior and chemical reactivity exhibited by epoxy-cast Al+Fe2O3 materials when exposed to high stress and high-strain loading conditions. The understanding of fundamental aspects and the results of impact experiment measurements provide information needed for the design of structural energetic materials.Ph.D.Committee Chair: Dr. Naresh N. Thadhani; Committee Member: Dr. David L. McDowell; Committee Member: Dr. Kenneth A. Gall; Committee Member: Dr. Min Zhou; Committee Member: Dr. Ronald W. Armstrong; Committee Member: Dr. Yasuyuki Hori

Art of Modeling in Contact Mechanics

International audienceIn this chapter, we will first address general issues of the art and craft of modeling-contents, concepts, methodology. Then, we will focus on modeling in contact mechanics, which will give the opportunity to discuss these issues in connection with non-smooth problems. It will be shown that the non-smooth character of the contact laws raises difficulties and specificities at every step of the modeling process. A wide overview will be given on the art of mod-eling in contact mechanics under its various aspects: contact laws, their mechanical basics, various scales, underlying concepts, mathematical analysis, solvers, identification of the constitutive parameters and validation of the models. Every point will be illustrated by one or several examples. 1 Modeling: the bases It would be ambitious to try to give a general definition of the concept either of a model itself or of model processing. Modeling relates to the general process of production of scientific knowledge and also to the scientific method itself. It could be deductive (from the general to the particular, as privileged by Aristotle) or inductive (making sense of a corpus of raw data). Descartes (38) saw in the scientific method an approach to be followed step by step to get to a truth. Modeling can be effectively regarded as a scientific method that proceeds step by step, but its objective is more modest: to give sense of an observation or an experiment, and above all to predict behaviors within the context of specific assumptions. This concept of " proceeding step by step " is fundamental in modeling. In this first section, we will examine the notion of model in the general context of mechanical systems

ALERT Doctoral School 2013, Soil-Structure Interaction

International audienc

Fracturing of Layered Reservoir Rocks

The development of fractures in rock layers reflects a history of complex, non-linear, time-dependent mechanical processes. The processes strongly depend on the rock rheology, particularly the behavior during progressive deformation, layering effects such as the mechanical stratigraphy, and the local stress conditions. In the past, the complex mechanics associated with fracture initiation and propagation contributed to the application of simplified models based on linear rheology and using quasi-static solutions. While this approach is effective in solving infinitesimal strain problems, it provides no explanation for strain localization, damage accumulation and rock failure, and it oversimplifies fracture propagation. The objective of the present work is to contribute to the understanding of these processes.The approach of this study is as follows. (Chapter 1) Theoretical advancements on fracturing and the concept of continuum damage mechanics are compared with rock mechanics experiments to understand progressive deformation, failure, and fracture propagation for rock. It is demonstrated that non-local (away from the crack-tip) yielding behavior must be considered to understand complex fracturing. (Chapter 2) A numerical rheology based on the elastic-plastic-damage properties of Berea sandstone is developed and calibrated to experimental rock mechanics data. A method for translating the stress-strain curve and acoustic emissions data into a material model included in the commercial finite element code Abaqus is presented. Two rock mechanics experiments are simulated in 3-D to test the rheology model. (Chapter 3) The rheology is implemented into finite element models based on classical hydraulic fracturing configurations. The explicit dynamic finite element method is used to simulate damage and transient propagation of a hydrofracture segment. It is shown that the complexity of fracturing depends on the local stress-strain response, which is controlled by the evolving damage pattern. The dynamical characteristics of arrest, rupture, branching, and segmentation of the fracture are described in terms of damage evolution. (Chapter 4) An analytical model for natural fracture reactivation is paired with the finite element simulations to understand the development of complex hydraulic fracture networks in the subsurface. The models' predictions are compared with data from hydraulically stimulated wells in the Barnett Shale. Recommendations are made for optimizing hydrofracture operations in wells for different states of stress (Chapter 5). The occurrence of zones of anomalously high fracture density is characterized in a carbonate sequence near Cedar Mountain Utah, and in Jackfork Group sandstone layers in Oklahoma and Arkansas. The results indicate that fracture density should be examined as a function of the evolving rock properties of the host layer in addition to the layer thickness.The investigation contributes to understanding the process of damage and fracturing during the deformation of rock layers. The results describe the development of mechanical inhomogeneity in fractured rock layers and can be applied to explain the formation of complex hydraulic fractures in unconventional reservoirs

Using the fracture mechanics parameters in assessment of integrity of rotary equipment

In this paper is presented the principle of application of fracture mechanics parameters in determining the integrity of rotary equipment. The behavior of rotary equipment depends on presence of cracks and basically determines the integrity and life of such equipment. The locations of stress concentration (i.e. radius changes) represent a particular problem in rotary equipment, and they are the most suitable places for the occurrence of microcracks i.e. cracks due to fatigue load. This problem is most common in the shaft of relatively large dimensions, for example, turbine shafts in hydropower plants made of high-strength carbon steel with relatively low fracture toughness, and relatively low resistance to crack formation and growth. Having in mind that rotary equipment represents the great risk in the exploitation, whose occasional failures often had severe consequences, it is necessary detail study of their integrity. For this purpose, it is necessary application of parameters of linear-elastic fracture mechanics, such as stress intensity factor, which range defines the rate of crack growth (Parisian law), and its critical value (fracture toughness) determines the critical crack length. The procedures for determining the critical crack length will be described using the fracture mechanics parameters