Many engineering structures and components contain cracks or crack-like flaws and it is widely recognized that crack growth must be considered both in the design and analysis of failures. The complete solution of a crack growth problem therefore includes determination of the crack path. At present the factors controlling the path taken by a propagating crack are not completely understood. In general crack paths are difficult to predict, while in practice their development in structures is often determined by large-scale structural tests. In introductory texts on fracture mechanics it is usually assumed that the crack path is known, either from theoretical considerations, or from the results of laboratory tests.
This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.
Biomateriomics is the holistic study of biological material systems. While such systems are undoubtedly complex, we frequently encounter similar components -- universal building blocks and hierarchical structure motifs -- which result in a diverse set of functionalities. Similar to the way music or language arises from a limited set of music notes and words, we exploit the relationships between form and function in a meaningful way by recognizing the similarities between Beethoven and bone, or Shakespeare and silk. Through the investigation of material properties, examining fundamental links between processes, structures, and properties at multiple scales and their interactions, materiomics explains system functionality from the level of building blocks. Biomateriomics specifically focuses the analysis of the role of materials in the context of biological processes, the transfer of biological material principles towards biomimetic and bioinspired applications, and the study of interfaces between living and non-living systems. The challenges of biological materials are vast, but the convergence of biology, mathematics and engineering as well as computational and experimental techniques have resulted in the toolset necessary to describe complex material systems, from nano to macro. Applying biomateriomics can unlock Nature’s secret to high performance materials such as spider silk, bone, and nacre, and elucidate the progression and diagnosis or the treatment of diseases. Similarly, it contributes to develop a de novo understanding of biological material processes and to the potential of exploiting novel concepts in innovation, material synthesis and design.
This work comprises edited versions of papers presented at the 6th Pacific Rim International Conference on Advanced Materials and Processing (PRICM-6), held on Jeju Island, Korea between the 5th and 9th November, 2007.
This book provides practicing engineers, researchers, and students with a working knowledge of the fatigue design process and models under multiaxial states of stress and strain. Readers are introduced to the important considerations of multiaxial fatigue that differentiate it from uniaxial fatigue.
