Catalin Picu - Mechanics of Fibrous Materials and Applications: Physical and Modeling Aspects

For more than 40 years the book series edited by CISM, International Centre for Mechanical Sciences: Courses and Lectures, has presented groundbreaking developments in mechanics and computational engineering methods. It covers such fields as solid and fluid mechanics, mechanics of materials, micro- and nanomechanics, biomechanics, and mechatronics. The papers are written by international authorities in the field. The books are at graduate level but may include some introductory material.

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Materials containing fibers are present in a large variety of applications due to their high mechanical performances at low weight. Reinforcement of continua with fibers has a long history which led to the widely used class of fiber-reinforced composites. Examples include polymers reinforced with fiberglass, high-performance composites made from woven yarns, and 3D woven composites used in cutting-edge areas such as aeronautics.

Different classes of fibrous materials are those containing a crosslinked network of fibers, which may or may not be embedded in a matrix. A prominent example is nonwovens, which are used in many applications such as sound and thermal insulation, clothing, filtration, and geotextiles. Many biological materials have a random complex fibrous structure. Examples include soft connective tissue, such as tendons and ligaments, the arterial walls, and the cellular cytoskeleton. Damage accumulation, fracture, and the related nonlinear behavior under large deformations are important considerations in all these materials.

Due to their discrete architecture, fibrous media have a rather complex mechanical response, especially since multiscale aspects are essential in such structures. Individual fibers or filaments may be assembled in multiscale architectures, from fibers to complex yarns up to woven or braided structures. Their geometrical configuration, which results from the manufacturing method used and the geometry of the fibers, are not easy to capture and characterize. Moreover, they exhibit strong geometrical and material nonlinearities due to the collective motion of the fibers, fiber bundles or yarns, associated nonlinear interactions that include friction and adhesion, and the presence of large local and global deformations with evolving anisotropy and couplings between different deformation modes.

This book brings together lecture notes organized for the CISM course titled Mechanics of Fibrous Materials and Applications: Physical and Modelling Aspects , held in Udine from July 9 to July 13, 2018. The course objective was to present the state-of-the-art understanding in this area and to provide an overview of the theoretical, modeling and practical aspects of designing and working with fibrous materials. Six lecturers contributed to the course: Philippe Boisse (INSA Lyon, France), Jean-Francois Ganghoffer (Universite de Lorraine, France), Edoardo Mazza (ETH Zurich, Switzerland), Mohammad Mofrad (Berkeley University, USA), Catalin Picu (Rensselaer Polytechnic Institute, USA), and Luca Placidi (Universita Uninettuno, Italy). This book summarizes this information through the perspective of four of these six lecturers, and their collaborators.

Chapter by Catalin Picu, titled Mechanics of Random Fiber Networks: StructureProperties Relation, discusses aspects of the mechanical behavior of fibrous materials containing a random network of fibers. The focus is on identifying the network parameters that control the mechanics of the structure. Such random networks are encountered in biological tissues, scaffolds for tissue growth, and many engineering materials. The chapter presents a classification of networks based on their architecture, the type of fibers, and the essential interactions that define their overall mechanical behavior. Further, it presents key results for the linear and nonlinear response of networks subjected to tension and compression, including relations between various parameters of the network and the described mechanical behavior. A similar analysis is presented for the strength of networks and its dependence on network parameters. A separate subsection is devoted to crosslinked and non-crosslinked networks in which fibers interact adhesively. In this case, adhesion reorganizes the network and imparts a particular mechanical behavior to the ensemble.