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ochsner composite mechanics 2023

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Textbook in PDF format Composite materials, especially fiber-reinforced composites, are gaining increasing importance since they can overcome the limits of many structures based on classical metals. Particularly the combination of a matrix with fibers provides far better properties than the constituents alone. Despite their importance, many engineering degree programs do not treat the mechanical behavior of this class of advanced structured materials in detail, at least on the bachelor degree level. Thus, some engineers are not able to thoroughly apply and introduce these modern engineering materials in their design process. This volume in the Advanced Structured Materials series provides first an introduction to the micromechanics of fiber-reinforced laminae, which deals with the prediction of the macroscopic mechanical lamina properties based on the mechanical properties of the constituents, i.e., fibers and matrix. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations. Three classical approaches to predict the elastic properties, i.e., the mechanics of materials approach, the elasticity solutions with contiguity after Tsai, and the Halpin–Tsai relationships, are presented. The quality of each prediction is benchmarked based on two different sets of experimental values. This chapter concludes with optimized representations, which were obtained based on the least square approach for the used experimental data sets. The second part of this monograph provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear-rigid) plate elements. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. The continuum mechanical approach reviews that partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. Based on the three basic equations of continuum mechanics, i.e., the kinematic relationship, the constitutive law, and the equilibrium equation, these partial differential equations describe the physical problem. The here introduced classical laminate theory provides a simplified stress analysis and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements in the three coordinate directions. This theory provides the solution of the statically indeterminate system based on a generalized stress–strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. Nevertheless, the fundamental knowledge from the first years of engineering education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills, might be required to master this topic. The monograph concludes with a short introduction to a calculation program, the so-called Composite Laminate Analysis Tool (CLAT), which allows the application of the classical laminate based on a sophisticated Python script

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ochsner composite mechanics 2023

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