Advanced Continuum Theories and Finite Element Analyses - (Frontier Research in Computation and Mechanics of Materials) by James D Lee & Jiaoyan Li
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<p/><br></br><p><b> About the Book </b></p></br></br>This comprehensive volume presents a unified approach to continuum theories, showing microcontinuum theories (including micromorphic theory and micropolar theory) are natural extension of classical continuum mechanics, and classical continuum mechanics is a special case of microcontinuum theories. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermos-visco-elastic-plastic solid. The material force and the electromagnetic interactions are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are rigorously formulated. Relevant numerical methods are included.<p/><br></br><p><b> Book Synopsis </b></p></br></br>This comprehensive volume presents a unified framework of continuum theories. It indicates that (i) microcontinuum theories (micromorphic and micropolar theories) are natural extension of classical continuum mechanics, and (ii) classical continuum mechanics is a special case of microcontinuum theories when the deformable material point is idealized as a single mathematical point. The kinematics and basic laws are rigorously derived. Based on axiomatic approach, constitutive theory is systematically derived for various kinds of materials, ranging from Stokesian fluid to thermo-visco-elastic-plastic solid. Material force and Thermomechanical-electromagnetic coupling are introduced and discussed. Moreover, general finite element methods for large-strain thermomechanical coupling physical phenomena are systematically formulated. Also, non-classical continuum theories (Nonlocal Theory, Mechanobiology, 4D printing, Poromechanics, and Non-Self-Similar Crack Propagation) are rigorously formulated with applications and demonstrated numerically.As an advanced monograph, this unique compendium can also be used as a textbook for several graduate courses, including continuum mechanics, finite element methods, and advanced engineering science theories. Extensive problems are provided to help students to better understand the topics covered.
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