Advanced Continuum Theories and Finite Element Analyses

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.
Contents: Classical Continuum Mechanics:Kinematics of Classical Continuum MechanicsStressesBalance LawsConstitutive TheorySimple ThermoviscoelasticityFluid DynamicsThermoelasticity and ViscoelasticityElasticityPlasticityElectromagnetic InteractionsMicrocontinuum Field Theories:Kinematics of Microcontinuum Field TheoriesStresses and Balance LawsConstitutive TheoryThermomechanical MaterialsMicromorphic and Micropolar FluidsMicromorphic PlasticityMaterial ForceThermomechanical-Electromagnetic CouplingFinite Element Analyses:PreliminariesFinite Element Formulation of Classical Continuum MechanicsDynamic Crack PropagationFinite Element Formulation of General Micromorphic TheoryFinite Element Formulation of Linear Micromorphic TheoryPassage to Finite Element Formulation of Micropolar TheorySpecial Topics:Nonlocal TheoryMechanobiology4D PrintingPoroelasticityNematic Liquid CrystalAppendices:Tensor AnalysisRepresentation Theorem
Readership: Professionals, researchers, academics, and graduate students in engineering mechanics, mechanical engineering, general materials science, continuum physics and mathematical modeling.Continuum Mechanics;Microcontinuum Theories;Finite Element Analyses;Mechanobiology;Nonlocal Theory;Poromechanics00