Geometric Continuum Mechanics

Part I: Kinematics, Forces, and Stress Theory.- Manifolds of Mappings for Continuum Mechanics.- Notes on Global Stress and Hyper-Stress Theories.- Applications of Algebraic Topology in Elasticity.- De Donder Construction for Higher Jets.- Part II: Defects, Uniformity, and Homogeneity.- Regular and Singular Dislocations.- Homogenization of Edge-Dislocations as a Weak Limit of de-Rham Currents.- A Kinematics of Defects in Solid Crystals.- Limits of Distributed Dislocations in Geometric and Constitutive Paradigms.- On the Homogeneity of Non-Uniform Material Bodies.

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• Mecânica clássica
• Física Matemática
• Geometria diferencial e riemaniana
• Cálculo e análise matemática
• Engenharia mecânica

Continuum Mechanics;Geometric Continuum Mechanics;Geometry and mechanics;Differential geometry;Stress functions;de Rham currents;de Rham differential;Groupoids;Manifolds of Mappings;Force and Stress Theory;Geometry of Defects and Dislocations;Analysis of Homogeneity of Material Bodies