Manual for the course of lectures at MSTU. N.E. Bauman "Theory of metal forming" in the 5th semester for students of specialty 150201.

Table of contents (under spoiler)Use the arrow to expand or collapse this sectionTheory of stress stateBasic hypotheses of continuum mechanics.External forces and stresses.Stresses in coordinate sites. Indexing. Sign rule. Stress state at a point. Law of pairing of tangential stresses. Stress tensor. Principal normal stresses. Invariants of the stress tensor. Stress ellipsoid. Decomposition of the stress tensor into a spherical tensor and deviator. Maximum tangential stresses. Octahedral stresses. Stress intensity. Mohr stress diagrams. Differential equations of equilibrium (motion). Differential equations of equilibrium for an axisymmetric stress state. Plane deformed and plane stress states. Approximate equilibrium equations in the analysis of form-changing operations of sheet stamping. Theory of deformed state. Description of the motion of a continuous medium. Euler and Lagrange variables. Concept of deformation, types of deformation. Components of displacements and small deformations. Deformation tensor. Deformation intensity, maximum shear and octahedral deformations. True deformations. Increments of strains. Law of constancy of volume during plastic deformation. Condition for compatibility of strains. Strain rates and strain rates. Schemes of stress and strain states. Mechanical scheme of deformation. Relationships between stresses and strains in the elastic region. Generalized Hooke's law. Experimental determination of stresses based on strain measurement results. Subject index

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