Postgrado

CONTINUUM MECHANICS FOR ENGINEERS

Contents
• Continuum Theory
• The Continuum Concept • Continuum Mechanics

• Essential Mathematics
• • • • • • • Scalars, Vectors, and Cartesian Tensors Tensor Algebra Summation Convention Indicial Notation Matrices and Determinants Transformations of Cartesian Tensors Principal Values and Principal Directions of Symmetric Second-Order Tensors TensorFields, Tensor Calculus Integral Theorems of Gauss and Stokes

• •

Stress Principles
Body and Surface Forces, Mass Density Cauchy Stress Principle The Stress Tensor Force and Moment Equilibrium, Stress Tensor Symmetry Stress Transformation Laws Principal Stresses, Principal Stress Directions Maximum and Minimum Stress Values Mohr’s Circles for Stress Plane Stress Deviator and Spherical StressStates Octahedral Shear Stress

Kinematics of Deformation and Motion
Particles, Configurations, Deformation, and Motion Material and Spatial Coordinates Lagrangian and Eulerian Descriptions The Displacement Field The Material Derivative Deformation Gradients, Finite Strain Tensors Infinitesimal Deformation Theory Stretch Ratios Rotation Tensor, Stretch Tensors Velocity Gradient, Rate ofDeformation, Vorticity Material Derivative of Line Elements, Areas, Volumes

Fundamental Laws and Equations
Balance Laws, Field Equations, Constitutive Equations Material Derivatives of Line, Surface, and Volume Integrals Conservation of Mass, Continuity Equation Linear Momentum Principle, Equations of Motion The Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion Moment of Momentum(Angular Momentum) Principle

Law of Conservation of Energy, The Energy Equation
Entropy and the Clausius-Duhem Equation Restrictions on Elastic Materials by the Second Law of Thermodynamics Invariance Restrictions on Constitutive Equations from Invariance Constitutive Equations

Linear Elasticity
Elasticity, Hooke’s Law, Strain Energy Hooke’s Law for Isotropic Media, Elastic Constants ElasticSymmetry; Hooke’s Law for Anisotropic Media Isotropic Elastostatics and Elastodynamics, Superposition Principle Plane Elasticity Linear Thermoelasticity Airy Stress Function Torsion Three-Dimensional Elasticity

Classical Fluids
Viscous Stress Tensor, Stokesian, and Newtonian Fluids Basic Equations of Viscous Flow, Navier-Stokes Equations Specialized Fluids Steady Flow, Irrotational Flow,Potential Flow The Bernoulli Equation, Kelvin’s Theorem

BIBLIOGRAFIA

[1] G. Thomas Mase, Ronald Smelser. Continuum Mechanics for Engineers. CRC Press 2010 [2] Julio Melián Pérez. Elasticidad y resistencia de materiales en los medios continuos. Universidad de las Palmas de Gran Canaria. 2010 [3] Xavier Oliver Olivella, Carlos Agelet de Saracibar Bosch . Mecánica de Medios Continuos paraIngenieros. Ed. Alfa Omega. 2002. [4] I. S. Sokolnikoff. Mathematical Theory of Elasticity. Ed. McGraw-Hill.1956.

The Continuum Concept
A body is really a collection of discrete atoms stacked on one another in a particular repetitive lattice. On an even smaller scale, the atoms consist of a core of protons and neutrons around which electrons orbit. Thus, matter is not continuous. At the same time,the physical space in which we live is truly a continuum, for mathematics teaches us that between any two points in space we can always find another point, regardless of how close together we choose the original pair. Clearly then, although we may speak of a material body as “occupying” a region of physical space, it is evident that the body does not totally “fill” the space it occupies.Material Body

CRISTALINOS

AMORFOS

The continuum model for material bodies is important to engineers for two very good reasons. On the scale by which we consider bodies of steel, aluminum, concrete, etc., the characteristic dimensions are extremely large compared to molecular distances so that the continuum model provides a very useful and reliable representation. Additionally, our knowledge...