Haupt Peter. Continuum Mechanics and Theory of Materials

Springer, 2000. — 595 p.This treatise is an attempt to portray the ideas, the general principles and also some concrete procedures of the theory of materials. This exposition is adapted from phenomenological continuum mechanics; the fundamental terms of continuum mechanics required here are therefore quoted in the appropriate form as well. The entire presentation refers exclusively to the classical continuum of material points; non-classical continua such as Cosserat continua, oriented
media, higher-gradient materials or non-local theories are not taken into consideration. Anyone practising continuum mechanics, given a set of experimental data, should be suitably equipped for devising a constitutive model to represent the phenomena ascertained in a consistent manner and thus render such a model serviceable for practical applications in connection with a reliable prediction of the thermo mechanical behaviour of material structures and systems.Kinematics
Material Bodies
Material and Spatial Representation
Deformation Gradient
Strain Tensors
Convective Coordinates
Velocity Gradient
Strain Rate Tensors
Strain Rates in Convective Coordinates
Geometric Linearisation
Incompatible Configurations
Balance Relations of Mechanics
Preliminary Remarks
Mass
Linear Momentum and Rotational Momentum
Conclusions from the Balance Equations of Mechanics
Balance Relations of Thermodynamics
Preliminary Remarks
Energy
Temperature and Entropy
Initial and Boundary Conditions
Balance Relations for Open Systems
Summary: Basic Relations of Thermomechanics
Objectivity
Frames of Reference
Affine Spaces
Change of Frame: Passive Interpretation
Change of Frame: Active Interpretation
Objective Quantities
Observer-Invariant Relations
Classical Theories of Continuum MechanicsElastic Fluid
Linear-Viscous Fluid
Linear-Elastic Solid
Linear-Viscoelastic Solid
Perfectly Plastic Solid
Plasticity with Hardening
Visco plasticity with Elastic Range
Remarks on the Classical Theories
Experimental Observation and Mathematical Modelling
General Aspects
Information from Experiments
Four Categories of Material Behaviour
Four Theories of Material Behaviour
Contribution of the Classical Theories
General Theory of Mechanical Material Behaviour
General Principles
Constitutive Equations
Properties of Material Symmetry
Kinematic Conditions of Internal Constraint
Formulation of Material Models
Dual Variables
Tensor-Valued Evolution Equations
Elasticity
Elasticity and Hyperelasticity
Isotropic Elastic Bodies
Anisotropic Hyperelastic Solids
10 Viscoelasticity
Representation by Means of Functionals
Representation by Means of Internal Variables
Plasticity
Rate-Independent Functionals
Representation by Means of Internal Variables
Elastoplasticity
Viscoplasticity
Preliminary Remarks
Visco plasticity with Elastic Domain
Plasticity as a Limit Case of Viscoplasticity
A Concept for General Visco plasticity
Constitutive Models in Thermomechanics
Thermomechanical Consistency
Thermoelasticity
Thermoviscoelasticity
Thermoviscoplasticity with Elastic Domain
General Thermoviscoplasticity
Anisotropic Material Properties