Mechanics of Strain Gradient Materials

Preface
Contents
1 The Experimental Evidence for Higher Gradient Theories
	The Need for Higher Gradient Continuum Theories
	Theoretical Background
		Some Constitutive Equations for Higher Gradient Fluids
		Some Constitutive Equations for Higher Gradient Solids
	The Experimental Facts
		Data and Results for Second Gradient Fluids
		Data and Results for Second Gradient Solids
	Summary
	References
2 Balance Laws for Gradient Materials
	Tensor Notations
	Kinematics
	Dynamics
	Balance Laws for Gradient Materials
	References
3 Strain Gradient Elasticity From Capillarity to the Mechanics  of Nano-objects
	Capillarity in Elastic Strain Gradient Fluids
		Korteweg's Equation and First Strain Gradient Model
		Application of Second Strain Gradient Theory
	Second Strain Gradient Elasticity of Nano-objects
		Balance Equations and Boundary Conditions
		Constitutive Equations in Isotropic Linear Elasticity
		Surface Energy Effects in Third Gradient Elasticity
		Surface Elasticity Effect
		Apparent Tensile Elastic Behavior of Second Strain Gradient Nano-Films
	Dispersion of Waves in Strain Gradient Media
	Stress Gradient Elasticity
		Construction of an Elastic Stress Gradient Material Theory
		Method of Virtual Power for the Stress Gradient Medium
		Comparison with Mindlin's Strain Gradient Model
		Relation to Germain's General Micromorphic Theory
		Simple Tension in Stress Gradient Elasticity
	Conclusions
	References
4 Microscopic Interpretation of Strain-Gradient and Generalized Continuum Models
	Introduction: The Energetic Point of View
		Definitions
		Well-Posedness and Approximation
		Equilibrium Equations
		Boundary Conditions
	The Need for Microscopic Models
	The Homogenization Framework
		Mathematical Tools: Γ-convergence
		Mathematical Tools: Double-Scale Convergence
	A General Result for Structures Based on a Periodic Graph
		The Discrete Problem
		The Homogenization Result for Structures Based on Periodic Graphs
	Examples
		Regular Triangle Lattice
		Square Grid
		Square Grid Without Any Constraint
		Honeycomb Structure
		Couple-Stress Structure
		Pantographic Lattice
		Structure Leading to a Cosserat 2D Continuum
		Cosserat and Second-Gradient Effect Together
		Other Examples
	References
5 Strain Gradient Plasticity: Theory  and Implementation
	Introduction
		Notation
	Experimental Motivation
	Kinematics
		Basics of Linearized Kinematics
		Nye's Dislocation Density Tensor
		The Kinematics of the Torsion of Thin Wires
	Conventional Crystal Plasticity
		Principle of Virtual Work
		Constitutive Relations
	Micromechanical Motivations for the Introduction of Higher-Order Stresses
	Strain Gradient Crystal Plasticity
		Constitutive Relations
		On the Higher-Order Boundary Conditions
		Size-Effects Describable by Strain Gradient Crystal Plasticity
	Phenomenological Strain Gradient Plasticity
		Distortion Gradient Plasticity
		Strain Gradient Plasticity
	References
6 Finite Gradient Elasticity and Plasticity
	Introduction
	Second Gradient Elasticity
	Finite Elastoplasticity
	References
Index