6.2.2 Stresses and Material Laws -- 6.2.3 Coordinate Transformations and Principal States -- 6.3 Isotropy, Linearity, and Orthotropy -- 6.3.1 Isotropy and Linear Elasticity -- 6.3.2 Orthotropy -- 6.3.3 Plane Stress and Strain -- 6.4 Nonlinear Material Behaviour -- 6.4.1 Tangential Stiffness -- 6.4.2 Principal Stress Space and Isotropic Strength -- 6.4.3 Strength of Concrete -- 6.4.4 Nonlinear Material Classification -- 6.5 Elasto-Plasticity -- 6.5.1 A Framework for Multi-Axial Elasto-Plasticity -- 6.5.2 Pressure-Dependent Yield Functions -- 6.6 Damage -- 6.7 Damaged Elasto-Plasticity -- 6.8 The Microplane Model -- 6.9 General Requirements for Material Laws -- 7 Crack Modelling and Regularisation -- 7.1 Basic Concepts of Crack Modelling -- 7.2 Mesh Dependency -- 7.3 Regularisation -- 7.4 Multi-Axial Smeared Crack Model -- 7.5 Gradient Methods -- 7.5.1 Gradient Damage -- 7.5.2 Phase Field -- 7.5.3 Assessment of Gradient Methods -- 7.6 Overview of Discrete Crack Modelling -- 7.7 The Strong Discontinuity Approach -- 7.7.1 Kinematics -- 7.7.2 Equilibrium and Material Behaviour -- 7.7.3 Coupling -- 8 Plates -- 8.1 Lower Bound Limit State Analysis -- 8.1.1 General Approach -- 8.1.2 Reinforced Concrete Resistance -- 8.1.3 Reinforcement Design -- 8.2 Cracked Concrete Modelling -- 8.3 Reinforcement and Bond -- 8.4 Integrated Reinforcement -- 8.5 Embedded Reinforcement with a Flexible Bond -- 9 Slabs -- 9.1 Classification -- 9.2 Cross-Sectional Behaviour -- 9.2.1 Kinematics -- 9.2.2 Internal Forces -- 9.3 Equilibrium of Slabs -- 9.3.1 Strong Equilibrium -- 9.3.2 Weak Equilibrium -- 9.3.3 Decoupling -- 9.4 Reinforced Concrete Cross-Sections -- 9.5 Slab Elements -- 9.5.1 Area Coordinates -- 9.5.2 Triangular Kirchhoff Slab Element -- 9.6 System Building and Solution Methods -- 9.7 Lower Bound Limit State Analysis -- 9.7.1 Design for Bending. |