Xiv Contents 8.2.1 Rubber and cord properties 446 8.2.2 Unidirectional composites 447 8.2.3 Laminated composites 449 8.2.4 Cord loads in tires 453 8.3 Coated fabrics 456 8.4 Nonlinear elastic behavior-incremental analysis 459 8.4.1 Geometry of wavy fibers 460 8.4.2 Axial tensile behavior 462 8.4.2.1 Iso-phase model 462 8.4.2.2 Random-phase model 465 8.4.2.3 Nonlinear tensile stress-strain behavior 467 8.4.3 Transverse tensile behavior 471 8.4.3.1 Iso-phase model 471 8.4.3.2 Random-phase model 472 9 Nonlinear elastic finite deformation of flexible composites 474 9.1 Introduction 474 9.2 Background 478 9.2.1 Tensor notation 478 9.2.2 Lagrangian and Eulerian descriptions 480 9.3 Constitutive relations based on the Lagrangian description 485 9.3.1 Finite deformation of a composite lamina 485 9.3.2 Constitutive equations for a composite lamina 487 9.3.2.1 Strain-energy function 487 9.3.2.2 General constitutive equations for a unidirectional lamina 488 9.3.2.3 Pure homogeneous deformation 490 9.3.2.4 Simple shear 492 9.3.2.5 Simple shear superposed on simple extension 495 9.3.3 Constitutive equations of flexible composite laminates 499 9.3.3.1 Constitutive equations 499 9.3.3.2 Homogeneous deformation 500 9.3.3.3 Simple extension of a symmetric composite laminate 502 9.3.4 Determination of elastic constants 505 9.3.4.1 Tensile properties 505 9.3.4.2 Shear properties 506xiv Contents 8.2.1 Rubber and cord properties 446 8.2.2 Unidirectional composites 447 8.2.3 Laminated composites 449 8.2.4 Cord loads in tires 453 8.3 Coated fabrics 456 8.4 Nonlinear elastic behavior - incremental analysis 459 8.4.1 Geometry of wavy fibers 460 8.4.2 Axial tensile behavior 462 8.4.2.1 Iso-phase model 462 8.4.2.2 Random-phase model 465 8.4.2.3 Nonlinear tensile stress-strain behavior 467 8.4.3 Transverse tensile behavior 471 8.4.3.1 Iso-phase model 471 8.4.3.2 Random-phase model 472 9 Nonlinear elastic finite deformation of flexible composites 474 9.1 Introduction 474 9.2 Background 478 9.2.1 Tensor notation 478 9.2.2 Lagrangian and Eulerian descriptions 480 9.3 Constitutive relations based on the Lagrangian description 485 9.3.1 Finite deformation of a composite lamina 485 9.3.2 Constitutive equations for a composite lamina 487 9.3.2.1 Strain-energy function 487 9.3.2.2 General constitutive equations for a unidirectional lamina 488 9.3.2.3 Pure homogeneous deformation 490 9.3.2.4 Simple shear 492 9.3.2.5 Simple shear superposed on simple extension 495 9.3.3 Constitutive equations of flexible composite laminates 499 9.3.3.1 Constitutive equations 499 9.3.3.2 Homogeneous deformation 500 9.3.3.3 Simple extension of a symmetric composite laminate 502 9.3.4 Determination of elastic constants 505 9.3.4.1 Tensile properties 505 9.3.4.2 Shear properties 506