Showing papers on "Orthotropic material published in 2003"

Mechanics of composite structures

Abstract: Preface List of symbols 1. Introduction 2. Displacements, strains, stresses 3. Laminated composites 4. Thin plates 5. Sandwich plates 6. Beams 7. Beams with shear deformation 8. Shells 9. Finite element analysis 10. Failure criteria 11. Micromechanics Appendix A. Cross-sectional properties of thin-walled composite beams Appendix B. Buckling loads and natural frequencies of orthotropic beams with shear deformation Appendix C. Typical material properties Index.

Advanced Mechanics of Materials

Abstract: Each chapter starts with a Summary and ends with References and Problems. Preface 1. Introduction Reference 2. Stress and Equilibrium Equations 2.1: Concept of Stress 2.2: Stress Components and Equilibrium Equations 2.2.1: Stress Components in Cartesian Coordinates--Matrix Representation 2.2.2: Symmetry of Shear Stresses 2.2.3: Stresses Acting on an Inclined Plane 2.2.4: Normal and Tangential Stresses--Stress Boundary Conditions 2.2.5: Transformation of Stress Components--Stress as a Tensor 2.2.7: Equilibrium Equations in Cartesian Coordinates 2.2.8: Equilibrium Equations in Polar Coordinates 2.2.9: Applicability of Equilibrium Equations 2.3: Principal Stresses and Invariants 2.3.1: Characteristic Equation 2.3.2: Principal Stresses and Principal Directions 2.3.3: Plane Stress--Principal Stresses and Principal Directions 2.3.4: Plane Stress--Mohr's Circle 2.3.5: Octahedral Stresses 2.3.6: Mean and Deviatoric Stresses 2.4: Three-dimensional Mohr's Circles 2.5: Stress Analysis and Symbolic Manipulation 3. Displacement and Strain 3.1: Introduction 3.2: Strain-Displacement Equations 3.3: Compatibility 3.4: Specification of the State of Strain at a Point 3.4.1: Strain Gages 3.5: Rotation 3.6: Principal Strains 3.7: Strain Invariants 3.8: Volume Changes and Dilatation 3.9: Strain Deviator 3.10: Strain-Displacement Equations in Polar Coordinates 4. Relationships Between Stress and Strain 4.1: Introduction 4.2: Isotropic Materials--A Physical Approach 4.2.1: Coincidence of Principal Stress and Principal Strain Axes 4.2.2: Relationship between G and E 4.2.3: Bulk Modulus 4.3: Two Dimensional Stress-Strain Laws--Plane Stress and Plane Strain 4.3.1: Plane Stress 4.3.2: Plane Strain 4.4: Restrictions on Elastic Constants for Isotropic Materials 4.5: Anisotropic Materials 4.6: Material Symmetries 4.7: Materials with a Single Plane of Elastic Symmetry 4.8: Orthotropic Materials 4.8.1: Engineering Material Constants for Orthotropic Materials 4.8.2: Orthotropic Materials under Conditions of Plane Stress 4.8.3: Stress-Strain Relations in Coordinates Other than the Principal Material Coordinates 4.9: Transversely Isotropic Materials 4.10: Isotropic Materials--A Mathematical Approach 4.11: Stress-Strain Relations for Viscoelastic Materials 4.12: Material Behavior beyond the Elastic Limit 4.12.1: Additional Experimental Observations 4.13: Criteria for Yielding 4.13.1: Maximum Shear Theory 4.13.2: Distortion Energy Theory 4.13.3: Comparison of the Two Theories 4.14: Stress-Strain Relations for Elastic-Perfectly Plastic Materials 4.15: Stress-Strain Relations when the Temperature Field is Nonuniform 4.16: Stress-Strain Relations for Piezoelectric Materials 5. Energy Concepts 5.1: Fundamental Concepts and Definitions 5.2: Work 5.2.1: Work Done by Stresses Acting on an Infinitesimal Element 5.3: First Law of Thermodynamics 5.4: Second Law of Thermodynamics 5.5: Some Simple Applications Involving the First Law 5.5.1: Maxwell's Reciprocity Theorem 5.6: Strain Energy 5.6.1: Complementary Strain Energy 5.6.2: Strain Energy in Beams 5.7: Castigliano's Theorem 5.8: Principle of Virtual Work 5.8.1: Principle of Virtual Work for Particles and Rigid Bodies 5.8.2: Principle of Virtual Work for Deformable Bodies 5.9: Theorem of Minimum Total Potential Energy 5.10: Applications of the Theorem of Minimum Total Potential Energy 5.11: Rayleigh-Ritz Method 5.12: Principle of Minimum Complementary Energy 5.13: Betti-Rayleigh Reciprocal Theorem 5.14: General Stress-Strain Relationships for Elastic Materials 6. Numerical Methods I 6.1: Method of Finite Differences 6.1.1: Application to Ordinary Differential Equations 6.1.2: Application to Partial Differential Equations 6.2.: Method of Iteration 6.3.: Method of Collocation 7. Numerical Methods II: Finite Elements 7.1: Introduction 7.2: Two-Dimensional Frames 7.3: Overall Approach 7.4: Member Force-Displacement Relationships 7.5: Assembling the Pieces 7.6: Solving the Problem 7.7: An Example 7.8: Notes Concerning the Structure Stiffness Matrix 7.10: Finite Element Analysis 7.11: Constant Strain Triangle 7.12: Element Assembly 7.13: Notes on Using Finite Element Programs 7.13.1: Interelement Compatibility 7.13.2: Inherent Overstiffness in a Finite Element 7.13.3: Bending and the Constant Strain Triangle 7.14: Closure 8. Beams 8.1: Bending of Continuous Beams 8.1.1: Introduction 8.1.2: Method of Initial Parameters 8.1.3: Application of Castigliano's Theorem 8.2: Unsymmetric Bending of Straight Beams 8.3: Curved Beams 8.3.1: Out-of-Plane Loaded Beams and Rings 8.3.2: A Transversely Loaded Circular Ring Supported by Three or More Supports (Biezeno's Theorem) 8.3.3: In-Plane Loaded Curved Beams (Arches) and Rings 8.3.4: Bending, Stretching, and Twisting of Springs 8.4: Beams on Elastic Foundations 8.4.1: Equilibrium Equation for a Straight Beam 8.4.2: Infinite Beams 8.4.3: Finite Beams 8.4.4: Stresses in Storage Tanks 8.5: Influence Functions (Green's Functions) for Beams 8.5.1: Straight Beams 8.5.2: Straight Beams on Elastic Foundations 8.6: Thermal Effects 8.7: Composite Beams 8.7.1: Stresses, Bending Moments, and Bending Stiffness of a Laminated Beam 8.7.2: Differential Equation for Deflection of a Laminated Beam 8.8: Limit Analysis 8.9: Fourier Series and Applications 8.10: Approximate Methods in the Analysis of Beams 8.10.1: Finite Differences--Examples 8.10.2: Rayleigh-Ritz Method--Examples 8.11: Piezoelectric Beams 8.11.1: Piezoelectric Bimorph 8.11.2: Piezoelectric Multimorph 8.11.3: Castigliano's Theorem for Piezoelectric Beams 8.11.4: Thin Curved Piezoelectric Beams 8.11.5: Castigliano's Theorem for Thin Curved Piezoelectric Beams 9. Elementary Problems in Two- and Three-Dimensional Solid Mechanics 9.1: Problem Formulation--Boundary Conditions 9.2: Compatibility of Elastic Stress Components 9.3: Thick-Walled Cylinders and Circular Disks 9.3.1: Equilibrium Equation and Strains 9.3.2: Elastic, Homogeneous Disks and Cylinders 9.3.3: Thermal Effects 9.3.4: Plastic Cylinder 9.3.5: Composite Disks and Cylinders 9.3.6: Rotating Disks of Variable Thickness 9.4: Airy's Stress Function 9.5: Torsion 9.5.1: Circular Cross Section 9.5.2: Noncircular Prisms--Saint-Venant's Theory 9.5.3: Membrane Analogy 9.5.4: Rectangular and Related Cross Sections 9.5.5: Torsion of Hollow, Single-Cell and Multiple-Cell Members 9.5.6: Pure Plastic Torsion 9.6: Application of Numerical Methods to Solution of Two-Dimensional Elastic Problems Elastic Problems 10. Plates 10.1: Introduction 10.2: Axisymmetric Bending of Circular Plates 10.2.1: General Expressions 10.2.2: Particular Solutions for Selected Types of Axisymmetric Loads 10.2.3: Solid Plate: Boundary Conditions, Examples 10.2.4: Solid Plate: Influence Functions (Green's Functions) 10.2.5: Solid Plate with Additional Support 10.2.6.: Annular Plate: Boundary Conditions and Examples 10.2.7: Annular Plate: Influence Functions (Green's Functions) 10.3: Bending of Rectangular Plates 10.3.1: Boundary Conditions 10.3.2: Bending of a Simply Supported Rectangular Plate 10.4: Plates on Elastic Foundation 10.5: Strain Energy of an Elastic Plate 10.6: Membranes 10.7: Composite Plates 10.7.1: Laminated Plates with Isotropic Layers 10.7.2: Laminated Plates with Orthotropic Layers 10.8: Approximate Methods in the Analysis of Plates and Membranes 10.8.1: Application of Finite Differences 10.8.2: Examples of Application of the Rayleigh-Ritz Method 11. Buckling and Vibration 11.1: Buckling and Vibration of Beams and Columns 1.1: Equation of Motion and Its Solution 11.1.2: Frequencies and Critical Loads for Various Boundary Conditions 11.1.3: Applications of Rayleigh-Ritz Method 11.2: Buckling and Vibration of Rings, Arches, and Thin-Walled Tubes 11.2.1: Equations of Motion and Their Solution 11.3: Buckling and Vibration of Thin Rectangular Plates 12. Introduction to Fracture Mechanics 12.1: Introductory Concepts 12.2: Linear Cracks in Two-Dimensional Elastic Solids--Williams' Solution, Stress Singularity 12.3: Stress Intensity Factor 12.4: Crack Driving Force as an Energy Rate 12.5: Relation Between G and the Stress Intensity Factors 12.6: Some Simple Cases of Calculation of Stress Intensity Factors 12.7: The J-Integral Appendix A. Matrices Appendix B. Coordinate Transformations

Handbook of elasticity solutions

Abstract: 1: Basic Equations of Elasticity. 1.1. Cartesian Coordinates. 1.2. Cylindrical Coordinates. 1.3. Spherical Coordinates. 1.4. Hooke's Law for Anisotropic Materials. 2: Point Forces and Systems of Point Forces in Three-Dimensional Space and Half-Space. 2.1. Point Force in an Infinite Isotropic Solid. 2.2. Systems of Forces Distributed in a Small Volume of an Infinite Isotropic Solid. 2.3. Dynamic Problems of a Suddenly Introduced Point Forces Couples and Dipoles in an Infinite Isotropic Solid. 2.4. Point Force in the Isotropic Half-Space (Mindlin's Problem). 2.5. Point Force Applied at the Boundary of the Isotropic Half-Space. 2.6. Point Force of an Infinite Transverse Isotropic Solid. 2.7. Point Force Applied at the Boundary of the Transversely Isotropic Half-Space. 2.8. Two Joined Isotropic Half-Spaces with Different Moduli: Solution for a Point Force. 3: Selected Two-Dimensional Problems. 3.1. Introductory Material. 3.2. Infinite 2-D Solid. Isotropic and Orthotropic Materials. 3.3. 2-D Isotropic Half-Plane. 3.4. Stress Concentrations near Holes and Inclusions. 3.5. Equilibrium of an Elastic Wedge. 3.6. Circular Ring Loaded by External and Internal Pressures. 4: Three-Dimensional Crack Problems for the Isotropic or Transversely Isotropic Infinite Solid. 4.1. Circular (Penny-Shaped) Crack. 4.2. Half-Plane Crack. 4.3. External Circular Crack. 4.4. Elliptical Crack. 5: A Crack in an Infinite Isotropic Two-Dimensional Solid. 5.1. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Pointof the Crack. 5.2. Uniform Loading at Crack Faces. 5.3. Crack Tip Fields. 5.4. Far Field Asymptotics. 6: A Crack in an Infinite Anisotropic Two-Dimensional Solid. 6.1. Notations and General Representations for a 2-D Anisotropic Elastic Solid. 6.2. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Point of the Crack. 6.3. Uniform Loading at Crack Faces. 6.4. Crack Tip Fields. 6.5. Far Field Asymptotics. 6.6. Crack Compliance Tensor. 6.7. Appendix. 7: Thermoelasticity. 7.1. Basic Equations. 7.2. Stationary 3-D Problems. 7.3. Non-Stationary 3-D Problems. 7.4. Stationary 2-D Problems. 7.5. Non-Stationary 2-D Problems. 7.6. Thermal Stresses in Heated Infinite Solid Containing an Inhomogeneity or a Cavity. 8: Contact Problems. 8.1. 2-D Problems for a Rigid Punch on the Isotropic and Anisotropic Elastic Half-Plane. 8.2. 3-D Problems for a Rigid Punch on the Isotropic and Transversely Isotropic Elastic Half-Space. 8.3. Contact of Two Elastic Bodies (Hertz' Problem). 9: Eshelby's Problem and Related Results. 9.1. Inclusion Problem. 9.2. Ellipsoidal Inhomogeneity. 9.3. Eshelby's Tensor for Various Ellipsoidal Shapes. 9.4. Alternative Form of Solution for Ellipsoidal Inhomogeneity. 9.5. Expressions for Tensors P, Q, A and GBPIiGBP. 9.6. Quantities Relevant for Calculation of the Effective Elastic Properties. 10: Elastic Space Containing a Rigid Ellipsoidal Inclusion Subjected to Translation and Rotation. 10.1.

Nonlinear Elasticity, Anisotropy, Material Stability and Residual Stresses in Soft Tissue

Abstract: In this chapter the basic equations of nonlinear elasticity theory needed for the analysis of the elastic behaviour of soft tissues are summarized. Particular attention is paid to characterizing the material symmetries associated with the anisotropy that arises in soft tissue from its fibrous constituents (collagens) that endow the material with preferred directions. The importance of the issue of convexity in the construction of constitutive laws (strain-energy functions) for soft tissues is emphasized with reference to material stability. The problem of extension and inflation of a thick-walled circular cylindrical tube is used throughout as an example that is closely associated with arterial wall mechanics. This is discussed first for isotropic materials, then for cylindrically orthotropic materials. Since residual stresses have a very important role in, in particular, arterial wall mechanics these are examined in some detail. Specifically, for the tube extension/inflation problem the residual stresses arising from the assumption that the circumferential stress is uniform under typical physiological conditions are calculated for a representative constitutive law and compared with those calculated using the ‘opening angle’ method.

On the Sensitivity of Wall Stresses in Diseased Arteries to Variable Material Properties

Abstract: Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.

Structural Analysis of Polymeric Composite Materials

Abstract: "Structural Analysis of Polymeric Composite Materials" studies the mechanics of composite materials and structures and combines classical lamination theory with macromechanic failure principles for prediction and optimization of composite structural performance. This reference addresses topics such as high-strength fibers, commercially-available compounds, and the behavior of anisotropic, orthotropic, and transversely isotropic materials and structures subjected to complex loading. It provides a wide variety of numerical analyses and examples throughout each chapter and details the use of easily-accessible computer programs for solutions to problems presented in the text.

Free and Forced Vibrations of Thick Rectangular Plates using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Petrov-Galerkin (MLPG) Method

Abstract: We use a meshless local Petrov-Galerkin Liu (2001) have used the MLPG method to find natu- (MLPG) method to analyze three-dimensional infinitesi- ral frequencies and forced plane ,strain deformations.of mal elastodynamic deformations of a homogeneous rect- a cantilever beam. Batra and Chmg .(2002~ have de!m- angular plate subjected to different edge conditions. We eated the time evolution of the stress-mtenslty factor m a employ a higher-order plate theory in which both trans- double edge-cracked plate. verse shear and transverse normal deformations are con- Atluri and Shen (2002a,b) have compared the perfor- sidered. Natural frequencies and the transient response manceof six' variants of the MLPG method for solving to external loads have been computed for isotropic Poisson's equation. Qian et al. (2002) used two of these and orthotropic plates. Computed results are found to formulations to study elastostatic deformations of a thick agree with those obtained from the analysis of the 3- rectangular plate with a compatible higher-order shear dimensional problem either analytically or by the finite and normal deformable plate theory (HOSNDPT) pro- element method.

A multi-surface plasticity model for clear wood and its application to the finite element analysis of structural details

Abstract: Recent biaxial experiments on spruce wood show that consideration of an elliptic failure surface according to Tsai and Wu, and of an elastic model for stress states within this envelope, gives an insufficient description of the mechanical behavior. As compression perpendicular to grain occurs, a nonlinear stress path results from a proportional biaxial strain path. Moreover, a phenomenological single-surface model does not permit easy identification of failure modes and thus renders the description of different post-failure mechanisms very difficult. Investigation of characteristic samples for various biaxial loading conditions enables the identification of four basic mechanisms covering the behavior of wood under plane stress conditions. The experimentally observed mechanical behavior will be described by means of a multi-surface plasticity model. It consists of four surfaces representing four basic failure modes. The first is a modified tension cut-off for the description of fiber rupture. The second is a mixed mode radial tension-shear model by Weihe applied to the perpendicular to grain direction. The third is an extension of the authors' prior model for perpendicular to grain compression, and the fourth surface covers the compressive failure parallel to grain. The model represents the orthotropic multi-surface elasto-plastic material clear wood. The aim of this paper is to present and discuss selected experimental data from biaxial tests with respect to distinct failure modes, and to develop an orthotropic plasticity model for its mathematical description. Since available experimental data cover only plane stress in the LR-plane,, both orthotropic failure and yield surfaces, respectively, are restricted to this case.

Asymptotical Mechanics of Thin-Walled Structures

Abstract: 1 Asymptotic Approximations.- 2 Regular Perturbations of Parameters.- 3 Singular Perturbation Problems.- 4 Boundary Value Problems of Isotropic Cylindrical Shells.- 5 Boundary Value Problems - Orthotropic Shells.- 6 Composite Boundary Value Problems - Isotropic Shells.- 7 Composite Boundary Value Problems - Orthotropic Shells.- 8 Averaging.- 9 Continualization.- 10 Homogenization.- 11 Intermediate Asymptotics - Dynamical Edge Effect Method.- 12 Localization.- 13 Improvement of Perturbation Series.- 14 Matching of Limiting Asymptotic Expansions.- 15 Complex Variables in Nonlinear Dynamics.- 16 Other Asymptotical Approaches.- Afterword.- References.

On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole

Abstract: Scale factors (SFs) are widely used in engineering applications to describe the stress concentration factor (SCF) of a finite width isotropic plate with a circular hole and under uniaxial loading. In this paper, these SFs were also found to be valid in an isotropic plate with biaxial loading and an isotropic cylinder with uniaxial loading or internal pressure, if a suitable hole to structure dimension ratio was chosen. The study was further expanded to consider orthotropic plates and cylinders with a center hole and under uniaxial loading. The applicable range of the SFs was given based on the orthotropic material parameters. The influence of the structural dimension on the SCF was also studied. An empirical calculation method for the stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole was proposed and the results agreed well with the FEM simulations. This research work may provide structure engineers a simple and efficient way to estimate the hole effect on plate structures or pressure vessels made of isotropic or orthotropic materials.

Exact Solutions of Cross-Ply Laminates with Bonding Imperfections

Abstract: State-space approach is developed to analyze the bending and free vibration of a simply supported, cross-ply laminated rectangular plate featuring interlaminar bonding imperfections, for which a general linear spring layer model is adopted The analysis is directly based on the three-dimensional theory of orthotropic elasticity and is completely exact Numerical comparison is made, showing that although the plate theory developed in the literature behaves well for moderately thick perfect laminates it can become inaccurate when bonding imperfections are present The special problem of the laminate in cylindrical bending is also considered, and the validity of the assumption of cylindrical bending is investigated through numerical examples

An interaction integral method for analysis of cracks in orthotropic functionally graded materials

Abstract: This paper presents two new interaction integrals for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional orthotropic functionally graded materials of arbitrary geometry. The method involves the finite element discretization, where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as meshless method, boundary element method, and others. Three numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed interaction integrals. Comparisons have been made between the SIFs predicted by the proposed interaction integrals and available reference solutions in the literature, generated either analytically or by finite element method using various other fracture integrals or analyses. An excellent agreement is obtained between the results of the proposed interaction integrals and the reference solutions.

Shear buckling of sandwich, fiber composite and lattice columns, bearings, and helical springs: Paradox resolved

Abstract: As shown three decades ago, in situations where the initial stresses before buckling are not negligible compared to the elastic moduli, the geometrical dependence of the tangential moduli on the initial stresses must be taken into account in stability analysis, and the stability or bifurcation criteria have different forms for tangential moduli associated with different choices of the finite strain measure. So it has appeared paradoxical that, for sandwich columns, different but equally plausible assumptions yield different formulas, Engesser’s and Haringx’ formulas, even though the axial stress in the skins is negligible compared to the axial elastic modulus of the skins and the axial stress in the core is negligible compared to the shear modulus of the core. This apparent paradox is explained by variational energy analysis. It is shown that the shear stiffness of a sandwich column, provided by the core, generally depends on the axial force carried by the skins if that force is not negligible compared to the shear stiffness of the column (if the column is short). The Engesser-type, Haringx-type, and other possible formulas associated with different finite strain measures are all, in principle, equivalent, although a different shear stiffness of the core, depending linearly on the applied axial load, must be used for each. The Haringxtype formula, however, is most convenient because it represents the only case in which the shear modulus of the core can be considered to be independent of the axial force in the skins and to be equal to the shear modulus measured in simple shear tests (e.g., torsional test). Extensions of the analysis further show that Haringx’s formula is preferable for a highly orthotropic composite because a constant shear modulus of the soft matrix can be used for calculating the shear stiffness of the column, and further confirm that Haringx’s buckling formula with a constant shear stiffness is appropriate for helical springs and built-up columns (laced or battened). @DOI: 10.1115/1.1509486#

Singularity analysis of anisotropic multimaterial corners

Abstract: Singular stress states induced at the tip of linear elastic multimaterial corners are characterized in terms of the order of stress singularities and angular variation of stresses and displacements. Linear elastic materials of an arbitrary nature are considered, namely anisotropic, orthotropic, transversely isotropic, isotropic, etc. Thus, in terms of Stroh formalism of anisotropic elasticity, the scope of the present work includes mathematically non-degenerate and degenerate materials. Multimaterial corners composed of materials of different nature are typically present at any metal-composite, or composite-composite adhesive joint. Several works are available in the literature dealing with a singularity analysis of multimaterial corners but involving (in the vast majority) only materials of the same nature (e.g., either isotropic or orthotropic). Although many different corner configurations have been studied in literature, with almost any kind of boundary conditions, there is an obvious lack of a general procedure for the singularity characterization of multimaterial corners without any limitation in the nature of the materials. With the procedure developed here, and implemented in a computer code, multimaterial corners, with no limitation in the nature of the materials and any homogeneous orthogonal boundary conditions, could be analyzed. As a particular case, stress singularity orders in corners involving extraordinary degenerate materials are, to the authors’ knowledge, presented for the first time. The present work is based on an original idea by Ting (1997) in which an efficient procedure for a singularity analysis of anisotropic non-degenerate multimaterial corners is introduced by means of the use of a transfer matrix.

Frame-Invariant Polyconvex Strain-Energy Functions for Some Anisotropic Solids:

Abstract: We present a set of simple sufficient conditions for the polyconvexity and coercivity of strainenergy functions for transversely isotropic and orthotropic elastic solids. The formulation is based on appropriate function bases for the right stretch tensor in the polar decomposition of the deformation gradient and furnishes numerical analysts with a priori existence criteria for boundary-value problems.