Showing papers on "Orthotropic material published in 2013"

Finite Element Analysis of Composite Materials using Abaqus

Abstract: Mechanics of Orthotropic Materials Lamina Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Introduction to Finite Element Analysis Basic FEM Procedure General Finite Element Procedure Solid Modeling, Analysis, and Visualization Elasticity and Strength of Laminates Kinematic of Shells Finite Element Analysis of Laminates Failure Criteria Predefined Fields Buckling Eigenvalue Buckling Analysis Continuation Methods Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macromechanics of Viscoelastic Composites FEA of Viscoelastic Composites Continuum Damage Mechanics One-Dimensional Damage Mechanics Multidimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Discrete Damage Mechanics Overview Approximations Lamina Constitutive Equation Displacement Field Degraded Laminate Stiffness and CTE Degraded Lamina Stiffness Fracture Energy Solution Algorithm Delaminations Cohesive Zone Method Virtual Crack Closure Technique Appendix A: Tensor Algebra Appendix B: Second-Order Diagonal Damage Models Appendix C: Software Used Index Problems appear at the end of each chapter.

Finite Element Analysis of Composite Materials Using ANSYS

Abstract: Mechanics of Orthotropic Materials Material Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Suggested Problems References Introduction to Finite Element Analysis Basic FEM Procedure General FEM Procedure FE Analysis with CAE Systems Suggested Problems References Elasticity and Strength of Laminates Kinematics of Shells FE Analysis of Laminates Failure Criteria Suggested Problems References Buckling Bifurcation Methods Continuation Methods Suggested Problems References Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Suggested Problems References Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Suggested Problems References Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macro-Mechanics of Viscoelastic Composites FEA of Viscoelastic Composites Suggested Problems References Continuum Damage Mechanics One-Dimensional Damage Mechanics Multi-Dimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Suggested Problems References Discrete Damage Mechanics Theoretical Formulation Numerical Implementation Model Identification Laminate Damage References Bibliography Delaminations Two-Dimensional Delamination Delamination in Composite Plates Suggested Problems References Appendices ANSYS BMI3 References Index

Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements

Abstract: An accurate description of the mechanical response of α-titanium requires consideration of mechanical anisotropy. In this work we adapt a polycrystal self-consistent model embedded in finite elements to simulate deformation of textured α-titanium under quasi-static conditions at room temperature. Monotonic tensile and compressive macroscopic stress–strain curves, electron backscattered diffraction and neutron diffraction data are used to calibrate and validate the model. We show that the model captures with great accuracy the anisotropic strain hardening and texture evolution in the material. Comparisons between predictions and experimental data allow us to elucidate the role that the different plastic deformation mechanisms play in determining microstructure and texture evolution. The polycrystal model, embedded in an implicit finite element code, is then used to simulate geometrical changes in bending experiments of α-titanium bars. These predictions, together with results of a macroscopic orthotropic elasto-plastic model that accounts for evolving anisotropy, are compared with the experiments. Both models accurately capture the experimentally observed upward shift of the neutral axis as well as the rigidity of the material response along hard-to-deform crystallographic direction.

New convex yield functions for orthotropic metal plasticity

Abstract: Two new yield functions for orthotropic sheet metals are proposed. The first one, called Yld2011-18p, provides 18 parameters that may be calibrated to experimental data. The second one, called Yld2011-27p, is a straightforward extension and provides 27 parameters. Both yield functions are unconditionally convex. Their formulations are based on the established concept of multiple linear transformations of the stress deviator. Furthermore, they are able to account for planar as well as for three-dimensional stress states. The proposed yield functions are applied to describe complex plastic anisotropies of different alloys. The ability of accurately predicting earing in cup-drawing is demonstrated by means of a non-linear finite element analysis.

Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory

Abstract: Free vibration analysis of laminated conical shells is presented by using the numerical solution of governing differential equations of motion based on transverse shear deformation theory. Results are presented for isotropic, orthotropic, and laminated cases for conical shells. Free vibrations of circular cylindrical shells and annular plates are treated as special cases. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Numerical results in vibrations of laminated conical shells are presented for different geometric and material parameters.

XFEM fracture analysis of orthotropic functionally graded materials

Abstract: In the present study, the extended finite element method (XFEM) has been used for fracture analysis of orthotropic functionally graded materials. Orthotropic crack tip enrichments have been used to reproduce the singular stress field near a crack tip. Moreover, the incompatible interaction integral method has been employed to extract the stress intensity factor components. Accuracy and convergence of the proposed method have been evaluated by numerical examples and quality results have been obtained by far fewer DOFs. Also, crack propagation in isotropic and orthotropic FGMs in the presence of crack tip enrichments has been investigated and various propagation criteria have been compared, and verified, if available, by experimental and numerical data in the literature. Application of XFEM in combination of the maximum circumferential tensile stress criterion for investigation of crack propagation in orthotropic FGM problems is performed for the first time.

Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction:

Abstract: At any point in space the material properties of the myocardium are characterized as orthotropic, that is, there are three mutually orthogonal axes along which both electrical and mechanical parame ...

New Nonpolynomial Shear-Deformation Theories for Structural Behavior of Laminated-Composite and Sandwich Plates

Abstract: In the present study, new nonpolynomial shear-deformation theories are proposed and implemented for structural responses of laminated-composite and sandwich plates. The theories assume nonlinear distribution of transverse shear stresses, and also satisfy the traction-free boundary conditions at the top and bottom layers of the laminates. The governing differential equations are derived for a generalized shear-deformation theory by implementing the dynamic version of principle of virtual work and calculus of variations. A generalized closed-form solution methodology of the Navier type is implemented to ensure the validity and efficiency of the present theories for bending, buckling, and free-vibration responses of the laminated-composite and sandwich plates. It is observed that the proposed formulation in conjunction with the solution methodology is capable of handling all existing five-degree-of-freedom-based shear-deformation theories. The comparison of results also shows that the adequate choice of shea...

Thermo-mechanical XFEM crack propagation analysis of functionally graded materials

Abstract: A computational method based on the extended finite element method (XFEM) is implemented for fracture analysis of isotropic and orthotropic functionally graded materials (FGMs) under mechanical and steady state thermal loadings. The aim is set to include the thermal effects in loading, governing equations, and the interaction integral for inhomogeneous materials with a complementary study on available crack propagation criteria in orthotropic FGMs under thermal loading conditions. The isotropic and orthotropic crack tip enrichments are applied to reproduce the singular stress field near crack tips. Mixed-mode stress intensity factors are evaluated in isotropic and orthotropic FGMs by means of the interaction integral. In addition, the mesh dependency and number of elements around the crack tip are substantially reduced in comparison with the standard finite element method with the same level of accuracy. Both mode-I and mixed-mode fracture problems with various types of mechanical and thermo-mechanical functionally graded material properties are simulated and discussed to assess the accuracy and efficiency of the proposed numerical method. Good agreements are observed between the predicted results and the reference results available in the literature with far lower degrees of freedom.

Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations

Abstract: In this study, the torsional vibration and stability problems of functionally graded (FG) orthotropic cylindrical shells in the elastic medium, using the Galerkin method was investigated Pasternak model is used to describe the reaction of the elastic medium on the cylindrical shell Mixed boundary conditions are considered The material properties and density of the orthotropic cylindrical shell are assumed to vary exponentially in the thickness direction The basic equations of the FG orthotropic cylindrical shell under the torsional load resting on the Pasternak-type elastic foundation are derived The expressions for the critical torsional load and dimensionless torsional frequency parameter of the FG orthotropic cylindrical shell resting on elastic foundations are obtained The effects of variations of shell parameters, the exponential factor characterizing the degree of material gradient, orthotropy, foundation stiffness and shear subgrade modulus of the foundation on the critical torsional load and dimensionless torsional frequency parameter are examined

An anisotropic elastic-viscoplastic damage model for bone tissue

Abstract: A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain \({D(\kappa)}\) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems With Interfacial Resistance

Abstract: In this paper, a new and more general solution for thermal spreading resistance in compound, orthotropic systems with interfacial resistance is considered. This new solution, which extends beyond previously published results, is obtained for a finite rectangular heat source of uniform strength arbitrarily located on a rectangular substrate. By means of superposition, one can obtain the temperature field in the source plane for multiple heat sources as well as the source mean and centroid temperatures. By means of orthotropic transformations, systems containing orthotropic materials can be easily modeled. Extension of the present solutions using a computationally efficient influence coefficient method is also given, such that the effects of large numbers of heat sources are superimposed. The application of these closed-form expressions for the temperature rise is demonstrated with calculations for Gallium nitride (GaN) high electron mobility transistors (HEMTs). These solutions are shown to be more flexible than previously reported analytical expressions and much more computationally efficient than 3-D finite element analysis, especially for a large number of discrete heat sources associated with multifinger GaN HEMTs.

Non-linear flexural and dynamic response of CNT reinforced laminated composite plates

Abstract: The paper presents the non-linear flexural and dynamic response of CNT reinforced laminated composite plates using fast converging finite double Chebyshev polynomials. Halpin–Tsai model is used for evaluating the properties of matrix by dispersing CNT in it. Thereafter, CNT reinforced polymer matrix is treated as new matrix and then reinforced with E-Glass fiber in an orthotropic manner. Mathematical formulation of the laminated plate is based on first order shear deformation theory and von-Karman non-linear kinematics. Houbolt time marching scheme and quadratic extrapolation techniques are used for temporal discretization and linearization, respectively. The effects of CNT % and its aspect ratio on the non-linear flexural and dynamic response of the laminated composite plates are presented.

Analytical solution for a functionally graded beam with arbitrary graded material properties

Abstract: The plane stress problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams.

Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method

Abstract: In this article, transverse nonlinear vibration of orthotropic double-layered graphene sheets embedded in an elastic medium (spring and shear constants of the Winkler and Pasternak models) under thermal gradient is studied using nonlocal elasticity orthotropic plate theory. The equations of motion are derived based on application of Hamilton’s principles. These are coupled, two-dimensional and time-dependent equations, which cannot be solved analytically due to their nonlinear terms. Hence, differential quadrature method is employed to solve the governing differential equations for the two boundary conditions of simply and clamped support in all four sides. The plots for the ratio of nonlinear to linear frequencies versus maximum transverse amplitude for armchair and zigzag graphene sheet structures are presented to investigate the effects of nonlocal parameters, Winkler and Pasternak effects, temperature, and various aspect ratios. The study also indicates that the nonlinear effect represented by nonlinear frequency ratio is considerable at lower Winkler and Pasternak constants, length aspect ratio and thickness aspect ratio while it might be neglected for higher values of these parameters. Regarding the influence of temperature difference on support type, with increased temperature difference, nonlinear frequency ratio increases when the graphene sheet is simply supported, but for clamped one, no specific change in nonlinear frequency ratio is observed.

Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

Abstract: In this article, the nonlinear buckling characteristics of multi-layered graphene sheets are investigated. The graphene sheet is modeled as an orthotropic nanoplate with size-dependent material properties. The graphene film is subjected by non-uniformly distributed in-plane load through its thickness. To include the small scale and the geometrical nonlinearity effects, the governing differential equations are derived based on the nonlocal elasticity theory in conjunction with the von Karman geometrical model. Explicit expressions for the postbuckling loads of single- and double-layered graphene sheets with simply supported edges under biaxial compression are obtained. For numerical results, six types of armchair and zigzag graphene sheets with different aspect ratio are considered. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Excellent agreement between the obtained and available results is observed. Finally, the effects of nonlocal parameter, buckling mode number, compression ratio and non-uniform parameter on the postbuckling behavior of multi-layered graphene sheets are studied.

Identification of Material Parameters of PVC Foams using Digital Image Correlation and the Virtual Fields Method

Abstract: This paper presents an effective methodology to characterize all the constitutive (elastic) parameters of an orthotropic polymeric foam material (Divinycell H100) in one single test using Digital Image Correlation (DIC) in combination with the Virtual Fields Method (VFM). A modified Arcan fixture is used to induce various loading conditions ranging from pure shear or axial loading in tension or compression to bidirectional loading. A numerical optimization study was performed with different loading angles of the Arcan test fixture and off-axis angles of the principal material axes. The objective is to identify the configuration that gives the minimum sensitivity to noise and missing data on the specimen edges, which are the two major issues when identifying the stiffness components from actual DIC measurements. Two optimized Arcan test configurations were chosen. The experimental results obtained for these two optimized test configurations show a significant improvement of the measurement accuracy compared with a pure shear load configuration. The larger sensitivity of the pure shear test to missing data as opposed to the tensile test is also evident from the experimental data and confirms the analysis from the optimization study. The recovery of missing data along the specimen edges is a promising way to further improve the identification results.

Surface waves in orthotropic incompressible materials

Abstract: The secular equation for surface acoustic waves propagating on an orthotropic incompressible half-space is derived in a direct manner, using the method of first integrals.