M. Reza Eslami

Bio: M. Reza Eslami is an academic researcher from Amirkabir University of Technology. The author has contributed to research in topics: Nonlinear system & Finite element method. The author has an hindex of 17, co-authored 71 publications receiving 1257 citations.

Thermal Stresses -- Advanced Theory and Applications

Abstract: 1 Basic Laws of Thermoelasticity 1 Introduction 2 Stresses and Tractions 3 Equations of Motion 4 Coordinate Transformation. Principal Axes 5 Principal Stresses and Stress Invariants 6 Displacement and Strain Tensor 7 Compatibility Equations. Simply Connected Region 8 Compatibility Conditions. Multiply Connected Regions 9 Constitutive Laws of Linear Thermoelasticity 10 Displacement Formulation of Thermoelasticity 11 Stress Formulation of Thermoelasticity 12 Two-Dimensional Thermoelasticity 13 Michell conditions 2 Thermodynamics of Elastic Continuum 1 Introduction 2 Thermodynamics Definitions 3 First Law of Thermodynamics 4 Second Law of Thermodynamics 5 Variational Formulation of Thermodynamics 6 Thermodynamics of Elastic Continuum 7 General Theory of Thermoelasticity 8 Free Energy Function of Hookean Materials 9 Fourier's Law and Heat Conduction Equation 10 Generalized Thermoelasticity. Second Sound 11 Thermoelasticity without Energy Dissipation 12 Uniqueness Theorem 13 Variational Principle of Thermoelasticity 14 Reciprocity Theorem 15 Initial and Boundary Conditions 3 Basic Problems of Thermoelasticity 1 Introduction 2 Temperature Distribution for Zero Thermal Stress 3 Analogy of Thermal Gradient with Body Forces 4 General Solution of Thermoelastic Problems 5 General Solution in Cylindrical Coordinates 6 Solution of Two-Dimensional Navier Equations 7 Solution of Problems in Spherical Coordinates 4 Heat Conduction Problems 1 Introduction 2 Problems in Rectangular Cartesian Coordinates 2.1 Steady State One-Dimensional Problems 2.2 Steady Two-Dimensional Problems. Separation of Variables 2.3 Fourier Series 2.4 Double Fourier Series 2.5 Bessel Functions and Fourier-Bessel series 2.6 Nonhomogeneous Differential Equations and Boundary Condition 2.7 Lumped Formulation 2.8 Steady State Three-Dimensional Problems 2.9.Transient Problems 3 Problems in Cylindrical coordinates 3.1 Steady-State One-Dimensional Problems (Radial Flow) 3.2. Steady -State Two-Dimensional Problems 3.3 Steady-State Three-Dimensional Problems 3.4 Transient Problems 4 Problems in Spherical Coordinates 4.1 Steady-State One-Dimensional Problems 4.2 Steady-State Two- and Three-Dimensional Problems 4.3 Transient Problems 5 Thermal Stresses in Beams 1 Introduction 2 Elementary Theory of Thermal Stresses in Beams 3 Deflection Equation of Beams 4 Boundary Conditions 5 Shear Stress in a Beam 6 Beams of Rectangular Cross Section 7 Transient Thermal Stresses in Rectangular Beams 8 . Beam with Internal Heat Generation 9 Bimetallic Beam 10 Functionally Graded Beams 11 Transient Thermal Stresses in Functionally Graded Beams 12 Thermal Stresses in Thin Curved Beams and Rings 13 Deflection of Thin Curved Beams and Rings 6 Disks, Cylinders, and Spheres 1 Introduction 2 . Cylinders with Radial Temperature Variation 3 Thermal Stresses in Disks 4 Thick Spheres 5 Thermal Stresses in a Rotating Disk 6 Non-Axisymmetrically Heated cylinders 7 Method of Complex Variables 8 Functionally Graded Thick Cylinders 9 Axisymmetric Thermal Stresses in FGM Cylinders 10.Transient Thermal Stresses in Thick Spheres 11 Functionality Graded Spheres 7 Thermal Expansion in Piping Systems 1 Introduction 2 Definition of the Elastic Center 3 . Piping Systems in Two Dimensions 4 Piping Systems in Three-dimensions 5 Pipelines with Large Radius Elbows 8 Coupled and Generalized Thermoelasticity 1 Introduction 2 Governing Equations of Coupled Thermoelasticity 3 Coupled Thermoelasticity for Infinite Space 4 Variable Heat Source 5 One-Dimensional Coupled Problem 6 Propagation of Discontinuities 7 Half-Space Subjected to a Harmonic Temperature 8 Coupled Thermoelasticity of Thick Cylinders 9 Green-Naghdi Model of a Layer 10 Generalized Thermoelasticity of Layers 11 Generalized Thermoelasticity of Spheres and Cylinders

Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity

Abstract: An eXtended Finite Element Method (XFEM) is presented that can accurately predict the stress intensity factors (SIFs) for thermoelastic cracks. The method uses higher order terms of the thermoelastic asymptotic crack tip fields to enrich the approximation space of the temperature and displacement fields in the vicinity of crack tips—away from the crack tip the step function is used. It is shown that improved accuracy is obtained by using the higher order crack tip enrichments and that the benefit of including such terms is greater for thermoelastic problems than for either purely elastic or steady state heat transfer problems. The computation of SIFs directly from the XFEM degrees of freedom and using the interaction integral is studied. Directly computed SIFs are shown to be significantly less accurate than those computed using the interaction integral. Furthermore, the numerical examples suggest that the directly computed SIFs do not converge to the exact SIFs values, but converge roughly to values near the exact result. Numerical simulations of straight cracks show that with the higher order enrichment scheme, the energy norm converges monotonically with increasing number of asymptotic enrichment terms and with decreasing element size. For curved crack there is no further increase in accuracy when more than four asymptotic enrichment terms are used and the numerical simulations indicate that the SIFs obtained directly from the XFEM degrees of freedom are inaccurate, while those obtained using the interaction integral remain accurate for small integration domains. It is recommended in general that at least four higher order terms of the asymptotic solution be used to enrich the temperature and displacement fields near the crack tips and that the J- or interaction integral should always be used to compute the SIFs.

Cohesive and non-cohesive fracture by higher-order enrichment of XFEM

Abstract: SUMMARY A comprehensive study is performed on the use of higher-order terms of the crack tip asymptotic fields as enriching functions for the eXtended FEM (XFEM) for both cohesive and traction-free cracks. For traction-free cracks, the Williams asymptotic field is used to obtain highly accurate stress intensity factors (SIFs), directly from the enriched degrees of freedom without any post-processing. The low accuracy of the results of the original research on this subject by Liu et al. [Int. J. Numer. Meth. Engng., 2004; 59:1103–1118] is remedied here by appropriate modifications of the enrichment scheme. The modifications are simple and can be easily included into an XFEM computer code. For cohesive cracks, the relevant asymptotic field is used, and two widely used criteria including the SIFs criterion and the stress criterion are examined for the crack growth simulation. Both linear and nonlinear cohesive laws are used. For the stress criterion, averaging is avoided due to the highly accurate crack tip approximation because of the higher-order enrichment. Then, a modified stress criterion is proposed, which is shown to be applicable to a wider class of problems. Several numerical examples, including straight and curved cracks, stationary and growing cracks, single and multiple cracks, and traction-free and cohesive cracks, are studied to investigate in detail the robustness and efficiency of the proposed enrichment scheme. Copyright © 2012 John Wiley & Sons, Ltd.

A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Abstract: Being one of the most promising candidates for the modeling of localized failure in solids, so far the phase-field method has been applied only to brittle fracture with very few exceptions. In this work, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics. Specifically, the crack phase-field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context. The energy dissipation functional due to crack evolution and the stored energy functional of the bulk are characterized by a crack geometric function of polynomial type and an energetic degradation function of rational type, respectively. Standard arguments of thermodynamics then yield the macroscopic balance equation coupled with an extra evolution law of gradient type for the crack phase-field, governed by the aforesaid constitutive functions. The classical phase-field models for brittle fracture are recovered as particular examples. More importantly, the constitutive functions optimal for quasi-brittle failure are determined such that the proposed phase-field theory converges to a cohesive zone model for a vanishing length scale. Those general softening laws frequently adopted for quasi-brittle failure, e.g., linear, exponential, hyperbolic and Cornelissen et al. (1986) ones, etc., can be reproduced or fit with high precision. Except for the internal length scale, all the other model parameters can be determined from standard material properties (i.e., Young’s modulus, failure strength, fracture energy and the target softening law). Some representative numerical examples are presented for the validation. It is found that both the internal length scale and the mesh size have little influences on the overall global responses, so long as the former can be well resolved by sufficiently fine mesh. In particular, for the benchmark tests of concrete the numerical results of load versus displacement curve and crack paths both agree well with the experimental data, showing validity of the proposed phase-field theory for the modeling of damage and quasi-brittle failure in solids.

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Abstract: SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element-free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells

Abstract: Thermal postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a uniform temperature rise. The SWCNTs are assumed to be aligned and straight with a uniform layout. Two kinds of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation theory with a von Karman-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. Based on the multi-scale approach, numerical illustrations are carried out for perfect and imperfect, FG- and UD-CNTRC shells under different values of the nanotube volume fractions. The results show that the buckling temperature as well as thermal postbuckling strength of the shell can be increased as a result of a functionally graded reinforcement. It is found that in most cases the CNTRC shell with intermediate nanotube volume fraction does not have intermediate buckling temperature and initial thermal postbuckling strength.