A generalized finite element method for linear thermoelasticity

We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by M{\aa}lqvist and Peterseim (Math. Comp., 83(290): 2583--2603, 2014). We prove convergence of optimal order, independent of the derivatives of the coefficients, in the spatial $H^1$-norm. The theoretical results are confirmed by numerical examples

Analytical Solutions and Multiscale Creep Analysis of Functionally Graded Cylindrical Pressure Vessels

This study deals with the time-dependent creep analysis of functionally graded thick-cylinders under various thermal and mechanical boundary conditions. Firstly, exact thermoelastic stress, and iterative creep solutions for a heat generating and rotating cylindrical vessel made of functionally graded thermal and mechanical properties are proposed. Equations of equilibrium, compatibility, stress-strain, and strain-displacement relations are solved to obtain closed-form initial stress and strain solutions. It is found that material gradient indices have significant influences on thermoelastic stress profiles. For creep analysis, Norton’s model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. Validity of our solutions are at first verified using finite element analysis, and numerical results found in the recent literature have been enhanced. Investigation of effects of material gradients reveals that radial variation of density and creep coefficient have significant effects on strains histories, while Young’s modulus and thermal property distributions only influence stress redistribution at an early stage of creep deformation. Next, a more realistic model of introducing microscale creep effects into a macroscopic modeling is employed to investigate the creep behavior of functionally graded hollow cylinders. Finite element (FE) simulations are employed to evaluate the position-dependent parameters associated with creep constitutive law at the microscale. A macroscopic FE model solves the non-linear boundary value problem to determine the time-varying creep stresses and strains. The framework proposed is capable of predicting the creep response of functionally graded pressure vessels based on the constitutive behavior of the creeping matrix, and volume fraction profile. Effective creep properties have been computed using three different micromechanical models and the homogenized creep response and its effect on the macroscopic behavior are compared. Considering the computational expenses associated with the large 3D finite element models, the simple 2D axisymmetric model is able to closely capture the creep behavior in such multiscale methods. Finally, a multi-objective particle swarm optimization algorithm is implemented to minimize the initial stress and final creep strain of functionally graded cylinder subjected to mechanical and thermal loads

Multiscale Investigation of Random Heterogenous Media in Materials and Earth Sciences

This dissertation is concerned with three major areas pertaining to the characterization and analysis of heterogeneous materials. The first is focused on the modeling of heterogeneous materials with random microstructure and understanding their thermomechanical properties as well as developing a methodology for the multiscale thermoelastic analysis of random heterogeneous materials. Realistic random microstructures are generated for computational analyses using random morphology description functions. The simulated microstructures closely resemble actual micrographs of random heterogeneous materials. The simulated random microstructures are characterized using statistical techniques and their homogenized material properties computed using the asymptotic expansion homogenization method. The failure response of random media is investigated via a direct micromechanical failure analysis which utilizes stresses at the microstructural level coupled with appropriate phase material failure models to generate initial failure envelopes. The homogenized material properties and failure envelopes are employed to perform accurate coupled macroscale and microscale analyses of random heterogeneous material components. The second area addressed in this dissertation involves the transient multiscale analysis of two-phase functionally graded materials within the framework of linearized thermoelasticity. The two-phase material microstructures, which are created using a morphology description function, have smoothly varying microstructure morphologies that depend on the volume fractions of the constituent phases. The multiscale problem is analyzed using asymptotic expansion homogenization coupled with the finite element method. Model problems are studied to illustrate the versatility of the multiscale analysis procedure which incorporates a direct micromechanical failure analysis to accurately compute the factors of safety for functionally graded components. The last area of this dissertation is concerned with determining the role of heterogeneous rock fabric features in quartz/muscovite rich rocks on seismic wave speed anisotropy. The bulk elastic properties and corresponding wave velocities are calculated for synthetic heterogeneous rock microstructures with varying material and geometric features to investigate their influence on seismic wave speed anisotropy. The asymptotic expansion homogenization method is employed to calculate precise bulk stiffness tensors for representative rock volumes and the wave speed velocities are obtained from the Christoffel equation. The obtained results are also used to assess the performance of analytic homogenization schemes currently used in the geophysics community

Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of random composite materials with temperature-dependent properties

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of random composite materials, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale. By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite materials both in the macro-scale and micro-scale. Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum. Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite materials. Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach

Multiscale Modeling of Advanced Materials for Damage Prediction and Structural Health Monitoring

abstract: Advanced aerospace materials, including fiber reinforced polymer and ceramic matrix composites, are increasingly being used in critical and demanding applications, challenging the current damage prediction, detection, and quantification methodologies. Multiscale computational models offer key advantages over traditional analysis techniques and can provide the necessary capabilities for the development of a comprehensive virtual structural health monitoring (SHM) framework. Virtual SHM has the potential to drastically improve the design and analysis of aerospace components through coupling the complementary capabilities of models able to predict the initiation and propagation of damage under a wide range of loading and environmental scenarios, simulate interrogation methods for damage detection and quantification, and assess the health of a structure. A major component of the virtual SHM framework involves having micromechanics-based multiscale composite models that can provide the elastic, inelastic, and damage behavior of composite material systems under mechanical and thermal loading conditions and in the presence of microstructural complexity and variability. Quantification of the role geometric and architectural variability in the composite microstructure plays in the local and global composite behavior is essential to the development of appropriate scale-dependent unit cells and boundary conditions for the multiscale model. Once the composite behavior is predicted and variability effects assessed, wave-based SHM simulation models serve to provide knowledge on the probability of detection and characterization accuracy of damage present in the composite. The research presented in this dissertation provides the foundation for a comprehensive SHM framework for advanced aerospace materials. The developed models enhance the prediction of damage formation as a result of ceramic matrix composite processing, improve the understanding of the effects of architectural and geometric variability in polymer matrix composites, and provide an accurate and computational efficient modeling scheme for simulating guided wave excitation, propagation, interaction with damage, and sensing in a range of materials. The methodologies presented in this research represent substantial progress toward the development of an accurate and generalized virtual SHM framework.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Fully coupled thermo-viscoplastic analysis of composite structures by means of multi-scale three-dimensional finite element computations

The current paper presents a two scale Finite Element approach (FE 2 ), adopting the periodic homogenization method, for fully coupled thermo-mechanical processes. The aim of this work is to predict the overall response of rate-dependent, non-linear, thermo-mechanically coupled problems of 3D periodic composite structures. The material constituents implicated in the analyses obey generalized standard materials laws, while the characteristic equations of the problem (balance law, first law of thermodynamics) are expressed and satisfied in both microscopic and macroscopic scales. For the numerical implementation in both scales, the finite element commercial software ABAQUS is utilized in the framework of small strains and rotations. A set of dedicated scripts and a specially designed Meta-UMAT subroutine allow the connection between the macroscopic structure and the microscopic unit cells attached to every macroscopic integration point. The two-scale finite element framework is applied to simulate thermoelastic-viscoplastic materials of complex 3D composite structures, and its capabilities are demonstrated with proper numerical examples. It is worth mentioning that the proposed computational strategy can be applied for any kind of 3D periodic microstructure and non-linear constitutive law