Numerical modeling of inverse problem of parameter identification for viscoelastic functionally graded materials/structures

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Linlin Zhang ◽  
Haitian Yang
Keyword(s):  
Inverse Problem ◽  
Recursive Algorithm ◽  
Functionally Graded ◽  
High Fidelity ◽  
Graded Materials ◽  
Content Type ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Constitutive Parameters ◽  
Derivatives Of

PurposeThis paper attempts to develop an efficient algorithm to solve the inverse problem of identifying constitutive parameters in VFG (viscoelastic functionally graded) materials/structures.Design/methodology/approachAn adaptive recursive algorithm with high fidelity is developed to acquire the derivatives of displacements with respect to constitutive parameters, which are required for the accurate and stable gradient based inverse analysis. A two-step strategy is presented in the process of identification, by which the unknown parameters can be separately identified and the scale and complexity of the inverse VFG problem are reduced. At each step, the process of identification is treated as an optimization problem that is solved by the Levenberg–Marquardt method.FindingsThe solution accuracy of forward problems and derivatives of displacements can be stably achieved with different step sizes, and constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures can be effectively and accurately identified. By examining the reliability, resolution, impacts of reference information and noisy data, the effectiveness of the proposed approach is numerically verified via three numerical examples.Originality/valueAn adaptive recursive algorithm is developed for derivatives computing with high fidelity, providing a solid platform for the sensitivity analysis and thereby a two-step strategy in conjunction with Levenberg–Marquardt method is presented in the process of identification. Consequently, an effective algorithm is developed to identify constitutive parameters of homogenous/regional-inhomogeneous VFG materials/structures.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

Modeling of functionally graded materials to estimate effective thermo-mechanical properties

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Royal Madan ◽  
Shubhankar Bhowmick
Keyword(s):  
Experimental Data ◽  
Functionally Graded Materials ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Content Type ◽  
Wide Range ◽  
Metal Metal ◽  
Novel Material ◽  
First Time

Purpose Functionally graded materials are a special class of composites in which material are graded either continuously or layered wise depending upon its applications. With such variations of materials, the properties of structure vary either lengthwise or thickness wise. This paper aims to investigate models for effective estimation of material properties, as it is necessary for industries to identify the properties of composites or functionally graded materials (FGM’s) before manufacturing and also to develop novel material combinations. Design/methodology/approach Available models were compared for different material combinations and tested with experimental data for properties such as Young’s modulus, density, coefficient of thermal expansion (CTE) and thermal conductivity. Combinations of metal–ceramic and metal–metal were selected such that their ratios cover a wide range of materials. Findings This study reveals different models will be required depending on the material used and properties to be identified. Practical implications The results of the present work will help researchers in the effective modeling of composites or FGM’s for any analysis. Originality/value This paper presents a comparison and review of various analytical methods with experimental data graphically to find out the best suitable method. For the first time, the Halpin-Tsai model was extended in the analysis of the CTE which shows good approximations.

Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehmet Eker ◽  
Durmuş Yarımpabuç ◽  
Kerimcan Çelebi
Keyword(s):  
Heat Generation ◽  
Internal Heat ◽  
Functionally Graded ◽  
Graded Materials ◽  
Content Type ◽  
Chebyshev Method ◽  
External Conditions ◽  
Cylinders And Spheres ◽  
Solid Bodies ◽  
Selection Of

Purpose This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation. Design/methodology/approach Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. Findings It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels. Originality/value In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

2017 ◽  
Vol 34 (4) ◽  
pp. 1314-1331 ◽  
Author(s):  
W.X. Zhang ◽  
R.G. Liu ◽  
Y. Bai
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Graded Materials ◽  
Content Type ◽  
Displacement Constraints

Purpose For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs. Design/methodology/approach Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods. Findings In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints. Originality/value The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

A two-stage homogenization for modelling of elastic-plastic functionally graded composites

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Witold Ogierman
Keyword(s):  
Volume Fraction ◽  
Mean Field ◽  
Functionally Graded ◽  
Two Stage ◽  
Graded Materials ◽  
Content Type ◽  
Elastic Plastic ◽  
Functionally Graded Composites ◽  
Homogenization Approach ◽  
Arbitrary Volume

Purpose The purpose of this study is to develop a homogenization approach that ensures both high accuracy and time-efficient solution for elastic-plastic functionally graded composites. Design/methodology/approach The paper presents a novel two-stage hybrid homogenization approach that combines advantages of the mean field homogenization and homogenization based on the finite element method (FEM). The groundbreaking nature of the developed approach is associated with division of the hybrid homogenization procedure into two stages, which allows to very efficiently determine the solution for arbitrary volume fraction of the reinforcement. This paper concerns also on modelling of composites with randomly distributed prolate and oblate particles. For this purpose, the hybrid homogenization was implemented in the framework of the discrete orientation averaging procedure involving pseudo-grain discretization method. Findings Agreement between the results obtained using the proposed approach and the standard FEM-based homogenization is very good (up to the volume fraction of 0.3). Originality/value The proposed two-stage homogenization approach allows to obtain the solution for materials with arbitrary volume fraction of the reinforcement very efficiently; therefore, it is highly beneficial for the two-scale modeling of nonlinear functionally graded materials and structures.

Toolpaths for additive manufacturing of functionally graded materials (FGM) parts

2014 ◽  
Vol 20 (6) ◽  
pp. 511-522 ◽  
Author(s):  
Pierre Muller ◽  
Jean-Yves Hascoet ◽  
Pascal Mognol
Keyword(s):  
Additive Manufacturing ◽  
Path Planning ◽  
Functionally Graded Materials ◽  
Process Modeling ◽  
Functionally Graded ◽  
System Control ◽  
Graded Materials ◽  
Content Type ◽  
Manufacturing Procedure ◽  
Selection Of

Purpose – The purpose of this paper is to propose an evaluation of toolpaths for additive manufacturing of functionally graded materials (FGM) parts to ensure the manufacturing of parts in compliance with the desired material distribution. The selection of an appropriate path strategy is critical when manufacturing FGM parts. Design/methodology/approach – The selection of a path strategy is based on a process modeling and an additive laser melting (ALM) system control. To do that, some path strategies are selected, simulated and compared. Findings – The comparison of some paths strategies was applied on a study case from the biomedical field. Test-parts were manufactured and analyzed. Results show a good correlation between the simulated and the deposited material distributions. The evaluation of toolpaths based on the process modeling and the system control was validated. Originality/value – Nowadays, FGM parts manufactured with ALM processes are not functional. To move from these samples to functional parts, it is necessary to have a global approach of the manufacturing procedure centered on the path planning. Few methodologies of path planning are adapted to FGM parts but are still limited.

FE modeling of creep in linear and non-linear FGM cylinder under internal pressure

2014 ◽  
Vol 10 (1) ◽  
pp. 94-105
Author(s):  
Manish Garg ◽  
Dharmpal Deepak ◽  
V.K. Gupta
Keyword(s):  
Creep Behavior ◽  
Outer Radius ◽  
Functionally Graded ◽  
Composite Cylinder ◽  
Linear Distribution ◽  
Graded Materials ◽  
Content Type ◽  
Functionally Graded Composite ◽  
Non Linear ◽  
Creep Strains

Purpose – The purpose of this paper is to investigate creep in an internally pressurized thick-walled, closed ends cylinder made of functionally graded composite, having linear and non-linear distribution of reinforcement, using finite element (FE) analysis. Design/methodology/approach – FE-based Abaqus software is used to investigate creep behavior of a functionally graded cylinder. The cylinder is made of composite containing linear and non-linearly varying distributions of reinforcement along the radius. The creep behavior has been described by Norton's power law. The creep stresses and strains have been estimated in linear and non-linear functionally graded materials (FGM) cylinders and compared with those estimated for a similar composite cylinder but having uniform distribution of reinforcement. Findings – The radial stress in the composite cylinder is observed to decreases over the entire radius upon imposing linear or non-linear reinforcement gradients. However, the tangential stress in the cylinder increases near the inner radius but decreases toward the outer radius, on imposing linear or non-linear reinforcement gradients. The creep strains in the FGM cylinders are significantly lower than those observed in a uniform composite cylinder. Originality/value – The creep strains in an internally pressurized functionally graded thick composite cylinder could be reduced significantly by employing non-linear distribution of reinforcement along the radial direction.

Slice data representation and format for multi-material objects for additive manufacturing processes

2017 ◽  
Vol 23 (1) ◽  
pp. 149-161 ◽  
Author(s):  
Zhengyan Zhang ◽  
Sanjay Joshi
Keyword(s):  
Additive Manufacturing ◽  
Functionally Graded Materials ◽  
Tool Path ◽  
Heterogeneous Material ◽  
Data Representation ◽  
Functionally Graded ◽  
Material Object ◽  
Graded Materials ◽  
Content Type ◽  
Wide Range

Purpose This paper aims to develop a slice-based representation of geometry and material information of a multi-material object to be produced by additive manufacturing. Representation of complex heterogeneous material allowing for the additive manufacturing-based build of a wide range of objects that are limited only by the constraints of the manufacturing process. Design/methodology/approach Initial 3D CAD models are created with multiple and functionally graded materials using an assembly model to create a single part with well-defined material regions. These models are then sliced to create the geometry and material boundaries required for each layer to enable layer-by-layer fabrication. Findings A representation schema is proposed to add multi-material attributes to a sliced file for additive manufacturing using the combination of material index and material geometry region. A modified common layer interface data format is proposed to allow for representation of a wide range of homogeneous and heterogeneous material for each slice. This format allows for a generic input for tool paths to be generated for each material of the layer. Originality/value The proposed approach allows for slice data representation for any material combination that can be defined mathematically. Three different material types, namely, composite material, functionally graded materials and combination thereof, are provided as examples. These data form the input data for subsequent tool path planning.

Convergence of Levenberg–Marquardt method for the inverse problem with an interior measurement

2019 ◽  
Vol 27 (2) ◽  
pp. 195-215 ◽  
Author(s):  
Yu Jiang ◽  
Gen Nakamura
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Loss Modulus ◽  
Circular Domain ◽  
Rectangular Domain ◽  
Scalar Model ◽  
Partial Differential ◽  
Marquardt Method ◽  
Levenberg Marquardt

AbstractThe convergence of Levenberg–Marquardt method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so-called scalar model by a single interior measurement. The scalar model is the most simplest model for data analysis used as the modeling partial differential equation in the diagnosing modality called the magnetic resonance elastography which is used to diagnose for instance lever cancer. The convergence of the method is proved by showing that the measurement map which maps the above unknown moduli to the measured data satisfies the so-called the tangential cone condition. The argument of the proof is quite general and in principle can be applied to any similar inverse problem to reconstruct the unknown coefficients of the model equation given as a partial differential equation of divergence form by one single interior measurement. The performance of the method is numerically tested for the two-layered piecewise homogeneous scalar models in a rectangular domain and a circular domain.

An Inverse Analysis Algorithm of Material Parameters for Functional Graded Materials

2011 ◽  
Vol 243-249 ◽  
pp. 6011-6017
Author(s):  
Li Xin Huang ◽  
Qi Yao ◽  
Lin Wang ◽  
Xiao Jun Zhou
Keyword(s):  
Inverse Analysis ◽  
Element Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Graded Materials ◽  
Analysis Algorithm ◽  
Material Parameters ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Measured Displacement

An inverse analysis algorithm is proposed to identify the material parameters of functional graded materials (FGMs). The inverse analysis of the material parameters is formulated as the problem of minimizing the objective function defined as a square sum of differences between the measured displacement and the computed displacement by a finite element model. Levenberg-Marquardt method is used to solve the minimization problem. The sensitivities of displacements with respect to the material parameters are based on the finite difference approximation method. A numerical example is given to demonstrate the effectiveness of the proposed algorithm.

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