Numerical modeling of functionally graded materials using a variational formulation

Abali, Bilen Emek; Völlmecke, Christina; Woodward, B.; Kashtalyan, Maria; Guz, I. A.; Müller, Wolfgang

doi:10.1007/s00161-012-0244-y

Cited by 26 publications

(10 citation statements)

References 18 publications

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“…(18) which takes into account the gradient of the change of porosity allows us to also apply boundary conditions on the porosity which otherwise are not sustainable. Some studies have been proposed to better characterize the complex behavior of systems as bone tissue, see, e.g., Li et al (2019); Camar-Eddine and Seppecher (2001); Lekszycki et al (2017); Misra and Poorsolhjouy (2015); Abali et al (2012); Chatzigeorgiou et al (2014).…”

Section: A Model For Growing Bone Tissues Using Concepts From Poromecmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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In the past years, many attempts have been made in order to model the process of bone remodeling. This process is complex, as it is governed by not yet completely understood biomechanical coupled phenomena. It is well known that bone tissue is able to self-adapt to different environmental demands of both mechanical and biological origin. The mechanical aspects are related to the functional purpose of the bone tissue, i.e., to provide support to the body and protection for the vitally important organs in response to the external loads. The many biological aspects include the process of oxygen and nutrients supply. To describe the biomechanical process of functional adaptation of bone tissue, the approach commonly

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Section: A Model For Growing Bone Tissues Using Concepts From Poromecmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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“…Herein we will use quadratic elements for the displacements, i.e., u i ∈ H 2 , that induce linear stress distribution, which is discontinuous across elements. The implementation with linear elements is realized in Abali et al (2012). We shall give a brief outline of the variational formulation and implement the point load next.…”

Section: Numerical Modelingmentioning

confidence: 99%

“…The variational formulation above is well-known. For a convergence study with heterogeneous materials we refer to Abali et al (2012). In the following we discretize the domain automatically with an approximate global size for each element.…”

Section: Numerical Modelingmentioning

confidence: 99%

Three-dimensional elastic deformation of functionally graded isotropic plates under point loading

Abali

Völlmecke²,

Woodward

et al. 2014

Composite Structures

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In this paper, three-dimensional elastic deformation of isotropic functionally graded plates subjected to point loading is investigated using a combination of analytical and computational means. The analytical approach is based on the displacement functions method, while numerical modeling, which requires high accuracy in the representation of the point loading, uses Galerkin type finite element method. Three different plate geometries are examined for validation purposes, and the difficulties associated with an optimum choice of the element size are discussed. It is shown that by using a posteriori error estimation based on the equivalent stress measure accurate results can be obtained even in the neighborhood of the point loading.

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“…For contacts of complicated geometries or contacts under arbitrary loading, it is usually impossible to obtain an analytical solution for both elastically homogenous and nonhomogeneous materials, so that the numerical methods are widely developed for contact problems, e.g. finite element method (FEM) (Hyun, Pei, Molinari & Robbins, 2004;Abali, Völlmecke, Woodward, Kashtalyan, Guz & Müller, 2012), boundary element method (BEM) (Putignano, Afferrante, Carbone & Demelio, 2012;Paggi & Ciaveralla, 2010;Pohrt & Popov, 2012;Aleynikov, 2010) and molecular dynamics simulation (Yang & Persson, 2008;Campana & Muser, 2007). For contacts of linearly elastic or viscoelastic materials (Kusche, 2016).…”

Section: Introductionmentioning

confidence: 99%

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

Popov

2017

Comput Mech

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Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single force acting on the surface of a half space with a power-law varying elastic modulus, the deformation produced by constant pressure acting on a rectangular element was calculated and the influence matrix was obtained for a rectangular grid. The inverse problem for the calculation of required stress in contact area from a known surface deformation was solved by use of conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used which drastically reduces the computation time. For the adhesive contact of graded material, the detachment criterion based on the method of Pohrt and Popov was proposed. A number of numerical test for the problem having exact analytical solution have been carried out confirming the correctness of underlying ideas and numerical implementation.

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Numerical modeling of functionally graded materials using a variational formulation

Cited by 26 publications

References 18 publications

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Three-dimensional elastic deformation of functionally graded isotropic plates under point loading

Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials

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