scholarly journals Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

2016 ◽  
Vol 68 (5) ◽  
Author(s):  
Saba Saeb ◽  
Paul Steinmann ◽  
Ali Javili
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Linear Displacement ◽  
Computational Homogenization ◽  
Finite Strains ◽  
Underlying Assumption ◽  
Numerical Examples ◽  
Various Boundary Conditions ◽  
Computational Aspects

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill–Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

Three-Dimensional FEM Simulation of the Ship-Bridge Collision

2013 ◽  
Vol 405-408 ◽  
pp. 3243-3247
Author(s):  
Wei Su ◽  
Ying Sun ◽  
Shi Qing Huang ◽  
Ren Huai Liu
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Reference Values ◽  
Large Scale ◽  
Three Dimensional ◽  
Fem Simulation ◽  
Structural Safety ◽  
Fem Model ◽  
Finite Element Software

In this paper, the structural safety of the Niuwan Bridge subjected to vessel collision is investigated by the large-scale commercial finite element software ANSYS. A whole FEM model is built and a reasonable analysis and illustration for taking the value of vessel-collision forces is presented. Additionally, under the premise of reasonable simulation of the boundary conditions, the effects of the support abutments, the prestress and the carloads are considered. The analysis results have certain reference values for the anti-collision and reinforcement of bridges.

NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 237-258 ◽  
Author(s):  
MOHAMMAD TALHA ◽  
B. N. SINGH
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Strain ◽  
Various Boundary Conditions ◽  
Transverse Loads ◽  
Nonlinear Mechanical ◽  
Graded Material ◽  
Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

Finite Element Analysis of Polyurethane Based Composite Shafts Under Different Boundary Conditions

2014 ◽  
Author(s):  
Mosfequr Rahman ◽  
F. N. U. Aktaruzzaman ◽  
Saheem Absar ◽  
Aniruddha Mitra ◽  
Awlad Hossain
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Three Dimensional ◽  
Woven Fabric ◽  
Bending Test ◽  
Matrix Composites ◽  
Fiber Glass ◽  
Different Boundary Conditions ◽  
Simply Supported

Depending on the type of matrix materials, composites can be broadly divided into three different major classifications: Organic-matrix composites (OMC), metal-matrix composites (MMC), and ceramic-matrix composites (CMC). OMC can be further sub-classified into polymer-matrix composites (PMC) and carbon-matrix composites or carbon-carbon composites. In this paper the main objective is to focus on polyurethane based PMC composites. Polyurethane is one of the widely used polymer matrix materials. It has diversified applications, easily available and cheap. In this computational study a composite shaft with a core made of matrix material completely wrapped around by a woven fiber cloth with a very strong bonding between core and fibers is considered. Three different types of woven fibers: fiber glass, Kevlar 49, and carbon fibers, are considered. A woven fabric is the interlocking or weaving of two unidirectional fibers. This configuration is often used to produce curve surfaces because of the ease with which it could be placed on and conform to curved surfaces. Authors had fabricated these three composites in their in-house laboratory. They had also experimentally measured the mechanical properties of these composites using 3-point bending test which already been published. In this current study finite element analyses has been performed for the modeling of the static response of these three different polyurethane based composite shafts as fiber glass reinforced polyurethane epoxy, carbon fiber reinforced polyurethane epoxy, and Kevlar fibers reinforced polyurethane epoxy for three different boundary conditions. These three boundary conditions are simply supported, cantilever, both end fixed types with bending loads applied at the middle for simply supported case and distributed load along the length of the shaft for the last two types of boundary conditions. A three dimensional model of the composite beam has been implemented in this study using SolidWorks. A finite element commercial software ANSYS is used to investigate the stress response and deformation behavior of the model geometry for these three polyurethane based composite shafts for these three boundary conditions. A twenty node three dimensional element has been implemented for the finite element formulation of the modeled geometry such that it is applicable for the analysis of a layered composite structure, while providing support for linear, large rotation, and large strain nonlinear loading conditions. Convergence has also been ensured for various mash configurations in this work.

An Evaluation of Three-Dimensional Diarthrodial Joint Contact Using Penetration Data and the Finite Element Method

2001 ◽  
Vol 123 (4) ◽  
pp. 333-340 ◽  
Author(s):  
W. L. Dunbar, ◽  
K. U¨n ◽  
P. S. Donzelli ◽  
R. L. Spilker
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Contact Boundary ◽  
Element Analysis ◽  
Joint Contact ◽  
Three Dimensional Finite Element

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to the method includes: (i) kinematic information describing an in vitro joint articulation, measured while the cartilage is deformed under physiological loads, (ii) geometric properties for the relaxed (undeformed) cartilage layers, obtained for the analyses in this study via stereophotogrammetry, and (iii) material parameters for the biphasic constitutive relations used to represent cartilage. Solid models of the relaxed tissue layers are assembled in physiological positions, resulting in a mathematical overlap of the cartilage layers. The overlap distribution is quantified and converted via the biphasic governing equations into applied traction boundary conditions for both the solid and fluid phases for each of the contacting layers. Linear, biphasic, three-dimensional, finite element analysis is performed using the contact boundary conditions derived for each of the contacting layers. The method is found to produce results consistent with the continuity requirements of biphasic contact. Comparison with results from independent, biphasic contact analyses of axisymmetric problems shows that the method slightly underestimates the contact area, leading to an overestimation of the total traction, but yields a good approximation to elastic stress and solid phase displacement.

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