When an element is stretched in one direction, it tends to get thinner in the other two directions. Hence, the change in longitudinal and lateral strains are opposite in nature (generally). Poisson’s ratio ν, named after Simeon Poisson, is a measure of this tendency. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load. Since most common materials become thinner in cross section when stretched, Poisson’s ratio for them is positive.

For a perfectly incompressible material, the Poisson’s ratio would be exactly 0.5. Most practical engineering materials have ν between 0.0 and 0.5. Cork is close to 0.0, most steels are around 0.3, and rubber is almost 0.5. A Poisson’s ratio greater than 0.5 cannot be maintained for large amounts of strain because at a certain strain the material would reach zero volume, and any further strain would give the material negative volume.

Some materials, mostly polymer foams, have a negative Poisson’s ratio; if these auxetic materials are stretched in one direction, they become thicker in perpendicular directions.Foams with negative Poisson’s ratios were produced from conventional low density open-cell polymer foams by causing the ribs of each cell to permanently protrude inward, resulting in a re-entrant structure.

An example of the practical application of a particular value of Poisson’s ratio is the cork of a wine bottle. The cork must be easily inserted and removed, yet it also must withstand the pressure from within the bottle. Rubber, with a Poisson’s ratio of 0.5, could not be used for this purpose because it would expand when compressed into the neck of the bottle and would jam. Cork, by contrast, with a Poisson’s ratio of nearly zero, is ideal in this application.

It is anticipated that re-entrant foams may be used in such applications as sponges, robust shock absorbing material, air filters and fasteners. Negative Poisson’s ratio effects can result from non-affine deformation, from certain chiral microstructures, on an atomic scale, or from structural hierarchy. Negative Poisson’s ratio materials can exhibit slow decay of stress according to Saint-Venant’s principle. Later writers have called such materials anti-rubber, auxetic (auxetics), or dilatational. These materials are an example of extreme materials.

Finite Element Analysis (FEA) is a computer simulation technique used in engineering analysis. It uses a numerical technique called the finite element method (FEM). In this, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions — finite elements. Equations of equilibrium, in conjunction with applicable physical considerations such as compatibility and constitutive relations, are applied to each element, and a system of simultaneous equations is constructed. The system of equations is solved for unknown values using the techniques of linear algebra or nonlinear numerical schemes, as appropriate.

FEA has become a solution to the task of predicting failure due to unknown stresses by showing problem areas in a material and allowing designers to see all of the theoretical stresses within. This method of product design and testing is far superior to the manufacturing costs which would accrue if each sample was actually built and tested.

There are generally two types of analysis: 2-D modeling, and 3-D modeling. While 2-D modeling conserves simplicity and allows the analysis to be run on a relatively normal computer, it tends to yield less accurate results. 3-D modeling, produces more accurate results while it can only be run satisfactorily on a faster computer effectively. Within each of these modeling schemes, the programmer can insert numerous algorithms (functions) which may make the system behave linearly or non-linearly. Linear systems are far less complex and generally do not take into account plastic deformation. Non-linear systems do account for plastic deformation, and many also are capable of testing a material all the way to fracture.

While being an approximate method, the accuracy of the FEA method can be improved by refining the mesh in the model using more elements and nodes, though this will retard the process of converging.

Uses

A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. It is used in new product design, and also in existing product refinement. A company is able to verify whether a proposed design will be able to perform to the client’s specifications prior to manufacturing or construction. Modifying an existing product or structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design modifications to meet the new condition. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, fluid dynamics and electromagnetism. FEA is able to handle complex systems that defy closed-form analytical solutions.

Some FEA Software’s

Free/Open Source

ALBERTA

An adaptive hierarchical finite element toolbox

CalculiX

is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format. The pre/post-processor generates input data for many FEA and CFD applications.

Code Aster:

French software written in Python and Fortran, GPL license.

Deal.II

is a finite element differential equation library

DUNE,

Distributed and Unified Numerics Environment GPL Version 2 with Run-Time Exception, written in C++

Elmer FEM solver:

Open source multiphysical simulation software developed by Finnish Ministry of Education’s CSC, written in C, C++ and Fortran

FEAPpv

A general purpose finite element analysis program

FEBio

Finite Elements for Biomechanics

FEMM

is a Windows finite element solver for 2D and axisymmetric magnetic, electrostatic, heat flow, and current flow problems

FEMPACK

– Finite Element Routines

FEniCS

Project: a LGPL-licensed software package developed by American and European researchers

FETK

is an adaptive finite element method (AFEM) software libraries and tools for solving coupled systems of nonlinear geometric partial differential equations (PDE)

FRANC2D and FRANC3D:

is a two/three dimensional, finite element based program for simulating curvilinear crack propagation in planar (plane stress, plane strain, and axisymmetric) structures developed by Cornell Fracture Group US. software available for Windows and Linux/UNIX

Freefem++

is an implementation of a language dedicated to the finite element method

GetFEM++

An open-source finite element library

Hermes Project:

Modular C/C++ library for rapid development of space- and space-time adaptive hp-FEM solvers.

Impact:

Dynamic Finite Element Program Suite, for dynamic events like crashes, written in Java, GNU license

libMesh

a framework for the numerical simulation of partial differential equations

OFELI :

(Object Finite Element LIbrary)a library of finite element C++ classes for multipurpose development of finite element software

OOF:

finite element modeling for material science

OOFEM:

Object Oriented Finite EleMent solver, written in C++, GPL v2 license

OpenFOAM

(Field Operation And Manipulation). Originally for CFD only, but now includes finite element analysis through tetrahedral decomposition of arbitrary grids.

OpenSees

is an Open System for Earthquake Engineering Simulation

ParaFEM

is a freely available, portable library of subroutines for parallel finite element analysis. The subroutines are written in FORTRAN90/95 and use MPI for message passing.

WARP3D

Static and Dynamic Nonlinear Analysis of Fracture in Solids

Z88:

FEM-software available for Windows and Linux/UNIX, written in C, GPL license

Proprietary/Commercial

Abaqus:

Franco-American software from SIMULIA, owned by Dassault Systemes

ADINA

Advance Design BIM

software for FEM structural analysis, including international design eurocodes, a solution developed by GRAITEC

ALGOR

Incorporated

Altair HyperWorks

Altair Engineering’s HyperWorks is a computer-aided engineering (CAE) simulation software platform that allows businesses to create superior, market-leading products efficiently and cost effectively.

ANSA:

An advanced CAE pre-processing software for complete model build up.

ANSYS:

American software

COMSOL Multiphysics

COMSOL Multiphysics Finite Element Analysis Software formerly Femlab

Creo Elements / Pro Mechanica:

A p-version finite element program that is embedded in the MCAD application Creo Elements Pro, from PTC (Parametric Technology Corporation)

Diffpack

Software for finite element analysis and partial differential equations

Diana

(software) a multi-purpose finite element program (three-dimensional and nonlinear) by TNO

Falcon2.0 :

Lightweight FEM POST Processor and Viewer for 3D UNV and NASTRAN files

FEFLOW:

simulates groundwater flow, mass transfer and heat transfer in porous media

Femap,

Siemens PLM Software: A pre and post processor for Windows

FEM

-Design Structural analysis software from StruSoft (Swedish company).

FEMtools,

Dynamic Design Solutions: A toolbox for static and dynamic simulation, verification, validation and updating of finite element models. Includes also modules for structural optimization and for obtaining experimental reference data.

FENSAP-ICE

(Finite Element Navier–Stokes Package) the fully-integrated 3D in-flight CFD icing simulation system developed by Newmerical Technologies Intl.

FlexPDE

Flux :

American electromagnetic and thermal FEA

Genie:

DNV (Det Norske Veritas) Software

HydroGeoSphere:

A 3D control-volume finite element hydrologic model, simulating surface and subsurface water flow and solute and thermal energy transport

HyperSizer:

Software for composite material analysis

Infolytica MagNet :

North American electromagnetic, electric and thermal FEA software

JMAG:

Japanese software Actran: Belgian Software (Acoustic)

LINKpipe:

from LINKftr AS (Norwegian company). Special purpose non linear FE program for pipelines

LS-DYNA

LSTC – Livermore Software Technology Corporation

LUSAS:

UK Software

MADYMO:

TASS – TNO Automotive Safety Solutions

MSC.Marc:

from MSC Software

Nastran:

American software, from MSC Software

Nautics 3D Beam:

DNV (Det Norske Veritas) Software

Nastran/EM

Nastran Suit for highly advanced Durability & NVH Analyses of Engines; born from the AK32 Benchmark of Audi, BMW, Daimler, Porsche & VW; Source Code available

NEi Fusion, NEi Software:

3D CAD modeler + Nastran FEA

NEi Nastran, NEi Software:

General purpose Finite Element Analysis

NEi Works, NEi Software:

Embedded Nastran for SolidWorks users

NISA:

Indian software

PAK:

Serbian software for linear and nonlinear structural analysis, heat conduction, fluid mechanics with heat transfer, coupled problems, biomechanics, fracture mechanics and fatigue.

Plaxis:

Geotechnical 2D/3D FE suites, with support for stresses, deformations, groundwater flow and dynamics.

PZFlex:

American software for wave propagation and piezoelectric devices

Quickfield :

Physics simulating software

Radioss:

A linear and nonlinear solver owned by Altair Engineering

Range Software:

Multi physics simulation software

RFEM

SAMCEF:

CAE package developed by the Belgian company

SAP2000:

American software

STRAND7:

Developed in Sydney Australia by Strand7 Pty. Ltd. Marketed as Straus7 in Europe.

StressCheck

developed by ESRD, Inc (USA) emphasizing solution accuracy by utilizing high order elements

Vector Fields Concerto:

UK 2d/3d RF and microwave electromagnetic design software

Vector Fields Opera:

UK 2d/3d Electromagnetic and multi-physics finite element design software

Vflo:

Physics-based distributed hydrologic modeling software, developed by Vieux & Associates, Inc.

Finite Element Analysis | FEA In this article Introduction to Finite Element Analysis is discussed. FEA is a computerized method for analysis / simulation for...