nonlinear material guide

7/26/2019 Nonlinear Material Guide

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A Guide to HandleNonlinear aterial

in Your Analysis

This guide is made for non-experienced FEA users. It providesbasic knowledge needed to start analyzing plasticity in materials.

Experienced FEA analysts can also use this guide to get used to

the NFX workflow.
http://midasnfx.com/http://midasnfx.com/


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TABLE OF CONTENTS:

Nonlinear Materials in the Industry....... 3

Nonlinear Material Types....... 4

Engineering Stress Strain curve.... 5

True Stress Strain curve. 6

Converting Engineering Data to True Data.. 7

Work Hardening... 8

Why is nonlinear data required in FEA? 10

Nonlinear input in midas NFX 11

Nonlinear analysis types in midas NFX ... 13Examples... 16
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Nonlinear Materials in

the Industry

Page 3

1

Nonlinear Materials are omnipresent in various industries which

requires high resistance, light materials and components.

For example: Automotive, Marine, Defense, Aerospace, Heavy

Machinery, Consumer Goods, Electronics, Oil and Gas, Medical

Industry, etc.


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Nonlinear Material Types

Page 4

2Nonlinear Materials can be represented using different types of

models and rules.

Material types: Elasto-plastic, Hyper-elastic

Yield Criterions : Von Mises (Metals)

Nonlinear entries: Stress strain curve, Plastic hardening curve, perfect plastic

Hardening Rules: Isotropic, Kinematic, Combined

Dependence: Temperature, Strain rate


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Engineering Stress

Strain Curve3

Monotonic tension stress-strain properties are usually reported

in handbooks and are used in many specifications.

Monotonic behavior is obtained from a tension test where a

specimen with circular or rectangular cross sections within the

uniform gauge length is subjected to a monotonically increasing

tensile force until it fractures.

Engineering stress S from a uniaxial test is defined by dividing

the axial force by the original cross sectional area.

Sy - yield strength

Su - ultimate tensile strength

Page 5

Snom - Engineering Stress, nominal

A0 - Original cross sectional area

l - Instantaneous gage length

nom - Engineering Strain, nominal


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True Stress Strain Curve

Page 6

4

f- true fracture strength

f- true fracture strain or ductility

True stress sigma is defined by dividing the axial force by the

instantaneous cross sectional area.

True stress in tension is higher than engineering stress

because the cross section area decreases during the loading.

- true stress

- true strain

A - instantaneous cross sectional area

l - instantaneous gage length

L0 - original gage length

For constant volume up to necking assumption:

The following relationships can then be derived:


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Work Hardening5

Loading

UnloadingA

B

C

0

Work hardening is a consequence of plastic deformation, a

permanent change in shape. This is different to elastic

deformation, which is reversible.

Most materials do not exhibit only plastic deformation or elastic

deformation, but rather a combination of the two. The following

discussion mostly applies to metals, especially steels, which

are well studied. Work hardening occurs most notably for

ductile materials such as metals. Ductility is the ability of a

material to undergo plastic deformations before fracture (E.g.:

bending a steel rod until it finally breaks).

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K - strength coefficient (stress intercept at p = 1)n - strain hardening exponent (slope of the line)

p - plastic strain

Material:

Steel

SuMPa/(ksi)

E

GPa/ksi 103K/K

MPa/(ksi) n/n

1010 331/(48) 203/29.5534/867

(78)/(126)0.185/ 0.244

1020 441/(64) 203/29.5738/1962

(107)/(284)0.190/ 0.321

1038c 582/(84) 201/29.51106/1340

(160)/(195)0.259/ 0.220

Properties of Steel

= K (p)n

When describing Work hardening, Hollomon's equation is

mostly used. Hollomon's equation is a powerful law which

describes the relationship between the stress and the

amount of plastic strain it used to generate the hardening

curve of a nonlinear material.

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Nonlinear input in NFX7To assign material nonlinearity in NFX, you can choose to use

stress-strain curve or plastic hardening curve.

Stress-Strain Curve definition takes into account all the

material curves including elastic and plastic domains.

Stress-Strain Curve

Page 11


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Plastic Hardening Curve definition takes into account only the

plastic domain, so the initial value should be equal to the yield

stress.

Plastic Hardening Curve

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Nonlinear analysis Types

in NFX8

Static Analysis: time does not play any role.

Quasi-Static Analysis: is a type of dynamic analysis which

is solved using static loads.

Dynamic Analysis: takes into account the time by

considering fast changing events (load/displacements) and

inertia.

Time

Velocity,

Acceleration

Time

Velocity,

Ac

celeration

TimeVelocityorAcceleration

Page 13


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Nonlinear Static

Nonlinear Quasi-Static

Nonlinear Implicit Dynamic

Used to solve true static

equilibrium

Nonlinear Explicit Dynamic

Used to solve true dynamicequilibrium

Sequential Nonlinear

Implicit + Explicit Coupled

In Implicit analysis, the calculation of current quantities in one time

step is based on the quantities calculated during the previous time step.

This is called the Euler Time Integration Scheme. Using this scheme,

the solution remains stable even if large time steps are taken. This is

also called an unconditionally stable scheme. The disadvantage is thatthis algorithm requires you to inverse the stiffness matrix and this is

computationally intensive, especially when nonlinearities are present.

In Explicit analysis, the inversion of the complex stiffness matrix can

be avoided, and only the mass matrix [M] has to be inverted. When

lower order elements are used (always recommended in explicit), the

mass matrix is a lumped matrix, or a diagonal matrix, whose inversion

is a single step process, hence this is very easily done. Thedisadvantage is that the Euler Time integration scheme is not used in

explicit, and thus the solution is not unconditionally stable and very

small time steps have to be used.

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Static

Structural problems Metal forming Impact problems

IMPLICIT METHOD

EXPLICIT METHOD

In midas NFX all of the Static, Quasi-Static, Dynamic

analysis types can be performed in the functions for the

problem considered

Quasi-Static Dynamic

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Examples9

High speed solenoid driven rivet simulation

- Nonlinear Explicit Analysis

Page 17


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Now you are

ready to go !

Please contact us if you have any

questions during your trial:

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