CE#4006
Introduction#to#Computational#Mechanics#
of#Materials
Motivation
Assoc.Prof.Dr.>Ing.#S.#Göktepe
Necking(of(Metallic(Bar
Miehe, Apel & Lambrecht [2002]
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CE(4006(– Introduction(to(Computational(Mechanics(of(Materials
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Shear&Banding&in&Metallic&Strip
Miehe & Lambrecht [2002]
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CE&4006&– Introduction&to&Computational&Mechanics&of&Materials
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Cold%Drawing%of%Glassy%Polymers
Miehe, Göktepe & mendez [2009]
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CE%4006%– Introduction%to%Computational%Mechanics%of%Materials
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Shear&Banding&in&Geomaterials
Miehe & lambrecht [2002]
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CE&4006&– Introduction&to&Computational&Mechanics&of&Materials
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Deep$Drawing$of$Metal$Sheet
Apel [2004]
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CE$4006$– Introduction$to$Computational$Mechanics$of$Materials
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Structural(Model(vs Material(Model
Example
Necking
Axisymmetric Bar
(2<D(Continuum)
Shear(Band
Plane(Stress(– Sheet
(2<D Continuum)
Indentation(Test
Deep Drawing
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Structural Model
Plane(Strain
(2<D Continuum)
Plate/Shell Model
(3<D(Continuum)
Material Model
Elastoplasticity
at(finite(strains
Elastoplasticity
at(finite(strains
Elastoplasticity
at(finite(strains
Elastoplasticity
at(finite(strains
CE(4006(– Introduction(to(Computational(Mechanics(of(Materials
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Structural'Model
Geometrical'idealization'of'real'structural/continuum'elements
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CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Structural'Model
Structural'model'of'a'one?dimensional'bar'
Basic'equations
• Kinematics
• Balance'equations
Note'that'structural'equations'possess'no'information'about'material!
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CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Material'Model
Material'model'locally'describes'the'stress'response'through'strain
• Material'(Constitutive)'equations.'E.g.'Elasticity
Hooke’s'Element
Linear'Elasticity
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NonClinear'Elasticity
CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Material'Model
Basically,'a'material'model'may'be'elastic or'inelastic
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CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Material'Model
Typical'examples'for'inelastic material'models'are'rate@independent'
elastoplasticity and'rate@dependent'viscoelasticity
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CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Decoupling'of'Structural'and'Material'Models
In'many'cases,'it'is'possible'to'decouple'the'structural'model'from'
the'material'model'due'to'the'local'nature'of'material'equations
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CE'4006'– Introduction'to'Computational'Mechanics'of'Materials
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Main'Components'of'Computational'Model
A'computational'model'aiming'at'simulating'a'real'problem'can'be'
constructed'through'the'following'parts:
Theory
Construction of'a'structural'model
Setting5up5of a5material5model
Algorithms
Setting'up'of'a'solution method'for'the'
structural'model
Setting5up5of the5algorithmic5update5
methods5for5the5material5model
Application
Combining'the'four'modules'to'carry'out'a'computer'simulation'of'the'problem'at'hand
Experiments
Evaluate'the'results'obtained'from'the'computer'simulations'through'the'experimental'
data'in'order'to'value'the'theories'and'numerical'algorithms
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