Computational Mechanics in Support

of Additive Manufacturing

Ian Ashcroft
Contents

 3DPRG Research at Nottingham

 The role of computational
mechanics in AM research
 Examples
 SLM modelling – the effect of scan
strategy
 Multi-functional design for multi-
functional AM
 Lattices- generation, analysis &
optimisation
 Questions
3D Printing and Additive Manufacturing
Research Group (3DPRG)
 Group established in 1992
 Began AM research in 2000
 Over 100 staff and Post-Grads
dedicated to AM
 Host 2 Centres:
 Innovative Manufacturing in
AM (£6M)
 Doctoral Training in AM
(£5M)
 Current funding ~£25M
 Industrially focused, scientifically
driven
 Research focus on
underpinning work
 Spin out formed in 2015
EPSRC Centre for Doctoral Training
in AM and 3D Printing
 Specific AM training for PhD 66 PhD students over 5 years

 In partnership with Liverpool, Newcastle and Loughborough

 Bespoke training programme of AM training prior to PhD work
 Industry-base utilised for directing teaching activities
 Internships in companies
 Professional Environment Study Tours

 Industry partners providing £30-45k per student for enhanced stipend and
travel/consumables

 See Romina in the exhibition hall if you would like to get involved
 ADDED SCIENTIFIC
A University of Nottingham Spinout
Company
Added Scientific was established in 2015 as an efficient and flexible
vehicle to enable the expertise in the group to be accessed by industry.

Services include: consultancy, training and bespoke research and

development.

Areas of expertise include:

• Process Development
• Material Development
• Material Characterization and Testing
• Design and Design Systems
• Computational Modelling and Simulation

See Jaimie in the Exhibition Hall for more information

General Research Areas within
3DPRG
 Materials and Process Innovation
 New materials research – Polymer, Metallic, nano-composite
 Process innovation – New processes, process development
 AM process simulation and material modelling
 Process development of existing AM machinery
 Material Development for existing AM
 Design, Analysis and Optimisation
 Process and performance analysis
 New design methods and software
 Design Optimisation, Algorithms and Systems
 Lattice design systems
 Implementation
 Economics of AM
 Optimisation of AM systems for implementation
 The Role of Computational
Mechanics in Additive Manufacturing
The importance of computational
mechanics in AM
 AM has introduced new processes, new products and new
design potential
 Computational methods are needed to analyse these
 Applications include
 Process modelling – understanding, prediction and optimisation
 Use-phase modelling - to predict in-service performance
 Analysis based optimisation - for applications and process
 This modelling is challenging and requires the development
of new methods and computational tools
Design & Analysis Themes

Mass reduction: 48%

Topology Optimization Lattice

Simulation Meshing MFAM Design

 Modelling the Effect of Scan
Strategy in Selective Laser Melting
Luke Parry, Ricky Wildman
Motivation for work

• Cracks and distortion in SLM

builds through residual stress
• The observed dependence of
distortion on scan strategy
• The need to control this through
informed design of thermal history
and support structures

(5 x 50) mm Build
Intro: Simulation of Physical Phenomena

• Main Challenges:
– Complexity of modelling at multi-scales (spatial and
time)
– Large performance requirements
– Inclusion of various thermo/physical phenomena
• Main Assumptions:
– Microscopic powder/thermo-fluidic effects ignored
• e.g. Marangoni Flow, Rayleigh/Capillary instability
– Simple laser absorption model (e.g. no-keyhole like
effects)
– Powder shrinkage, effects of vaporisation ignored
– Effect of powder sintering ignored
 Intro: Previous Work

• In previous work we used a

thermo-mechanical finite
element analysis to
investigate the effect of
scan strategy on residual
stress generation in SLM
• It was seen that stress
distribution was dependent
on scan strategy, owing to
variations in thermal history
• The computational demand
of this method limits
application to large builds –
leading to development of a
multi-scale method
Parry, L, Ashcroft IA, Wildman RD, Understanding the effect of laser scan strategy on residual stress in
selective laser melting through thermo-mechanical simulation, Additive Manufacturing 12 (2016) 1-15.
Multiscale Modelling Methodology:
Modelling Assumptions

• Microscale effects (powder/melt /pool physics not explicitly

modelled
• A meso-scale is defined in which transient thermo-
mechanical finite element analysis is used to determine
residual stresses/plastic strains in an isolated scan region
• The manufactured part is represented by tesselating meso-
scale island ‘units’ to generate the stress field at a macro-
scale
• Validation is against full thermo-mechanical analysis at the
macro-scale and experiment
Methodology: Overview

• Three step Process

Meso-scale Pre-processing
Coupled Thermo-mechanical transient analysis Orientate tessellate ‘meso-scale’ units
Capture residual stress in ‘unit’ areas to form scalar fields representing part

Macro-Scale
Single mechanical analysis incorporating a pre-
generated fields and resolving overall part distortion
Methodology: Meso-Scale Simulation

• Commercial FE Software MSC Marc used

– Weakly coupled transient thermo-mechanical analysis
– State variable model used to track material phases
– Temperature dependent thermal and mechanical properties and
plasticity modelling
– Octree Adaptive Meshing
• Refinement along high thermal gradients / laser point
Methodology: Multi-scale Model
Methodology: Multi-scale Model

Transient thermo-mechanical Analysis

 Transient analysis performed on (5x5) mm on island
region to capture residual stress distribution

Temperature

Von Mises Stress [MPa]

Methodology: Multi-scale Model

Results extracted from meso-scale simulation to

form tesselating „unit‟
 Components extracted
 Components of Cauchy Stress 𝝈𝒊𝒋
 Equivalent Plastic Strain 𝝐𝒑
 State Variable 𝝓

Stress Field - 𝝈𝒙𝒙 Stress Field - 𝝈𝒚𝒚 Phase Field – 𝝓

Methodology: Multi-scale Model

Transformation of Island Units:

 Island fields are rotated to match orientation
 Stress components require tensor transformation
before image rotation
 𝝈′ = [𝑅] 𝝈 [𝑅]𝑇
 Rotated island units are tesselated according to the
geometry input

Rotation of Stress Tessellated Islands - 𝝈𝒙𝒙

Components for single island
Methodology: Large-Scale Analysis

• Single structural analysis pass

• Geometry independent mesh
• Stress/plastic strain fields applied
during simulation initialisation
• Single iteration of mechanical
structural analysis is performed until
convergence achieved.

Input grids assigned to stress

field instantaneously

Solid Substrate (1.8mm high)

Methodology: Numerical Experiments

• A comparison between a full

transient analysis and the multi-
scale analysis was performed

• Identify the validity of the

assumption that the thermo-
mechanical response of ‘island’
regions have negligible influence
on each other and independent
of order.

• Determine the overall

performance and accuracy of the
multi-scale analysis
Results and Discussion

Longitudinal stress remains constant

and independent of scan order

Transverse stress varies with scan

order

Von Mises stress for large-scale

analysis is skewed to lower values
Application to larger builds

Von Mises Stress[MPa]

Compressive region located

Tensile regions
pull vertically at bottom underneath centre of the part and
edges between substrate substrate
and part

σzz (Tensile) [MPa] σzz (Compressive) [MPa]

Multifunctional Design for
Multifunctional AM
Multifunctional AM
Centre Vision: To take AM beyond geometry and single materials to the
“printing” of multifunctional, multi-material components / devices / systems
in one operation.

 Further design freedom and complexity

added to the design process
 Closer to optimal system design…
Handling of interaction between cost,
mechanical, electrical, thermal etc.
to determine overall optimal solution

 Jetting process focused

 Voxel modelling environment
 Multimaterial fabrication: Ink
Jet Printing
Material Jetting
 An additive manufacturing process in which
material is selectively dispensed through a
nozzle or orifice.
 Multi-material capability

Related Projects:

 Reactive Jetting of Polymers

 Bio-printing
 Jetting Electronics
 Metaljet
 Structure-System
Multi-functional Optimization
Ajit Panesar, (Dave Brackett), Richard Hague, Ricky Wildman
Structure and System
Optimization Framework
Software for automated placement and routing

Panesar A, Brackett D, Ashcroft I, Wildman R, Hague R, Design Framework for Multifunctional Additive Manufacturing:
Placement and Routing of Three-Dimensional Printed Circuit Volumes, Journal of Mechanical Design 137 (2015)
Coupling Strategy

Test Case considered

Structural
System problem problem specification
specification: Placement and Routing
Coupling Strategy

Implementation
Combined Structure Routing

𝑆
𝐶 𝛼𝑖 + 𝜆1 × ( 𝑅 𝛼𝑖 )
𝛼𝑖 =
1 + 𝜆1
𝑅 1
𝛼𝑖 = (Unbounded)
1 + 𝑑𝑖 Initial Method

• A (normalized) weighted sum approach

• Heuristic definition for system sensitivities
• Unbounded vs Bounded

• Adaptive Scheme

𝑆 𝑆
𝐶 𝛼𝑖 + 𝜆1 × (𝜆2 × 𝑅 𝛼𝑖 ) 𝛼𝑖
𝛼𝑖 = 𝜆2 = 𝑅
1 + 𝜆1 𝛼𝑖
𝑅 1
𝛼𝑖 = (Bounded)
1 + 𝑑𝑖 New Method
Coupling Strategy

Mechanism
Coupling Strategy

The effect on optimality

Uncoupled Coupled
Magnetic-Structural Multi-functional
Optimization for Electric Motors
Michele Garibaldi, Richard Hague
Introduction

 Previous work has investigated SLM high Si steels for

potential electric motor applications
 Case study: Surface-Mount Permanent Magnet EM
 Application: aircraft starter/generator N
 Design requirements:
 Torque: 1Nm
 Speed: 10000rpm Rotor core
 Poles: 2 (design space)

37mm
Garibaldi M, Ashcroft I, Simonelli
M, Hague, R, Metallurgy of high-
silicon steel parts produced using Permanent
selective laser melting, Acta Mat magnets
110 (2016) 207-216.

S
Design Strategy

Structural Optimisation Magnetostatic Optimisation

 Elastic Strain Energy:  Magnetic Energy:

𝐸𝑠 = 𝑒 𝑑𝑉 𝐸𝑀 = 𝑒 𝑑𝑉
𝑉 𝑉
 V is the volume of the design  V is the volume of the design
space space
 e is the strain energy density  e is the magnetic energy density
 Sensitivity can be calculated  Sensitivity can be calculated
using FE form of e (BESO): using FE form of e:
𝑒𝑖 = 𝐮𝑇 𝑖 𝐊 𝑖 𝐮𝑖 𝑒𝑖 = 𝐡𝑇 𝑖 𝜇𝑖 𝐡𝑖
𝐮𝑖 is the elemental strain vector 𝐮𝑖 is the elemental strain vector
and K 𝑖 is the elemental stiffness and 𝜇𝑖 is the elemental
matrix magnetic permeability
2D Magnetostatic and Structural TO

 Combined sensitivity number (element i):

𝑤𝑠 𝑒𝑠 𝑤𝑚 𝑒𝑚
𝑒𝑠𝑚 = +
𝐸𝑠 𝐸𝑚
with 𝑤𝑠 + 𝑤𝑒 = 1

 Parametric study to design 𝑤𝑠 and 𝑤𝑚 values

 Element size: 0.2mm
 BESO filter scheme radius: 1mm
 Modify sensitivity number to guarantee symmetric solution:
average sensitivity numbers about horizontal axis
 2D Magneto-Structural TO - Results

ws=0.5, wm=0.5 ws=0.25, wm=0.75 ws=0.1, wm=0.9

Von Mises Stress

Most efficient use of material

Magnetic Induction
Towards 3D TO – Preliminary
Results
First step: 2D TO of Second step: 3D TO of solid
laminated portion portion (final Vt=50%)
2D design space
(laminated portion)

3D design space
(solid portion)
 Lattice Structures
Ian Maskery, Adeji Aremu, Meisam Abdi, (James Brennan-Craddock)
Ajit Panesar, (Dave Brackett), Ricky Wildman, Richard Hague Chris Tuck
Lattice (cellular) Structures
 Structures filled with repeating units (or
cells)
 Many cell types –different properties
 Various methods of
 Representing/generating geometry
 Conforming to complex geometry
 Skinning
 Advantages include
 Range of cell types – properties
 Light-weighting
 High surface area
 Open/closed structures
 Grading –cell, size, type, properties
 Multiple deformation mechanisms
 Ordered/random
 AM has clear advantage over other
manufacturing methods in manufacturing
lattices
 Generation, analysis and optimisation
remain difficult
 Lattices

Functionally Graded Lattices: Design, analysis and optimisation.

Graded Lattices

Error Diffusion Dithering Tessellation

Strut Surface

Maskery I, Hussey A, Panesar A, Aremu A, Tuck, C, Ashcroft I, Hague R, An investigation into

reinforced and functionally graded lattice structures, J Cellular Plastics (2016) in press
Cellular structures with variable cell size

 Dithering based method

 Used to design functionally graded
lattices where the size of the cells can be
varied. b)

 Definition of functional grading

 Error diffusion to generate dithered points
of boundary and area
 Application of connection scheme to Input grey-scale from topology
generate structure cells optimisation

c)

Brackett DJ, Ashcroft IA, Wildman RD, Hague RJM, An error diffusion based method to generate
functionally graded cellular structures, Computers and Structures 138 (2014) 102-111
 Tesselated cell structures -
Voxel based lattice method
2D voxel model 3D voxel model
 Voxel models:
White 'Void'
 More versatile than boundary pixel voxel
representation models for Grey
lattice generation pixel 'Solid'
voxel
 Synergistic with voxel based
manufacturing methods
 Offer a way to construct high
quality finite element meshes
 Can be used to write machine
files directly
 Simple to add multi-material
and multi-functionality
 Simple to assign functionality to Unit cell
voxels
 Internal complexity not memory
dependent
 Can be memory intensive
 Not good for complex surfaces
Lattice Domain Trimmed lattice
structure
Integrated design analysis
and manufacture
 A methodology has been developed to B-rep Unit cell, Domain
construct STL lattice from STL files

 Two voxelization algorithms was developed to Voxelize B-rep Voxelize B-rep

link STL file input with voxel lattice method Unit cell Domain

 Two net skin generation method have been

Unit cell Tessellation
used to improve trimmed lattice performance

Combining tessellated unit cell

 Algorithms have been developed to convert
with domain
voxel model into STL file and finite element
mesh
Skin generation

Combine skin with Lattice

FEA Trimmed
B-rep
Machine
File
Flatt Pack Software
 Flatt
GUI Pack Software

Create specimens or complete

components

5 step process for lattice design

 Flatt
GUI Pack Software

Control the 3D density profile

Choose from 16 lattice

cell types
 Flatt
GUI Pack Software

Optional lattice skin

View 3D density profile

before lattice creation
Flatt Pack Software

Functional grading
of density and cell type
Flatt Pack Software

Custom density map

from any greyscale image
(2D or 3D) such as a density
based topology optimisation
Flatt Pack Software

Custom geometry
based on STL input
Flatt Pack Software

Lattice skin
for increased stiffness and protection of
the lattice cells
Flatt Pack Software

STL output
+ sliced bitmaps
+ 3D voxel array
Flatt Pack Software

Evaluation copy

If you would like a free

evaluation copy of Flatt
Pack, please contact me
or give your details to
Jamie at the Added
Scientific Exhibition stand
Concluding Remarks
Summary

 Additive Manufacturing has opened up new opportunities

for the manufacture, design and optimization of products
 Computational mechanics is an essential tool in
 Understanding, predicting and optimizing processes
 Predicting the performance of manufactured parts in-service
 Providing the foundations for new design and optimization methods
tailored for AM processes
 Although computational mechanics is already being used I
these applications, modelling is challenging and current
tools and methods not ideal, hence, there is scope for
further research in developing AM specific tools and
methods.
Acknowledgements

 Funding Bodies: EPSRC, TSB/INNOVATE UK

 Past and Present PhD Students and RAs
Ian Maskery, Ajit Panesar, Luke Parry, Michele Garibaldi, James
Brennan-Craddock, Adeji Aremu, Meisam Abdi, Dave Brackett
 Academic colleagues
Richard Hague, Chris Tuck, Ricky Wildman, Ruth Goodridge,
Phil Dickens
 Thank you !

Any Questions ?

Ian.ashcroft@nottingham.ac.uk
www.nottingham.ac.uk/3dprg