![Large Strain Solid Dynamics in Total Lagrangian Framework
Ataollah Ghavamian a
(Doctoral candidate: 2016-present)
Supervisors: Prof. Antonio J. Gil a
and Dr. Chun Hean Lee a
in collaboration with Prof. Laurent Stainier b
and Prof. Javier Bonet c
(a) Swansea University (b) ´Ecole Centrale de Nantes (c) University of Greenwich
Motivation
Objectives:
Introduce a robust Total Lagrangian computational framework
to solve highly non-linear problems.
Introduce a unified modeling framework for thermoelasticity.
Develop a fast and efficient low order numerical scheme.
Key features:
• Upwinding stabilisation through Riemann solver.
• A vertex-centered Finite Volume Method (FVM) and Smooth
Particle Hydrodynamics (SPH) schemes.
• Explicit Runge-Kutta time integrator.
Novelties:
Alleviating the shortcomings of standard displacement-based
FEM/FVM(linear tedrahedral elements)/SPH formulations:
Equal order of convergence for strains and stresses.
Excellent performance in bending and shock dominated
scenarios.
No volumetric locking in nearly incompressible materials.
No tensile instability/spurious pressure oscillations.
Governing equations
First order conservation laws
Hyperbolic differential form: ∂U
∂t + ∂FI
∂XI
= S, ∀I = 1, 2, 3
Jump condition: c U = FN = FINI
U =
p
F
H
J
E
; FN = −
P N
1
ρ0
p ⊗ N
F 1
ρ0
p ⊗ N
H : 1
ρ0
p ⊗ N
1
ρ0
p · (P N) − Q · N
; S =
f0
0
0
0
s
Material model/EOS: Nearly incompressible neo-Hookean/Mie-Gr¨uneisen.
Numerical methodologies
VCFVM (left) and SPH(right)
dpa
dt
=
Aa
Va
ta
B + fa
0 −
1
Va
b∈Λb
a
P Ave
Cab + D(pa);
dF a
dt
=
1
Va
b∈Λb
a
pAve
ρ0
⊗ Cab;
dHa
dt
=
1
Va
F a
b∈Λb
a
pAve
ρ0
⊗ Cab;
VCFVM : Cab := Cab.
SPH : Cab := 2VaVb
˜ 0
˜Wb(Xa).
dJa
dt
=
1
Va
Ha :
b∈Λb
a
pAve
ρ0
⊗ Cab + D(Ja);
dEa
dt
=
1
Va
b∈Λa
1
ρ0
P T
p
Ave
− QAve
· Cab + D(Ea).
• Interface flux across discontinuity
through acoustic Riemann solver:
FC
N = FAve
N + FStab
N
=
1
2
[FN (Ua) + FN (Ub)]
Unstable flux
+
1
2
|AN | (U+
f − U−
f )
Upwinding stabilisation
n−
n+
n−
n+
c−
s
c+
s
c+
pc−
p
Time t
Figure 3: Contact mechanics (To be replaced!!!)
(23a) can be reduced to
dpa
dt
=
1
Va
Ea +
1
Va b
a
a
1
P Ave
Cab; P Ave
=
b
V (t)
V (t)a
b
Va
φ (X, t)
φ (X, t)
Vb
Time t = 0
Z, z
Y, y
X, x
−N
+N
Numerical results (VCFVM and SPH)
Shock scenario Convergence
Conservation
Robustness Plasticity
Tensile instability Pressure instability
Artificial Compressibility
Honeycomb-like structure Thin-walled cylinder
Future work
Development and implementation of an adapted Roe
Riemann solver in order to accurately capture a shock
response.
Extension of in-house software to include thermal effects
Formulation of enhanced Roe Riemann solver to account
for severe thermal shocks and interactions between several
materials
References
1. C. H. Lee, A. J. Gil, A. Ghavamian and J. Bonet. A
Total Lagrangian upwind Smooth Particle Hydrodynamics
algorithm for large strain explicit solid dynamics.
Submitted to CMAME (Under review).
2. M. Aguirre, A. J. Gil, J. Bonet and C. H. Lee. An upwind
vertex centred finite volume solver for Lagrangian solid
dynamics. JCP, 300, 387–422, 2015.
Funding and Collaboration:Contact info: Ataollah Ghavamian
Twitter: @ATAOLLAH–GH
E-mail: a.ghavamian@swansea.ac.uk
Youtube channel: Large Strain Computational Solid Dynamics](https://image.slidesharecdn.com/posterzcceataollah-180930190218/85/Poster-Presentation-1-320.jpg)
Recommended
Recommended
More Related Content
What's hot
What's hot (20)
Similar to Poster Presentation
Similar to Poster Presentation (20)
Recently uploaded
Recently uploaded (20)
Poster Presentation
- 1. Large Strain Solid Dynamics in Total Lagrangian Framework Ataollah Ghavamian a (Doctoral candidate: 2016-present) Supervisors: Prof. Antonio J. Gil a and Dr. Chun Hean Lee a in collaboration with Prof. Laurent Stainier b and Prof. Javier Bonet c (a) Swansea University (b) ´Ecole Centrale de Nantes (c) University of Greenwich Motivation Objectives: Introduce a robust Total Lagrangian computational framework to solve highly non-linear problems. Introduce a unified modeling framework for thermoelasticity. Develop a fast and efficient low order numerical scheme. Key features: • Upwinding stabilisation through Riemann solver. • A vertex-centered Finite Volume Method (FVM) and Smooth Particle Hydrodynamics (SPH) schemes. • Explicit Runge-Kutta time integrator. Novelties: Alleviating the shortcomings of standard displacement-based FEM/FVM(linear tedrahedral elements)/SPH formulations: Equal order of convergence for strains and stresses. Excellent performance in bending and shock dominated scenarios. No volumetric locking in nearly incompressible materials. No tensile instability/spurious pressure oscillations. Governing equations First order conservation laws Hyperbolic differential form: ∂U ∂t + ∂FI ∂XI = S, ∀I = 1, 2, 3 Jump condition: c U = FN = FINI U = p F H J E ; FN = − P N 1 ρ0 p ⊗ N F 1 ρ0 p ⊗ N H : 1 ρ0 p ⊗ N 1 ρ0 p · (P N) − Q · N ; S = f0 0 0 0 s Material model/EOS: Nearly incompressible neo-Hookean/Mie-Gr¨uneisen. Numerical methodologies VCFVM (left) and SPH(right) dpa dt = Aa Va ta B + fa 0 − 1 Va b∈Λb a P Ave Cab + D(pa); dF a dt = 1 Va b∈Λb a pAve ρ0 ⊗ Cab; dHa dt = 1 Va F a b∈Λb a pAve ρ0 ⊗ Cab; VCFVM : Cab := Cab. SPH : Cab := 2VaVb ˜ 0 ˜Wb(Xa). dJa dt = 1 Va Ha : b∈Λb a pAve ρ0 ⊗ Cab + D(Ja); dEa dt = 1 Va b∈Λa 1 ρ0 P T p Ave − QAve · Cab + D(Ea). • Interface flux across discontinuity through acoustic Riemann solver: FC N = FAve N + FStab N = 1 2 [FN (Ua) + FN (Ub)] Unstable flux + 1 2 |AN | (U+ f − U− f ) Upwinding stabilisation n− n+ n− n+ c− s c+ s c+ pc− p Time t Figure 3: Contact mechanics (To be replaced!!!) (23a) can be reduced to dpa dt = 1 Va Ea + 1 Va b a a 1 P Ave Cab; P Ave = b V (t) V (t)a b Va φ (X, t) φ (X, t) Vb Time t = 0 Z, z Y, y X, x −N +N Numerical results (VCFVM and SPH) Shock scenario Convergence Conservation Robustness Plasticity Tensile instability Pressure instability Artificial Compressibility Honeycomb-like structure Thin-walled cylinder Future work Development and implementation of an adapted Roe Riemann solver in order to accurately capture a shock response. Extension of in-house software to include thermal effects Formulation of enhanced Roe Riemann solver to account for severe thermal shocks and interactions between several materials References 1. C. H. Lee, A. J. Gil, A. Ghavamian and J. Bonet. A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics. Submitted to CMAME (Under review). 2. M. Aguirre, A. J. Gil, J. Bonet and C. H. Lee. An upwind vertex centred finite volume solver for Lagrangian solid dynamics. JCP, 300, 387–422, 2015. Funding and Collaboration:Contact info: Ataollah Ghavamian Twitter: @ATAOLLAH–GH E-mail: a.ghavamian@swansea.ac.uk Youtube channel: Large Strain Computational Solid Dynamics