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UID:event-5@tuemeche.nl
DTSTAMP:20261007T235033Z
DTSTART;TZID=Europe/Amsterdam:20261112T133000
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SUMMARY:A physics-based model order reduction framework for nonlinear con
 tact problems
DESCRIPTION:Speaker: Phani Ram Babbepalli (TU/e)\nHost: Olaf van der Slui
 s\n\nIn many engineering applications\, Finite Element (FE) models are vi
 tal for simulating real-world phenomena. However\, resolving complex geom
 etries or capturing nonlinear behaviour often makes these FE models compu
 tationally expensive. This challenge is particularly critical in scenario
 s that require repeated simulations\, such as design optimisation\, param
 etric studies\, or uncertainty quantification. In cases such as digital t
 win applications\, near-real-time simulations are needed\, further increa
 sing the computational burden. Model Order Reduction (MOR) techniques aim
  to address these challenges by reducing the dimensionality of the origin
 al Full Order Model (FOM)\, thereby producing a Reduced Order Model (ROM)
  that is significantly smaller and computationally more efficient\, while
  retaining the core physics of the FOM.\n\nMost conventional MOR techniqu
 es are data-driven. The most widely used among them\, Proper Orthogonal D
 ecomposition (POD)\, depends on the simulation data of the very FOM it se
 eks to reduce. While effective for interpolation within the well-sampled 
 parameter space\, POD is generally unreliable for extrapolation to unseen
  parameter ranges. As an alternative\, the primary objective of this thes
 is is to develop a physics-based MOR framework that does not rely on any 
 training data. The proposed approach utilises Modal Derivatives (MDs)\, w
 hich are the first-order derivatives of vibration modes\, and has been de
 monstrated to capture nonlinear behaviour within a reduced-order basis. I
 n this thesis\, this framework is adapted to address quasi-static geometr
 ically nonlinear solid mechanics and unilateral finite deformation contac
 t problems. \n\nInitially\, in Chapter 2\, the concept of MDs is explaine
 d in detail and applied to quasi-static geometrically nonlinear problems.
  To ensure an orthogonal projection and\, in turn\, numerical stability o
 f the reduction\, these MDs are orthogonalised using the modified Gram-Sc
 hmidt process. An online greedy selection is then employed to identify th
 e most significant orthogonalised MDs\, achieving an efficient reduction.
  This approach is validated through various test cases\, demonstrating it
 s validity and effectiveness in different scenarios.\n\nChapter 3 extends
  this framework to handle unilateral finite deformation contact problems 
 where contact constraints are enforced using the Lagrange multipliers. In
  addition to the orthogonalisation and greedy basis selection strategies 
 introduced earlier in Chapter 2\, an exclusion domain is introduced\, bas
 ed on the location of maximum shear stress from Hertzian Contact theory. 
 Within this exclusion domain\, the displacement degrees of freedom\, alon
 g with the Lagrange multipliers enforcing the contact constraints\, are m
 aintained at full FE resolution. In contrast\, the remaining displacement
  degrees of freedom are reduced using the earlier framework. This hybrid\
 , MD-based strategy performs well across various unilateral benchmark con
 tact problems\, highlighting the effectiveness of the chosen approach.\n\
 nAlthough the techniques established in Chapters 2 and 3 achieve reduced 
 dimensionality\, the resulting improvements in simulation time remain mod
 est. The principal challenge is that\, despite reducing the primary varia
 ble (displacement)\, computing the tangent stiffness matrix still require
 s integration over the entire FE mesh. This integration step remains a si
 gnificant bottleneck in reducing nonlinear FE problems. To overcome this 
 and accelerate simulations\, the developed MOR techniques are combined wi
 th a hyper-reduction strategy. Specifically\, Energy Conserving Sampling 
 and Weighing (ECSW) is employed\, which selects a subset of elements for 
 integration\, allowing for the efficient computation of reduced quantitie
 s. This combined approach is tested in the next chapter through a Bayesia
 n inference case study\, which requires multiple simulations and serves a
 s an ideal validation for the MOR framework enhanced with hyper-reduction
 . In this context\, two quasi-static\, geometrically nonlinear problems f
 rom Chapter 2 are utilised\, providing uncertainty quantification with si
 gnificantly faster runtimes.\n\nIn the penultimate chapter of the thesis\
 , all the developed tools are integrated to achieve hyper-reduction of un
 ilateral finite deformation frictional contact problems. Coulomb friction
  is incorporated into the contact formulation established in Chapter 3. T
 he ECSW hyper-reduction technique is adapted accordingly to include the e
 xclusion zone defined for reducing contact problems. Two examples are con
 sidered: first\, one of the benchmark problems used in Chapter 3 is revis
 ited to validate this improved framework. Then\, a more complex 3D case i
 nvolving the movement of a catheter inside a soft-tissue-like arterial tu
 be is examined. The results show that the proposed physics-based model or
 der reduction\, combined with ECSW\, can effectively capture complex\, no
 nlinear\, and contact phenomena with considerably lower computational cos
 t\, making it a promising tool for large-scale simulations in computation
 al mechanics. \n\nOverall\, the results presented in this thesis demonstr
 ate the potential of a fully physics-based model order reduction framewor
 k\, combined with ECSW hyper-reduction\, to efficiently simulate non-line
 ar contact FE problems. By eliminating reliance on training data\, the de
 veloped methods based on MDs achieve substantial computational savings wh
 ile preserving critical mechanical responses. The successful application 
 to both benchmark and complex use cases underscores the robustness and ve
 rsatility of the approach\, making it a promising tool for faster simulat
 ion responses.\n\nMore info: https://research.tue.nl/nl/persons/phani-ram
 -babbepalli/
LOCATION:Atlas 0.710
URL:https://tuemeche.nl/peoplepages/event.php?id=5
CATEGORIES:PhD Defense
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