Library · Simulation & modelling

What Finite Element Modeling got wrong, from 61 theses

Summary written by a model from the records below: The records describe various attempts to apply finite element modeling across structural mechanics, geotechnical media, contact dynamics, and coupled transport problems. Many simulations encountered fundamental failures including prohibitive computational expense, solver divergence under mesh distortion, artificial element stiffening, and difficulties capturing discrete fracture or dynamic deformations. These records come from graduate theses, 2021 to 2026, each labeled with its degree where the repository states it, and each links to its thesis. They were extracted by language models reading the full text, so treat each as a lead to read, not a verdict.

61
theses
19
institutions
62
failure records
7
failure modes

Plus 9 problems the authors left open, listed at the end.

Failure modes, by theses reporting them

Select a mode to jump to its records.

Prohibitive computational cost impedes fine mesh simulations and iterative workflows
17
17 theses · 12 institutions · 17 records
Mesh distortion and severe non-linearities trigger solver divergence and numerical instability
9
9 theses · 6 institutions · 10 records
Continuum damage models fail to represent discrete fractures and localized cracking
10
10 theses · 7 institutions · 10 records
Multiphysics transport models suffer from decoupling errors and convective instabilities
7
7 theses · 5 institutions · 7 records
Low-order and coarse element discretizations induce artificial stiffening and stress errors
7
7 theses · 6 institutions · 7 records
Simplified linear and static assumptions fail to predict dynamic and large-deflection behavior
8
8 theses · 5 institutions · 8 records
Inappropriate boundary conditions introduce numerical singularities and spurious structural buckling
3
3 theses · 2 institutions · 3 records

Prohibitive computational cost impedes fine mesh simulations and iterative workflows

17 theses · 12 institutions

Standard and three-dimensional solid finite element analyses require excessive runtime, memory, and licensing resources during optimization, inverse parameter estimation, and real-time execution. These high-fidelity formulations become intractable when resolving fine geometric details or repeated forward solutions compared to analytical, boundary, or finite difference alternatives.

Lost to a baseline

Pure-macro finite element model took 58.3 hours to solve the perforated plate problem, whereas the FFT-based multiscale model solved it in 138 minutes.

Multiscale modelling of the material degradation and failure in complex composite structures · Imperial · PhD

Lost to a baseline

Finite Element / strain parameterization method by Boyer/Renda took 32 hours 17 minutes for 10 s simulation of motion (and 48 minutes for a 2-mode model) vs. seconds for the proposed FDM approach

Geometric Recursive Dynamic Modelling and Simulation of Soft Robotic Systems · Carleton University · Master's

Considered and rejected

Considered and rejected: Rejected direct standard finite-element PDE solvers (e.g. FreeFem++) in favor of semi-analytical Green's function methods due to computational speed constraints

Plant calcium dynamics: signalling the way to sustainable food production · Nottingham · PhD

Considered and rejected

Considered and rejected: Rejected finite element method (FEM) iterations and numerical simulation due to high computational cost (several hours vs. <100 seconds for analytical).

Prediction of Part Quality in Laser Powder Bed Fusion Metal Additive Manufacturing · Georgia Tech · PhD

Considered and rejected

Considered and rejected: Rejected 3D solid continuum finite elements in favor of Timoshenko beam elements to model full-scale 3D elastic structures computationally efficiently with fewer degrees of freedom.

Topological States in Ordered and Disordered Mechanical Metamaterial · University of Washington · PhD

Considered and rejected

Considered and rejected: Rejected high-fidelity 3D solid continuum finite element models for online filtering because explicit solvers with fine meshes and tiny time steps exacerbate computational burden and convergence issues

Input-State Estimation of Inelastic Structural Systems: Theoretical Framework and Experimental Validation · Georgia Tech · PhD

Tried and failed

direct high-resolution volumetric scan to mesh conversion applied to structural finite element analysis. Outcome: infeasible cost. Reason: prohibitive computational expense, geometric feature loss, and required suboptimal tetrahedral elements

Frequency Response Modeling of Additive Friction Stir Deposition Parts with Print Defects · Virginia Tech · Master's

Tried and failed

quadratic basis functions in finite element method applied to dynamic frictional contact simulation. Outcome: infeasible cost. Reason: numerical integration for stiffness and contact matrices was overly complex and computationally costly

Predicting the Dynamics of Injection-Induced Earthquakes · Virginia Tech · Doctorate

Tried and failed

finite element method for inverse parameter estimation applied to resonant ultrasound spectroscopy of irregular crystals. Outcome: too slow. Reason: fine mesh requirements and high-dimensional parameter space made iterative forward solves computationally prohibitive

Cutting through the noise in quantum materials with ultrasound · Cornell · PhD

Tried and failed

direct 3D finite element simulation applied to cutting of soft bodies. Outcome: infeasible cost. Reason: requires roughly 10^6 tiny elements near moving blade edges

Modeling of fruit and vegetable cutting: Analysis, algorithms, and robot experiments · Iowa State · PhD

Tried and failed

global optimization with high-fidelity finite element simulations applied to axisymmetric nonlinear metamaterial dynamics. Outcome: too slow. Reason: computational cost of repeated nonlinear finite element runs prevented convergence within reasonable runtime limits

Nonlinear Dynamics in Metamaterials under Elastic and Plastic Excitation and Spectral Submanifold Parameterization · Georgia Tech · PhD

Tried and failed

Finite element function interpolation applied to Large regular multidimensional grid data. Outcome: infeasible cost. Reason: Interpolating large grid panels into finite element function spaces is computationally excessive compared to finite differences

Parameter selection in seismic data analysis problems · UT Austin · PhD

Considered and rejected

Considered and rejected: Rejected Finite Element Analysis (FEA) structural stress analysis for redesign due to high computational expense.

The Development of Intelligent Assessment and Re-Design Recommender Systems for Additive Manufacturing · University at Buffalo · PhD

Considered and rejected

Considered and rejected: Rejected weak finite element formulation for state and adjoint ODEs because it required computationally prohibitive implicit time-stepping systems at each layer.

Computational mathematics approaches to deep neural network architecture design · UT Austin · PhD

Considered and rejected

Considered and rejected: Rejected relying solely on finite element analysis (FEA) for design space exploration due to prohibitive temporal penalty in the early design stage

Design optimization of two-way spanning concrete systems for low-carbon, context-informed construction · MIT · PhD

Considered and rejected

Considered and rejected: Finite Element Models (FEM) rejected due to excessive computational cost, lengthy processing times, heavy hardware demands, and dependence on expensive external proprietary licenses.

Modelling of the removal of multi-layer coatings using high pressure water jet and the study of its material removal mechanisms · Nottingham · PhD

Considered and rejected

Considered and rejected: Rejected relying solely on finite-element simulations for displacement CNN training due to extreme computational expense and fixed focal geometry biases.

A 3-D Multiparametric Ultrasound Elasticity Imaging System for Targeted Prostate Biopsy Guidance · Duke · Doctorate

Mesh distortion and severe non-linearities trigger solver divergence and numerical instability

9 theses · 6 institutions

Iterative and linear solvers fail to converge when large deformations, high aspect ratios, and skew element distortions compromise mesh geometry. Unstabilized dynamic adaptation, contact non-linearities, and extreme material pressures lead to singular or ill-conditioned systems that terminate simulations unexpectedly.

Tried and failed

standard boundary conditions in finite element simulation applied to large displacement electromechanical structures. Outcome: did not converge. Reason: severe mesh distortion during large displacements prevented convergence

ADVANCED FREQUENCY OUTPUT RESONANT MEMS ACCELEROMETERS · Georgia Tech · PhD

Tried and failed

extreme finite element mesh refinement applied to large-deformation contact mechanics simulations. Outcome: unstable. Reason: severe mesh distortion caused automatic simulation termination

Biomechanics of soft tissue-device interactions-an investigation into skin and arterial tissue · Imperial · PhD

Tried and failed

omitting thermodynamic consistency terms in solver formulation applied to high-order finite element multiphase simulations. Outcome: did not converge. Reason: linear iterative solvers diverged under higher-order basis functions and fine meshes without consistency terms

Modeling high density ratio two-phase and three-phase flows using Cahn-Hilliard Navier-Stokes equations · Iowa State · PhD

Tried and failed

Mixed discontinuous Galerkin control volume finite element method applied to Multiphase flow on highly anisotropic meshes. Outcome: did not converge. Reason: Pressure solver failed to converge due to severe mesh element aspect ratio distortion

Numerical modelling of wave-structure interaction with rubble-mound breakwaters and dynamic mesh optimisation · Imperial · PhD

Tried and failed

Unstabilized finite element solver on anisotropic meshes applied to advection-diffusion equations. Outcome: did not converge. Reason: Lack of numerical stabilization causes linear solver failure on highly stretched, anisotropic mesh elements.

Mesh adaptation and adjoint methods for finite element coastal ocean modelling · Imperial · PhD

Tried and failed

stabilization parameter tuning with adaptive mesh refinement applied to multiphase flow finite element simulation. Outcome: did not converge. Reason: stabilization parameter tuning failed to converge when combined with dynamic mesh adaptation

Modeling high density ratio two-phase and three-phase flows using Cahn-Hilliard Navier-Stokes equations · Iowa State · PhD

Tried and failed

implicit finite element modeling with self-contact applied to cellular metamaterial lattice compression. Outcome: did not converge. Reason: solver diverged under severe deformation due to extensive self-contact during structural collapse

Triply Periodic Minimal Surface Lattices for Mechanically Tuning Structures and Designing Multifunctional Devices · Cornell · PhD

Tried and failed

descent-based optimization with finite element simulations applied to geometric field grading optimization. Outcome: did not converge. Reason: mesh regeneration introduced numerical noise and artificial local minima near singularities

Bayesian Optimization of PCB-Embedded Electric-Field Grading Geometries for a 10 kV SiC MOSFET Power Module · Virginia Tech · Master's

Tried and failed

finite element mesh refinement applied to contact eigenvalue stability analysis. Outcome: did not converge. Reason: Mesh refinement altered contact stiffness distribution, eliminating previously identified unstable modes while introducing new spurious frequencies.

An investigation of brake squeal from a coupled tribology and dynamics perspective · Imperial · PhD

Tried and failed

finite element analysis with hyperelastic material models applied to pneumatic soft continuum robot grasping. Outcome: did not converge. Reason: numerical instability and breakdown of hyperelastic constitutive models under high actuation pressures

Modeling, Planning, and Learning for Soft Robots in Human-Centric, Contact-Rich Environments · Harvard · PhD

Continuum damage models fail to represent discrete fractures and localized cracking

10 theses · 7 institutions

Continuum finite element assumptions and local damage formulations struggle to capture discrete crack paths, dynamic fracture process zones, and rock fragmentation. Relying on perfect bonding, uniform fine meshes, or standard cohesive zones produces pathological mesh dependencies and fails to capture confining pressure effects or shear bands.

Tried and failed

perfect bond assumption in finite element modeling applied to post-tensioned concrete shear failure prediction. Outcome: did not generalise. Reason: neglecting interface slip failed to capture localized stress concentrations causing web crushing

Shear behavior of post-tensioned girder containing grouted and ungrouted ducts · UT Austin · PhD

Tried and failed

linear elastic line tension models applied to crack front deformation prediction. Outcome: did not generalise. Reason: neglects the finite process zone size present during dynamic fracture

Friction and fracture: richness and complexity in dynamic rupture · EPFL · PhD

Tried and failed

Continuum finite element method applied to Dynamic rock indentation and fracture propagation. Reason: Inability to represent discrete radial crack propagation, crater enlargement, and fragment coalescence

High-fidelity modelling of impact breakage in percussive drilling · Imperial · PhD

Tried and failed

mesh-size dependent damage initiation strain assignment applied to crack-tip finite element fracture modeling. Outcome: no signal. Reason: Assigning size-dependent parameters across variable mesh shapes yielded virtually no difference in simulated mechanical response

A new approach to characterisation of the fracture behaviour of solid materials · Imperial · PhD

Considered and rejected

Considered and rejected: Rejected standard finite element method (FEM) due to ill-conditioning and singularities at stress-focusing cusps in very thin sheets.

Buckling, wrinkling, and crumpling of simulated thin sheets · Harvard · PhD

Considered and rejected

Considered and rejected: Rejected continuum/finite element models because they idealize masonry into a homogeneous material, simplifying crack paths and joint behavior

Seismic Analysis of Unreinforced Masonry Structures with Plan Irregularities · Carleton University · Master's

Considered and rejected

Considered and rejected: Rejected using uniform fine finite element mesh (h <= lc/2) due to intractability in 3D CPFEM without prior crack path knowledge.

MICROMECHANICAL MODELING OF DEFORMATION AND FRACTURE IN POLYCRYSTALLINE MICROSTRUCTURES · Johns Hopkins · PhD

Tried and failed

direct discontinuous gradient computation without nodal projection applied to coupled continuous-discontinuous finite element formulation. Outcome: worse than baseline. Reason: direct element-wise gradient evaluation was less accurate than consistent full nodal projection averaging

Coupled continuous/discontinuous Galerkin solver for hurricane storm surges and compound floods · UT Austin · PhD

Tried and failed

Local continuum damage modeling in finite elements applied to strain localization and fragmentation simulation. Outcome: unstable. Reason: Pathological mesh dependency caused artificial shear band narrowing and spurious force increases upon mesh refinement

Oral processing of micro-aerated chocolates: a computational mechanics, rheological and tribological study · Imperial · PhD

Tried and failed

standard cohesive zone modeling in finite elements applied to geomaterial shear failure under confining pressure. Outcome: did not generalise. Reason: failed to capture loading-history-dependent stiffness degradation and confining pressure dependence in shear

Numerical modeling of discontinuous processes in geomaterials and geosystems · Georgia Tech · PhD

Multiphysics transport models suffer from decoupling errors and convective instabilities

7 theses · 5 institutions

Decoupling thermal, hydraulic, and structural interactions prevents finite element models from tracking transient consolidation, void ratios, and pore pressure dissipation. Standard continuous formulations also introduce spurious oscillations, numerical diffusion, and mass conservation violations across sharp permeability contrasts and convective regimes.

Considered and rejected

Considered and rejected: Rejected using Finite Element Method (FEM) continuum models for soil, because FEM fails to capture soil flowability, separation, and reattachment during tyre interaction.

Evaluation of off-road uninhabited ground vehicle mobility using discrete element method and scalability investigation · Cranfield · PhD

Considered and rejected

Considered and rejected: Rejected finite element tools (e.g., COMSOL) in favor of finite volume methods (Delphin) due to FEM instability and inaccuracy across the non-linear overhygroscopic moisture retention and liquid conductivity range.

Evaluating Uncertainty in Hygrothermal Modelling of Heritage Masonry Buildings · Carleton University · PhD

Tried and failed

incremental 2D finite element modeling applied to transient multi-phase excavation response. Outcome: no signal. Reason: incremental 2D numerical analysis failed to capture transient geotechnical ground responses during excavation

Transient ground response during and after tunnelling · Imperial · PhD

Tried and failed

multiphysics numerical finite element fluid-thermal modeling applied to subsurface post-impact hydrothermal system evolution. Reason: failed to behave in a geologically reasonable manner under initial setup

Geophysical insights into the crater subsurface at the Chicxulub and Ries impact craters · UT Austin · PhD

Tried and failed

fully decoupled multiphysics finite element simulation applied to thermo-active pile foundations in clay. Outcome: worse than baseline. Reason: ignoring transient consolidation and heat transfer interactions severely overestimated thermally-induced structural stresses

Numerical modelling of complex thermo-hydro-mechanical interactions in thermo-active pile foundations · Imperial · PhD

Tried and failed

continuous Galerkin finite element method applied to heterogeneous porous media consolidation. Outcome: unstable. Reason: lack of local mass conservation without stabilization across high permeability contrasts

Effective finite element discretization schemes for simulating coupled multiphysics in porous media · UT Austin · PhD

Considered and rejected

Considered and rejected: Rejected using finite elements for the resuspension step due to excessive inter-grid numerical diffusion compared to cell-based finite differences.

Numerical simulation of sediment dynamics with free surface flows · EPFL · PhD

Low-order and coarse element discretizations induce artificial stiffening and stress errors

7 theses · 6 institutions

Linear tetrahedral elements, low-order shells, and coarse meshes exhibit excessive artificial stiffness and slow convergence rates in bending and torsional domains. These representations underestimate peak stresses and displacement gradients, causing structural constraint violations during design evaluation.

Tried and failed

linear shell finite element modeling applied to structural stress prediction under high loads. Reason: linear elements failed to capture nonlinear geometric effects under high stress yielding significant prediction errors

A Flexible Methodology for Analysis and Optimization of Unconventional Wing Structural Geometries Using a Computationally Efficient Aeroelastic Model · Georgia Tech · PhD

Considered and rejected

Considered and rejected: Rejected linear finite elements for anchor and clamping components subjected to dominant bending (e.g. at the anchor loading end and top flange clamped area) in favor of 3D quadratic reduced-integration solid elements due to stress inaccuracies.

Multiaxial fatigue behavior and strengthening of riveted double-angle connections in steel bridges using prestressed CFRP rods · EPFL · PhD

Tried and failed

Linear tetrahedral finite elements applied to structural dynamic calculations. Outcome: worse than baseline. Reason: Elements are overly stiff in coarse meshes and exhibit very slow convergence rates

Computational nonlinear vibration analysis for distributed geometrical nonlinearities in structural dynamics · Imperial · PhD

Tried and failed

coarse mesh discretization for structural finite element analysis applied to foundation pile deflection modeling. Reason: mesh resolution was too low to capture steep displacement gradients along the structural depth

Data Driven Early Stage Design Support for Offshore Wind Farms · University College Dublin · PhD

Tried and failed

first-order finite element reduced order modeling applied to stress-constrained topology optimization. Outcome: did not generalise. Reason: First-order elements underestimated peak stresses, leading to designs that violated constraints under higher-order validation.

Topology optimization and uncertainty quantification using component-wise reduced order modeling · UT Austin · PhD

Tried and failed

surrounding simulation domain with elastic buffer jackets applied to finite element elasticity on voxelized geometries. Outcome: did not generalise. Reason: failed to consistently mitigate numerical stiffening across varying porosity levels

Applicability of theoretical rock physics models in porous rock microgeometries : a computational modeling study · UT Austin · PhD

Considered and rejected

Considered and rejected: Rejected linear tetrahedral elements for finite element modeling of bending-dominated lattice structures due to inaccurate displacement field representations.

Analysis of defects in additively manufactured lattice structures · Nottingham · PhD

Simplified linear and static assumptions fail to predict dynamic and large-deflection behavior

8 theses · 5 institutions

Static and linear small-displacement formulations fail to capture time-varying deformation evolutions, impulse load deflections, and membrane folding. These models underestimate member deflections and miss higher-order plastic buckling modes observed under severe loading conditions.

Tried and failed

static finite element analysis applied to time-varying vessel wall displacement. Outcome: worse than baseline. Reason: failed to capture time-varying evolution of deformation, under-predicting peak displacement

Computational haemodynamic analysis of thoracic endovascular aortic repair for complex aortic arch diseases · Imperial · PhD

Tried and failed

geometrically and materially nonlinear finite element analysis applied to clad steel frame structures. Outcome: worse than baseline. Reason: premature member buckling caused severe capacity underprediction compared to experimental tests and geometrically linear analysis

Simulation and behaviour of single-span steel portal frames · Imperial · PhD

Tried and failed

omitting fillet geometry in finite element models applied to cross-section torsional stiffness estimation. Outcome: worse than baseline. Reason: neglecting root fillets led to significant discrepancies between numerical and analytical torsional stiffness

Stability and design of steel angle section members · Imperial · PhD

Tried and failed

static finite element structural analysis applied to impulse load pavement deflection modeling. Outcome: did not generalise. Reason: static models consistently overestimated field deflections under impulse loading, requiring transient dynamic analysis instead

Deflection Based Design Method for CRCP Whitetopping and Unbonded Overlays · Texas Tech · PhD

Tried and failed

linear static finite element analysis applied to truss structure deflection modeling. Outcome: worse than baseline. Reason: linear static models exhibited artificial stiffness leading to underestimated deflections under loading

Active Force Correction of Off-Nominal Structures Using Intelligent Scaffolding · Virginia Tech · Doctorate

Tried and failed

geometric nonlinear large displacement finite element analysis applied to single-lap joint stress analysis. Outcome: worse than baseline. Reason: provided minimal accuracy improvement over linear small displacement formulations while increasing computational cost

THE STRENGTH OF BRAZED SINGLE-LAP JOINTS · Cornell · PhD

Tried and failed

eigenvalue buckling finite element analysis applied to stiffened panels under plastic deformation. Outcome: did not generalise. Reason: linear eigenvalue analysis failed to capture higher-order plastic buckling modes observed in experiments

Buckling analysis of stiffened panels in creep age forming · Imperial · PhD

Considered and rejected

Considered and rejected: Linear deformation finite element model rejected because it could not capture tracheal shrinking and posterior membrane folding observed experimentally compared to large deflection non-linear model

Development of Adhesive Hydrogels for Tracheomalacia Treatment · EPFL · PhD

Inappropriate boundary conditions introduce numerical singularities and spurious structural buckling

3 theses · 2 institutions

Applying rigid encastre constraints across narrow sections produces artificial stress singularities that prematurely exceed material strength limits. Furthermore, unconstrained boundary meshes and infinite periodic assumptions induce premature collapse, spurious frequencies, or parasitic boundary oscillations.

Considered and rejected

Considered and rejected: Rejected using purely Eulerian velocity boundary conditions (V_wall(x,t)) for deforming elastic channels because they fail to capture finite longitudinal strain, material periodicity, and fluid-structure coupling.

MECHANISMS OF FLOW GENERATION IN ELASTIC VESSELS · Penn · PhD

Tried and failed

finite element method electrostatic field simulation applied to sharp electrode boundaries and corners. Reason: meshing limitations at sharp corners and edges caused significant numerical inaccuracies compared to boundary methods

Fine particle transport and separation using electrostatic travelling wave methods · Imperial · PhD

Tried and failed

finite element simulation with unconstrained boundary meshes applied to musculoskeletal biomechanics models. Outcome: unstable. Reason: merged mesh geometries and lack of tendon constraints caused structural buckling under compressive loads

Characterising the neck motor system of the blowfly · Imperial · PhD

Left open by the authors

Problems the authors named and did not get to.

Left open

Develop a predictive finite element model for brittle crack arrest in compact crack arrest (CCA) specimens using dynamic fracture mechanics. Blocker: None

Assesment of crack arrest behaviour in modern structural steels · Cranfield · Doctorate

Left open

Model fracture and failure modes of void-containing specimens under load using the multiscale voxel-based finite element framework. Blocker: None

Frequency Response Modeling of Additive Friction Stir Deposition Parts with Print Defects · Virginia Tech · Master's

Left open

Model ductile tearing of steel beams under extensive local buckling using finite element analysis to quantify degradation. Blocker: None

Seismic performance of composite steel/concrete moment resisting frames · Imperial · PhD

Left open

Investigate buckling load-displacement characteristics within the crash deformation framework. Blocker: Lacks specification of the exact crash deformation framework and finite element model parameters

High-Dimensional Generative Models for 3D Perception · Virginia Tech · Doctorate

Left open

Incorporate crack face friction into the cohesive and orthotropic damage formulations within the multi-scale finite element model. Blocker: None

Mechanics of alkali-silica reaction in concrete across scales · EPFL · PhD

Left open

Develop a machine learning-enhanced adaptive meshing scheme to dynamically refine finite element meshes in regions undergoing fracture. Blocker: None

Numerical modeling of discontinuous processes in geomaterials and geosystems · Georgia Tech · PhD

Left open

Couple weathering rates to fluid transport through micro-cracks and reactive surface exposure dynamically in a finite element homogenization framework. Blocker: Lacks specific governing equations, reaction kinetics formulations, or validation datasets defined in the thesis summary.

Homogenization of Coupled Deformation, Damage and Diffusion Processes in Rocks and Finite Element Applications in Geomechanics and Geomorphology · Georgia Tech · PhD

Left open

Implement and compare quadratic tetrahedral and beam element meshing methods for stretch-dominated and bending-dominated defective lattice structures in finite element analysis. Blocker: None

Analysis of defects in additively manufactured lattice structures · Nottingham · PhD

Left open

Prove error bounds for the full posterior distributions W(nu_star, nu_h) in statistical finite element methods (StatFEM). Blocker: Requires advanced mathematical proof/analysis in Bayesian PDE inversion and probability metrics rather than standard software engineering.

Bayesian uncertainty quantification for PDE models: new perspectives on inference and dimension reduction · Imperial · PhD

Who has worked on this

Authors of the public theses cited on this page, most-cited first.

Checking a claim in this area?

We can run the same search on any method or claim. If nothing turns up, we will say so, and that proves nothing on its own.