Chapter Four · failure evidence
What Finite Element Modeling got wrong, from 75 dissertations
The records document various modeling breakdowns and computational bottlenecks encountered when applying finite element methods across structural, geomechanical, and multiphysics domains. Practitioners frequently reported severe issues including prohibitive runtimes, linear solver divergence under large deformations, artificial element stiffening, and the inability of continuum formulations to capture discrete material separation. These records come from PhD theses at 18 institutions, 2021 to 2026. 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.
Prohibitive computational runtime and resource scaling bottlenecks impede finite element simulations
High element counts, fine volumetric meshing, and iterative nonlinear or inverse evaluations require excessive computational time and memory. These severe scaling penalties frequently make large three dimensional simulations or extensive design space explorations practically intractable compared to simpler analytical or finite difference alternatives.
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 · JScholarship
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
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 Institutional Repository
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 · University of Nottingham Repository
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
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 · ResearchWorks
Lost to a baseline
Finite element hybrid formulation required nearly double the computation time and showed boundary sensitivity/oscillations compared to the finite difference hybrid solution
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
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
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
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
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
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
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
Tried and failed
low-order shell and solid finite elements applied to torsional structural mechanics modeling. Outcome: infeasible cost. Reason: Lack of rotational degrees of freedom and linear behavior required excessive mesh density
Numerical modeling of corrugated metal pipe uplift with soil-structure interaction · Iowa State
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 · DSpace at SUNY Buffalo
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
Considered and rejected
Considered and rejected: Finite element deformable surface modeling (Terzopoulos et al.) rejected because solving differential equations is too computationally expensive for real-time rendering
Magnetic based force feedback applied to free form surface deformation · Iowa State
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
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 · University of Nottingham Repository
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 · DukeSpace
Simplified static linear or uncoupled assumptions fail to capture complex structural and multiphysics responses
Omitting transient dynamics, interface slip, or geometric nonlinearities leads models to underestimate peak deformations or trigger premature buckling predictions. Similarly, decoupled multiphysics formulations fail to represent coupled thermal, pore pressure, and stress interactions observed in experimental tests.
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
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
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
Tried and failed
infinite periodic boundary assumptions in structural models applied to finite four-edge supported stiffened panels. Outcome: did not generalise. Reason: infinite-width assumptions wrongly predicted unstable post-buckling and premature collapse for finite boundary conditions
The stability and post-buckling behaviour of stiffened plates in compression · Cranfield
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
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
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
Tried and failed
uncoupled thermal-displacement finite element modeling applied to porous media consolidation simulation. Outcome: worse than baseline. Reason: Inability to track pore pressure dissipation and changing void ratio during consolidation
Numerical modelling of the electro-kinetic effect on pipe-soil interaction. · Cranfield
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
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
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
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
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
Severe mesh distortion and contact nonlinearities cause iterative solver divergence
Large physical displacements, extreme mesh refinement, and contact interactions frequently induce high element aspect ratios and geometric skewness that prevent solver convergence. Without proper numerical stabilization or consistent thermodynamic formulations, linear and nonlinear solvers terminate prematurely or experience breakdown in constitutive models.
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
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
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
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
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
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
Tried and failed
mesh distortion sensitivity analysis in finite element solvers applied to laminar incompressible fluid flow simulation. Outcome: did not converge. Reason: High aspect ratio and skew element distortions prevented iterative segregated solver convergence.
Error control in finite elements for fluid modelling. · Cranfield
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
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
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
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
Tried and failed
Drucker-Prager elasto-plastic finite element modeling applied to soil-structure interaction under high load. Outcome: did not converge. Reason: tension failures induced by approximate initial geostatic stress state
Numerical modeling of corrugated metal pipe uplift with soil-structure interaction · Iowa State
Stabilization deficiencies and inappropriate boundary constraints produce spurious oscillations numerical diffusion and singularities
Standard finite element formulations for advective transport and wave propagation suffer from unphysical oscillations, boundary sensitivity, and excessive inter-grid diffusion. Additionally, applying over-constrained rigid boundary conditions creates artificial stress singularities that erroneously exceed material strength limits.
Tried and failed
Finite element analysis with rigid boundary constraints applied to mechanical joint stress modeling. Reason: Stress singularities at fixed boundary conditions artificially exceeded the material ultimate tensile strength
Lost to a baseline
Finite element Newton's method failed to resolve high-frequency contact-line oscillations captured by the boundary integral method.
Asymptotic Solutions and Numerical Methods for some Free-boundary Problems in Fluid Mechanics · University of Nottingham Repository
Considered and rejected
Considered and rejected: Rejected infinite element methods due to poor performance for elastodynamics.
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
Tried and failed
finite element method with non-aligned meshes applied to piecewise discontinuous coefficient elliptic PDEs. Outcome: worse than baseline. Reason: Non-integer mesh ratio misaligns element boundaries with coefficient discontinuities, degrading convergence orders
Numerical multiscale methods: from homogenization to milestoning · UT Austin
Tried and failed
standard finite element methods applied to convective diffusion equations. Outcome: unstable. Reason: standard numerical discretization yields spurious oscillatory solutions and excessive computation times
Finite element modeling of electrodynamic and magnetostrictive systems · Iowa State
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 Institutional Repository
Tried and failed
Fully fixed boundary condition along narrow section applied to Static finite element analysis. Outcome: did not converge. Reason: Numerical singularity caused by over-constrained encastre boundary condition along a localized section
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
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
Coarse discretizations and low-order elements cause artificial stiffening and stress underestimation
Linear tetrahedral elements, first-order representations, and coarse meshes exhibit excessive rigidity and slow convergence in bending-dominated loading scenarios. These discretization limitations underestimate steep displacement gradients and peak stresses, leading to designs that violate structural constraints.
Lost to a baseline
Finite element model with 5 elements predicted a stiffer, poorer postbuckling/bending response than a simpler 2-element beam-column model for cantilever and simply supported beam problems.
A comparison of two models for geometrically nonlinear finite element analysis of plane frames · Virginia Tech
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
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.
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
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 · Research Repository UCD
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
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
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 · University of Nottingham Repository
Continuum finite element formulations fail to capture discrete separation fracture and particulate flows
Homogenized continuum representations cannot capture physical crack paths, crater enlargement, fragmentation coalescence, or soil flowability during contact. Furthermore, standard cohesive zone and local continuum damage approaches suffer from pathological mesh dependency and fail to represent history-dependent shear degradation.
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
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
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
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.
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 Institutional Repository
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
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
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
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
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
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
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
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
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.
Left open
Implement analytical or semi-analytical derivative evaluation methods to replace finite-difference gradient computation in multilevel composite structural optimization. Blocker: None
Multilevel optimum design of large laminated composite structures · Cranfield
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 · University of Nottingham Repository
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.
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