Service overview
Stress, vibration, fatigue, nonlinear and composite structural simulation and design optimisation. This service is part of that division and is scoped individually around what you need to learn, decide or publish.
Linear analysis assumes that displacements are small, materials return to their original shape and contacts do not change as loads are applied. Many questions in engineering research violate at least one of those assumptions: how much load can a structure carry before it collapses, how does a metal deform during forming, how does a rubber seal behave when compressed? Nonlinear analysis is needed whenever geometry, material or contact conditions change appreciably during loading.
Nonlinear problems are harder in three ways. They are solved incrementally and iteratively, so convergence is not guaranteed. Their solutions can depend on the path and the load history. And they require material data that go beyond a single modulus and yield stress. A credible nonlinear study therefore invests in understanding the physics first, building up complexity step by step and checking each addition against simpler models.
If you plan to publish the outcome, see manuscript & publication support, for example computational & simulation manuscripts or original research article writing.
What this service covers
Problems this service can address
- Convergence difficulties in nonlinear solutions
- Buckling or collapse behaviour that linear analysis cannot capture
- Material models calibrated from limited test data
Methods and analytical approaches
- Large-displacement and plasticity modelling
- Contact and friction treatment
- Buckling and post-buckling analysis
- Load-stepping and convergence strategies
Applications
- Collapse and ultimate-load studies
- Metal-forming and impact-type problems
- Elastomer and hyperelastic components
Relevant engineering disciplines
Scope, inputs and deliverables
Scope of work
- Definition of the physics, geometry and quantities of interest
- Model set-up with verification and, where data allow, validation
- Parametric or sensitivity studies agreed at scoping
- Results and documentation suitable for reports or publication
- Feasibility check on: geometry and nonlinear material data
Typical inputs required from you
- Geometry and nonlinear material data
- Loading sequence
- Experimental load-displacement curves
Deliverables
- Nonlinear response curves
- Failure or instability load estimates
- Convergence and sensitivity discussion
Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.
Project workflow and method
- 01Enquiry and requirement assessment
- 02Technical scoping and proposal
- 03Execution
- 04Quality review and delivery, with an agreed round of revisions
Read the full project workflow.
In depth: how the work is done
Identifying the sources of nonlinearity
Geometric nonlinearity arises when deflections are large enough to change the load path, as in cables, thin shells and slender columns, or when loads follow the deformed shape. Material nonlinearity includes plasticity, hardening, creep, damage and hyperelastic behaviour. Contact nonlinearity occurs when parts touch, separate or slide. Estimating the magnitude of each, usually through a quick linear analysis and simple calculations, decides which effects need to be included. Omitting a significant source gives wrong answers; including an insignificant one costs time and convergence trouble.
Material models and calibration
Plasticity models require stress-strain data beyond yield, converted to true stress and true strain, with hardening behaviour appropriate to the loading. Hyperelastic models for elastomers are calibrated from multiple test modes, since fitting a single uniaxial curve can give poor predictions in other deformation states. Rate and temperature effects are included when relevant. Material parameters are documented with their source and fitting range, and predictions are restricted to deformation states close to those used in calibration.
Contact, friction and large displacements
Contact algorithms enforce non-penetration and transmit force and friction. Choices such as penalty or Lagrange formulations, contact stiffness, friction coefficient and initial gap or overlap influence both results and convergence. Large-displacement formulations update geometry during the solution. We check that contact pressure distributions are physically reasonable, that penetration is small and that results are not unduly sensitive to the friction coefficient, which is often poorly known.
Buckling, post-buckling and collapse
Linear buckling analysis estimates an upper-bound critical load for a perfect structure; real structures buckle at lower loads because of imperfections. Nonlinear analyses with imperfections introduced from the first buckling modes trace the load-displacement response, including post-buckling and collapse. Arc-length and related methods follow unstable paths where load control fails. The sensitivity of capacity to the imperfection amplitude is examined, because it is often the dominant uncertainty.
Load stepping, convergence and verification
Nonlinear solutions are obtained incrementally with equilibrium iterations at each step. Step size, convergence tolerances on force and displacement, and strategies for automatic step control affect robustness and accuracy. A converged solution is not necessarily correct: energy balance, reaction forces and comparison with analytical or experimental results provide checks. Where possible, simpler limiting cases are solved first, and the nonlinear model is verified against them before complexity is added.
Quality control and good practice
Quality-control approach
- Verification: mesh, time-step and solver sensitivity are examined before results are reported.
- Validation: results are compared with measurements or reference solutions where these exist, and the absence of such data is stated.
- Boundary conditions and material or fluid properties are recorded with their sources.
- Sensitivity to the least certain inputs is shown or explained.
Common pitfalls this service helps avoid
- Skipping the linear baseline. A linear model gives a reference that helps detect errors in the nonlinear one.
- Calibrating a material model on a single test. Parameters fitted to one deformation mode can mispredict others.
- Ignoring imperfections in buckling. Perfect-geometry analyses overestimate capacity for many structures.
- Accepting a converged answer without checks. Convergence of the solver does not confirm correctness of the model.
What good reporting looks like
A nonlinear analysis report describes the sources of nonlinearity and why they matter, material data and calibration, the geometry, contact and boundary conditions, the solution procedure and convergence controls, load-displacement or stress-strain results, comparison with linear and analytical or test results, sensitivity to imperfections, friction or material parameters, and limitations. It states the range of loading for which the model is considered valid and does not extrapolate collapse predictions beyond the calibrated conditions.
An illustrative scenario
Hypothetical example written for explanation. It is not a client case, a result or a testimonial.
Suppose a researcher is studying the collapse of a thin-walled tube under compression. A linear buckling analysis gives a critical load far higher than a physical test. A nonlinear analysis with an initial imperfection shaped like the first buckling mode and an elastic-plastic material predicts a much lower collapse load, close to the test, and shows the post-buckling drop. The researcher varies the imperfection amplitude and reports a range of capacity, noting that the measured imperfection of the test specimen lies inside the studied range.
Questions to settle before you begin
- Which nonlinearities are significant for my loading?
- What material tests do I have, and over which strain range?
- How uncertain are the friction and contact conditions?
- Which imperfections might reduce capacity?
- What simpler solution can I use to check the nonlinear model?
Key terms
- Geometric nonlinearity
- Change in structural response due to large displacements or rotations.
- Plasticity
- Permanent deformation that remains after unloading.
- Hyperelasticity
- A framework for large, recoverable deformation, typical of rubbers.
- Arc-length method
- A solution technique that follows unstable equilibrium paths.
- Imperfection
- A small deviation from the ideal geometry that affects buckling.
Working together on Finite Element Analysis (FEA) & Structural Engineering projects
Structural and FEA engagements begin by clarifying what must be predicted, such as stress, stiffness, frequency or life, and which loads and supports are known. We ask for geometry, material data, load cases, connection details and any test measurements. A hand calculation or benchmark is prepared alongside the finite element model to cross-check it. Reports show mesh convergence, state assumptions about supports and materials, and give margins with their uncertainty. The work is research-level analysis and does not replace code-based design checks or certification by licensed professionals.
Frequently asked questions
Why do nonlinear models need test data?
Material nonlinearity is often poorly defined by nominal properties. Calibrating against tests makes results defensible.
When is a linear analysis not enough?
When deformation changes the load path, when stresses exceed yield, or when contact changes during loading. Simple estimates often reveal which applies.
Do you need material test data?
For plasticity or hyperelasticity, yes, ideally covering the relevant deformation modes. Literature data can be used with clearly stated caveats.
Can you predict ultimate load?
A model can estimate it under stated assumptions. Real capacity depends on imperfections and material variability, so a range is more honest than a single number.
Can explicit dynamics be used?
For impact and rapid loading, explicit methods can be appropriate, and the choice is discussed at scoping.
How is this service scoped and priced?
After your enquiry we review what you need, ask for missing information and send a written scope and quotation. Price depends on complexity, deliverables and timeline. See the project workflow.