In engineering design, loads, deformations, and material behaviors are not always linear. Many structures and products behave differently under increasing loads; materials exceed their elastic limits, large deformations occur in geometries, or boundary conditions between contacting parts change. These situations must be captured accurately through nonlinear analysis.
In this article, we will cover the fundamental concepts of nonlinear analysis, its types, solution methods, and which Ansys modules can be used to perform it.
Nonlinear analysis is the study of systems whose load–deformation relationship is not proportional.
In linear analysis, doubling the load doubles the deformation; in nonlinear analysis this proportionality does not hold. The stiffness of the system changes with load, which requires more complex computations.
Nonlinearity can be grouped into three main categories:
Material Nonlinearity
Occurs when a material exceeds its elastic limit, resulting in plastic deformation, cracking, or hyperelastic behavior.
Examples: Yielding in steel, cracking in concrete, hyperelastic models for rubber and biomaterials.
Geometric Nonlinearity
Arises with large deformations, large rotations, and buckling.
Examples: Buckling of slender beams under load, collapse of shell structures.
Boundary Condition / Contact Nonlinearity
Occurs when contact, friction, separation, or compression between parts changes with load.
Examples: Change in contact area of bolted joints after preload, compression of gaskets.
| Feature | Linear Analysis | Nonlinear Analysis |
|---|---|---|
| Material model | Elastic | Inelastic (plastic, viscoelastic, etc.) |
| Deformation | Small | Large |
| Load–deformation relationship | Proportional | Non-proportional |
| Computation time | Fast | Longer and iterative |
Nonlinear problems cannot be solved analytically; they require incremental-iterative techniques. Common methods include:
Newton–Raphson Method: Finds the new equilibrium point at each load step iteratively.
Incremental Loading (Load Steps/Substeps): Divides the load into small steps to maintain stability.
Arc-Length Method: Ensures solution continuity at stability loss points (buckling, post-buckling).
Select the appropriate material model (elastoplastic, viscoelastic, creep, etc.).
Apply loads and boundary conditions incrementally.
Define contact regions and friction correctly.
Pay attention to mesh quality and element type (especially shell–solid transitions).
Adjust tolerances to handle convergence issues.
Advantages: Provides highly realistic results, enabling safe and optimized designs.
Challenges: Requires more complex modeling, longer computation times, and specialized expertise.
Ansys offers a wide range of solvers to address different types of nonlinearity and sector needs.
The most commonly used module. It handles material, geometric, and contact nonlinearities.
Elastoplastic, viscoelastic, creep material models
Large deformations and buckling
Frictional contact and separation
Incremental loading and Newton–Raphson iterations
Arc-length methods for stability loss
Use cases: Plastic deformation, gaskets, bolted joints, impact tests, buckling and stability problems.
Its Transient Structural and Explicit Dynamics options also solve high-speed nonlinear events.
Preferred for high-speed, highly nonlinear problems with complex contact and large deformations.
Material + geometric + contact nonlinearity
Crashworthiness, blast, delamination
Nonlinear dynamic solution
Extensive material model library (composites, foams, metals, etc.)
Use cases: Automotive crash tests, blast and ballistic analyses, metal forming (stamping).
Specialized solver for high-energy events such as impact, blast, and shock waves.
Explosive loads and shock waves
Fluid–structure interactions
Nonlinear material responses
Use cases: Defense (mines, bombs, armor), aerospace (meteorite impact).
The classic core solver with advanced nonlinear controls.
Advanced material models
Complex contact definitions
User-defined material models
Use cases: Research and projects requiring specialized solutions.
Provides built-in hyperelastic, viscoelastic, and creep material models integrated with Mechanical.
Ansys Additive: Thermal + structural nonlinear analysis in metal 3D printing
Ansys Discovery: Simplified nonlinear checks for concept designs
Ansys Composite PrepPost (ACP): Nonlinear behavior of layered composites
| Module | Type of Nonlinearity | Typical Use |
|---|---|---|
| Mechanical | Material, geometry, contact (static & transient) | General engineering analyses |
| LS-DYNA | High-speed impact, crash, forming | Automotive, defense |
| Autodyn | Blast, shock, ballistic | Defense, aerospace |
| MAPDL | Advanced nonlinear modeling & control | Research, specialized solutions |
Nonlinear analysis is an essential part of modern engineering design. Unaddressed nonlinearities in material, geometry, and boundary conditions can lead to design errors and safety risks. Thanks to Ansys’ comprehensive module portfolio, whether it is a static elastoplastic problem or a high-speed impact or blast event, there is a suitable solver for every type of nonlinear behavior.
This holistic approach allows engineers to develop safe, cost-effective, and innovative designs with results that closely match real-world performance.