Testing for Linear Material Models for CAE
Linear material models are among the most commonly used in finite element analysis (FEA) because of their simplicity and broad applicability. They are particularly suitable for small-strain simulations, such as static structural analysis, noise/vibration/harshness (NVH) problems, and some plastic or composite applications. These models require only three basic material parameters:
- Elastic modulus (Young's modulus)
- Poisson's ratio
- Yield stress
These inputs are typically easy to obtain from standard handbooks, databases, or straightforward mechanical testing, making linear models accessible and widely used.
To learn more regarding material testing and characterization in support of material models for CAE, see our TestPaks or contact us to talk with our materials testing experts.
Key Assumptions and Applications
Linear models assume:
- The material is linearly elastic up to a yield point or failure.
- Strain remains small (usually under a few percent).
- Deformation is reversible up to the yield point.
- Material behavior is isotropic, unless otherwise defined.
While commonly used for metals, linear elastic models can also approximate the behavior of ceramics, concrete, foams, and plastics, particularly when they fail soon after yielding. Linear models can also include simple plasticity through a defined hardening modulus.
For composites, linear models must be used with care because these materials are often anisotropic, meaning their properties differ by direction. Characterizing anisotropic linear behavior requires more extensive testing.
Implementation and Testing
Most material data for linear models is gathered from quasi-static tensile tests (low strain rates). These tests measure:
- Elastic modulus as the slope of the stress-strain curve before yield.
- Poisson's ratio by using two extensometers — one in the longitudinal and one in the transverse direction — calculating the lateral contraction per unit axial strain:
Test specimens are typically rectangular or cylindrical. For isotropic materials, the Poisson's ratio is direction-independent. For anisotropic materials (such as composites), different Poisson's ratios may exist along different axes.
Because most data is reported in engineering stress-strain terms (i.e., calculated using initial area and length), it may need to be converted into true stress-strain for FEA use. This is especially important for materials like plastics, where the strain at yield can be large. The difference is negligible in metals under small strains but becomes critical in nonlinear or large-strain applications.
Anisotropic Materials
Anisotropic linear modeling is common in structured and unstructured composites, and also in materials processed via methods like extrusion or rolling. These processes introduce direction-dependent properties.
Key challenges:
- Elastic tensile and compressive moduli, Poisson's ratio, and shear modulus all vary by direction.
- Each of these must be measured independently, increasing test complexity.
- Shear modulus can't be calculated from tensile data but must be directly measured.
- All values must be internally consistent to avoid errors in simulations.
Due to the complexity, many practitioners use simplifying assumptions to reduce the number of required tests while preserving model accuracy.
Limitations of Linear Models
Linear models are suitable when:
- Deformations are small.
- The material shows elastic behavior up to failure.
- The load path doesn't involve large, nonlinear strains or strain localization.
They are not ideal for materials with highly nonlinear stress-strain behavior (e.g., elastomers, highly ductile plastics), or for simulations involving post-yield behavior, strain-rate effects, or large deformations.
For metals and some fiber-filled plastics, linear models are often appropriate for simulated conditions of both small and larger induced strain. However, for plastics, crushable foams, composites, ceramics and concrete, linear models should only be applied under conditions of small induced strain.
Temperature-Dependent Linear Models
In thermo-mechanical simulations, material properties must be characterized at various temperatures. At minimum, temperature-dependent values of the following properties must be characterized:
- Elastic modulus
- Yield strength
- Thermal expansion coefficient
- (Optionally) Poisson's ratio
Data must be collected using tensile testing at different temperatures. For simplicity, the Poisson's ratio is often assumed constant unless significant variation is known. In plastics and composites, modulus and yield strength often change significantly with temperature — especially as materials approach their glass transition or melting point — and must be measured accordingly.
Supporting Properties
Two additional properties often accompany linear models:
Solid Density
Usually measured by Archimedes' principle: weighing the sample in air and then in water to calculate density. For porous materials or foams, physical volume and weight can be used.
Thermal Expansion Coefficient
Measured using a quartz-tube dilatometer. A specimen is heated in a precision quartz tube, and the expansion is measured as a function of temperature. This property is direction-dependent in filled plastics and composites, often requiring measurement along multiple axes. For example, glass-filled nylons may show 20–30% variation in expansion between flow and cross-flow directions.
Conclusion
Linear material models provide a practical, efficient foundation for many FEA applications. While limited to small-strain and linear behaviors, they remain useful in engineering design and analysis, especially for metals and composite systems. Accurate testing, including modulus, Poisson's ratio, and yield strength — along with careful handling of anisotropy and temperature effects — ensures these models perform reliably in simulation environments.
To explore the topics discussed on this page further, see Hubert Lobo (Founder, DatapointLabs) and Brian Croop (CEO, DatapointLabs), Determination and Use of Material Properties for Finite Element Analysis (NAFEMS, 2016), Ch.4.
