# Linear Elasticity

Published: March 26, 2019 | Last updated: July 5, 2023

## What Does Linear Elasticity Mean?

Linear elasticity is the property of a material to become deformed due to certain loading conditions without yielding. Materials that are linearly elastic obey Hooke's law i.e. the stress and strain relationship is linear. Trenchless installation techniques utilize pipes made of flexible materials, such as high density polyethylene (HDPE), polyvinyl chloride (PVC) and polyethylene (PE).

These materials are able to withstand loads better than other brittle pipe materials such as concrete and steel.

## Trenchlesspedia Explains Linear Elasticity

Linear elasticity of a material can be determined using a simple test that requires placing a sample whose ends are gripped in a tensile testing machine. Load is applied to the sample under controlled conditions and the longitudinal stress is calculated as:

σ = F/A where, σ is the longitudinal stress, F is the applied force, and A is the cross-sectional area of the sample.

Materials that exhibit linear elasticity return back to their initial state once the load is removed. Linear elastic behavior in the tension test is given by Hooke's law as:

σ = Eε, where E is the modulus of elasticity and ε is the true strain. 