Types of strain – basic definition:\nWhen a change in length occurs in a member under load, what is the appropriate name of the strain developed?

Introduction / Context:
Strain describes deformation normalized by original dimensions. Correctly naming the type of strain is important for applying the right constitutive relations and for interpreting test data such as tensile tests on bars or coupons.

Given Data / Assumptions:

• A prismatic bar changes its length under axial loading.
• Small deformations so engineering strain definitions apply.
• Isotropic homogeneous material (not essential for naming).

Concept / Approach:
Linear (or longitudinal) strain is the ratio of change in length to original length along the direction of the applied load. If the bar elongates by delta L from an original length L, linear strain epsilon = delta L / L. Lateral strain refers to the concurrent contraction/expansion perpendicular to the load due to Poisson’s effect. Volumetric strain sums the three principal linear strains.

Step-by-Step Solution:

Verification / Alternative check:
Tensile test stress–strain curves plot axial stress against axial (linear) strain; this is the primary measure reported for material properties such as Young’s modulus E.

Why Other Options Are Wrong:

• Lateral strain: transverse response, not the axial change described.
• Volumetric strain: sum of principal linear strains; more general measure.
• Shear strain: associated with angular distortion, not axial change.
• Thermal strain: cause-based descriptor; the question is geometric, not causal.

Common Pitfalls:
Confusing cause and effect (thermal vs mechanical). Regardless of cause, if the measured deformation is axial length change, the strain type is linear.

Final Answer:
Linear strain