Pure measures of bending for soft plates

Area of Science:

• Materials Science
• Solid Mechanics
• Continuum Mechanics

Background:

• Soft plates exhibit complex behaviors where stretching and bending are coupled.
• Existing models may not fully isolate bending effects, complicating analysis.
• A need exists for pure bending measures in soft plate mechanics.

Purpose of the Study:

• To define pure measures of bending for soft plates.
• To introduce and characterize bending-neutral deformations.
• To develop a tensorial measure of bending invariant under these deformations.

Main Methods:

• Introduction of the class of bending-neutral deformations.
• Characterization of the geometric compatibility condition for these deformations.
• Development of a tensorial pure measure of bending invariant under bending-neutral deformations.

Main Results:

• Pure measures of bending for soft plates are defined.
• Bending-neutral deformations are characterized by a specific geometric compatibility condition.
• A tensorial pure bending measure, invariant under bending-neutral deformations, has been derived.

Conclusions:

• The concept of pure bending measures offers a new perspective for soft plate theories.
• Separating stretching and bending energies can simplify the formulation of direct theories.
• This work provides a foundational tool for analyzing soft plate behavior.