Nonclassical nonlinear elasticity of crystalline structures.

Area of Science:

• Materials Science
• Solid Mechanics
• Condensed Matter Physics

Background:

• Hysteretic elastic nonlinearity leads to dynamic responses distinct from classical nonlinear behavior, termed nonclassical nonlinearity.
• Metallic structures typically exhibit weak, classical nonlinear material properties.
• Lattice defects in crystalline structures are investigated as a source of nonclassical nonlinearity.

Purpose of the Study:

• To present a material model explaining stress amplitude-dependent nonlinearity and damping.
• To demonstrate that mesoscale dislocation pinning and breakaway can cause nonclassical nonlinearity.
• To evaluate the dynamic nonlinearity arising from dislocations.

Main Methods:

• A material model was developed based on mesoscale dislocation pinning and breakaway.
• Dynamic nonlinearity was assessed using resonant frequency shift and higher order harmonic scaling.
• The model's ability to capture nonlinear dynamic responses across linear, classical nonlinear, and nonclassical nonlinear stress ranges was evaluated.

Main Results:

• The model successfully captures nonlinear dynamic responses across linear, classical nonlinear, and nonclassical nonlinear stress ranges.
• Amplitude-dependent damping was predicted to induce a softening-hardening nonlinear response.
• The model provides a framework for understanding nonclassical nonlinearity originating from lattice defects.

Conclusions:

• Lattice defects in crystalline structures can indeed give rise to nonclassical nonlinearity.
• The developed material model accurately predicts nonlinear dynamic responses in metallic structures.
• The model's generalization to various lattice defects offers a broader explanation for nonclassical nonlinearity.