Plastic failure of nonlocal beams

Area of Science:

• Structural Mechanics
• Materials Science
• Nanotechnology

Background:

• Classical structural models often overlook nonlocal effects in softening materials.
• Microcracking and plasticity can lead to localized failure modes in structural systems.
• Nanobeams represent a class of structures where nonlocal phenomena are significant.

Purpose of the Study:

• To investigate the collapse mechanisms of softening nonlocal structural systems.
• To develop and apply a nonlocal plasticity model for analyzing microcracking.
• To derive closed-form solutions for elastoplastic deflection and analyze scale effects.

Main Methods:

• Development of an implicit gradient plasticity model equivalent to a nonlocal integral plasticity model.
• Analysis of a homogeneous cantilever beam under concentrated load as a primary model.
• Derivation of closed-form solutions for elastoplastic deflection.

Main Results:

• The regularized nonlocal plasticity problem is shown to be well-posed.
• The plastic zone length grows during softening, reaching an asymptotic value dependent on material characteristic length.
• Scale effects are evident in static bending tests, confirming the nonlocal nature of collapse.

Conclusions:

• The mode of structural collapse in the studied systems is definitively a nonlocal phenomenon.
• The developed nonlocal plasticity model effectively controls the localization process induced by microcracking.
• The findings have implications for understanding the behavior of nanobeams and similar structures.