Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case. (English) Zbl 0945.74006

Braides, Andrea; Dal Maso, Gianni; Garroni, Adriana

Arch. Ration. Mech. Anal. 146, No. 1, 23-58 (1999).

Summary: We show that discrete models of atoms subject to nearest-neighbour nonlinear interactions approximate continua allowing for softening and fracture. A detailed study of local minima and stationary points is carried out. Scale effects are discussed.

MSC:

74A45	Theories of fracture and damage
74A60	Micromechanical theories
74R20	Anelastic fracture and damage
74G65	Energy minimization in equilibrium problems in solid mechanics

Keywords:

variational principle; scale effects; discrete models of atoms; nearest-neighbour nonlinear interactions; softening; fracture; local minima; stationary points