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