Abstract
Several toughening mechanisms for cracks in brittle solids depend on the restraining effects of material elements that bridge the faces of a crack. A standard way of quantifying the toughening effect is to smear-out the restraining stresses provided by the individual bridging elements. The present paper, by using a very simple simulation model which allows for the discreteness of the system, together with a general force-law for the behaviour of an individual bridging element, shows that the smearing-out procedure is valid if the bridging elements are ductile; however, it can underestimate the toughening effect when the elements are brittle.
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