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Bounds for element size in a variable stiffness cohesive finite element model. (English) Zbl 1075.74683
Summary: The cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction-separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack-tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi-phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross-triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al$$_{2}$$O$$_{3}$$ ceramic and in an Al$$_{2}$$O$$_{3}$$/TiB$$_{2}$$ ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74R99 Fracture and damage 74E30 Composite and mixture properties
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