However, for some boundary value problems the weight function is logarithmically singular and is of the form w(t) = log{(l+t)/(l-t)}. (5) Examples of problems with such weight functions include the analytical simulations of fiber pull out or fracture of fiber-reinforced composites with imperfect fiber-matrix interfaces. Solution of such problems in composites, where imperfection in fiber-matrix interfaces is accounted for, are becoming important in the development of more physically realistic models for studying the mechanical behavior of composites.
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