Shape optimization analysis of adhesive interface under multiaxial stress state using failure function with stress invariants

Abstract

The present paper proposes a shape optimization of the adhesive interface to improve the strength of adhesive structure under a multiaxial stress state. Its strength was evaluated by the failure function based on the first invariant of stress tensor I₁ and the second invariant of deviatoric stress tensor J₂, which has been discussed in the related previous paper. We defined a sum of squares of the failure function as an objective function in the optimization. Two types of the adhesive material properties, which put the major weights on only I₁ and J₂, respectively, were numerically examined. As a multi-material structure model bonded by the adhesive, a thin-walled butt-jointed cylinder was employed to avoid stress concentration at free edges in the adhesive layer. Three kinds of loadings were applied: only tension, only torsion, and a tension-torsion combined load. The shape of optimal adhesive layer according to each condition was in good agreement with the simplified theoretical solution. The kinked part of the optimal adhesive interface necessary for the pipe configuration was also reasonable to diminish the stress concentration around the corner. The obtained optimal shapes for the two typical adhesive material properties suggest that the present optimization method would be applicable dependent to the adhesive material parameters under multiaxial stress states.