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.

Shape optimization of adhesives of multi-materials under multiaxial stress failure criteria

“…These results are compared with the optimization results of acrylic adhesive in ref. [14]. The objective function and volume curves under three…”

“…In order to perform the shape optimal design of adhesive structures which is induced to minimize the stress operated in the adhesive layer under the multiaxial stress state, the objective function should be formulated [14]. The multi-material region with the adhesive layer is shown in Fig.…”

“…In order to enhance the strength of the adhesive structure, the values of failure function 𝑓 are supposed to become uniform throughout the adhesive layer for the applied stress to be minimized as much as possible. Therefore, the object function is to minimize it in the adhesive layer region 𝛺 𝐵 as the sum of squares of failure function f occurring in the whole adhesive layer as follows [14].…”

“…Some shape optimizations of adhesive layer have been demonstrated according to the failure criterion of acrylic adhesive. [14] As the strength of adhesives is influenced by both material and structural factors, this research aims to involve both these two factors and to discuss how those factors affect the strength of bonded structures. an epoxy adhesive is investigated using the same as the previous research [13], and the parameters defined in the failure criteria are experimentally determined.…”