This paper presents a finite element topology optimization framework for the design of two-phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction-separation constitutive relation. The non-penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi-static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two-phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics.LEVEL SET TOPOLOGY OPTIMIZATION WITH INTERFACE COHESION 991 known as topology optimization. To provide a high level of design freedom, a topology optimization framework is used in this paper.The interface conditions considered in this study are inherently nonlinear. For frictionless contact, interfacial forces act to prevent the penetration of bodies but vanish during separation. Material cohesion provides resistance to shear and normal separation of joined materials, but can result in rapid delamination when the cohesive limit is surpassed. Due to their complex behavior, problems with contact phenomena have only been considered in a few 2D topology optimization studies. This paper presents a novel topology optimization method for 2D and 3D problems involving interface cohesion and delamination.Density methods, such as the solid isotropic material with penalization approach, are the most common method of describing the geometry in topology optimization. The solid isotropic material with penalization approach was originally developed by [1,2] and describes the geometry of a body by defining the material distribution in the design domain as a function of design variables. A fictitious porous material with density, 0 ⩽ ⩽ 1, defines a continuous transition between two or more materials. For more information and an overview of recent developments, the reader is referred to [3][4][5]. The geometry of an interface is represented by either large spatial gradients or by jumps in the density fields, depending on the discretization of the density distribution and the method of enforcing converg...
