An assembly including a joining element and an object, the object having a first outer layer, a second outer layer, and a middle layer between the first and second outer layers. The object has an opening that extends through the first outer layer and the middle layer, and the joining element is anchored in the opening. The joining element includes a proximal end, a distal end, a contact face in the area of the proximal end, a wall anchoring portion, and a tubular portion. The contact face is engaged by a vibrating tool that applies mechanical vibration and axial force to the joining element. The joining element includes a thermoplastic material at least at the circumferential surface of the wall anchoring portion and at the distal end to anchor the joining element to the first and second outer layers, respectively.