In the event of an unsynchronised beam abort, the MSD extraction septum of the LHC beam dumping system is protected from damage by the TCDS diluter. The simultaneous constraints of obtaining sufficient beam dilution while ensuring the survival of the TCDS make the design difficult, with high thermally induced dynamic stresses occurring in the material needed to attenuate the particle showers induced by the primary beam impact. In this paper, full 3D simulations are described where the worst-case beam loading has been used to generate the local temperature rise and to follow the resulting time evolution of the mechanical stresses. The results and the accompanying design changes for the TCDS, to provide an adequate performance margin, are detailed. BEAM DUMP DILUTER TCDS To protect the beam dump extraction elements against particles in the abort gap and unsynchronised beam aborts, a fixed diluter TCDS [1] will be installed in front of the MSD extraction septum in the IR6 dump insertion. The TCDS is comprised of two 3.0 m long diluter blocks, with a graded composition to obtain the optimum compromise between absorbing power and robustness. The ~24 mm diluter thickness has been chosen to protect the downstream septum elements and vacuum chambers from badly extracted beams. The TCDS must protect the MSD septum when the worst-case beam load occurs following a pre-trigger of one extraction kicker and the subsequent asynchronous triggering of the remaining 14 kickers. The TCDS must also survive the worst-case thermal load. The conceptual and mechanical designs have been based on FLUKA [2] energy deposition simulations, together with numerical and stress calculations made using a specially developed Finite Element (FE) code ELSE [3]. In particular, numerical analyses of dynamic effects were made on different TCDS configurations, and have resulted in an updated design with improved robustness. The 6.0 m long unit is modelled as 24 separate 72×24×250 cm blocks, neglecting the slight differences in block widths and machining the entrance and exit blocks for beam impedance reasons.