To identify generalised principles for structural topology optimisation with respect to damage tolerance across multiple scales

Objectives
* Generate three discretised structural geometries: cubic lattice, sodalite cage and tetrahedral truss, at different length scales and with a range of geometric stochasticity and structural hierarchy
* Measure structural response with a non-linear dynamic discrete element simulation of structural collapse
* Verify simulations with physical testing on prototype 3D printed elements
* Optimise topologies algorithmically with respect to damage tolerance
* Form a set of principles for an a priori approach to robustness orientated design. Synthesising results from optimisation and effects of topological variation

This is an endeavour towards furthering robustness-oriented preliminary design. Meaningful contributions will be made towards the process of modelling and indexing progressive collapse resistance. With the state-of-the-art modelling methodologies developed and verified over the course of the project proving useful in determining optimally robust topologies.

1 Generate structural geometries
I will develop a Matlab script to generate topological information. continues geometries will be represented in the form of particle and connectivity data. Defining the locations of massive spherical discrete elements and force potentials connecting them.

2 Discrete element simulation of structural collapse
DEM was chosen in order to facilitate fracture and rupture of members, difficult to implement in a finite element approach. I will undertake simulation in the software LAMMPS. Conventionally used for materials modelling at the nano and micro scales, modified to include particle bonds that can capture structural responses at larger scales. Combining Hertzian contact forces with new bond interactions that will include local plasticity. At this stage the simulations will be element scale simulating response in compression and bending.

3 Verify simulations with 3D printed elements
Once results for the performance of the various structures are acquired it will be important to verify the modelling process and validate the results obtained before the next round of simulation can begin.
Prototype geometries will be printed out. In the lab it will then be possible to test their mechanical response to conditions representative of those applied during simulation. Comparison of simulated verses physical response will be made in terms of deflections, ultimate strength, and fracture propagation. If necessary, the model will be refined until a high level of correspondence exists between the two in all cases.
A workflow from geometry generation, to simulation, to manufacture will have been developed. To serve as a base for the further investigations.

4 Topological optimisation
I will conduct an extensive exploration into robustness-oriented design principles. The second stage of the simulation involves investigating the links between geometric parameters and damage tolerance. Simulations will be run with respect to specific scenarios of notional element loss simulating likely damage events.
This optimisation process will search for structural configurations optimally resistant to progressive collapse and catastrophic failure through an integrated algorithmic process linking Matlab to LAMMPS in Model centre. Allowing for the programming of a genetic optimisation loop to explore the effects of stochasticity and long-range connections on robustness.

5 A-priori robustness-oriented design principles
From the optimisation process will be obtained simulations of failure progression of both optimised and unoptimized structural forms as well as mechanisms of failure and measures of damage tolerance quantified in the form of a robustness index.

Compiling and analysis of this data will be undertaken to derive the kinds of robustness-oriented design procedures described in the project aim.