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Multi-scale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials

Periodic Reporting for period 1 - MOAMMM (Multi-scale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials)

Reporting period: 2020-01-01 to 2020-12-31

The emergence of meta-materials has opened a new paradigm in designing engineering parts in which the full structural parts can be optimised together with the meta-material they are locally composed of. Moreover, additional morphing at local and global scales may support their adaptation to variable loading conditions and shifted user needs. As polymeric materials can fulfil simultaneously structural mechanical and functional requirements, the combination of this design paradigm with additive manufacturing can support and generate novel applications.

However, many left challenges can only be addressed by considering experimental and numerical multi-scale methods. Nevertheless, current existing approaches are limited in several aspects because on the one hand of the difficulty in representing the microstructure and characterizing micro-scale constituent materials, and on the other hand in the computational cost inherent to these approaches.

The overall objective of this project is to develop a data-driven methodology relying on a structural properties-micro-structure linkage and able to design optimized devices based on meta-materials and printable using additive manufacturing. Two design approaches will be considered
i) Bi-stable metamaterials (i.e. structures having two stable equilibrium configurations -two local energy minima- and exhibiting a non-stable state) to improve shock-absorption devices.
ii) Regularly organised lattice metamaterials possibly working in irreversible regime (viscoplasticity, failure) to improve dissipative absorbers.

3D-printing of polymers has recently found a lot of interest and growth, a significant portion of which concerns real applications in products. Results of this project will support significantly drivers of this growth such as low investment cost, geometrical freedom, integration and individualisation, on a new level: this project is an opportunity to explore new concepts of architecture from an innovative design methodology that would enable it to offer unique products, both in terms of efficiency and comfort in different areas. The proposed microstructures can achieve light-weight designs and customised properties; and the simulation approach will guarantee the required robustness of process and a repeatable high product quality.

As a proof of concept, the methodology will be applied to design metamaterial-based structures:
i) Shock-absorbers, such as athletic shoe soles, relying on reversible deformation of the metamaterials that absorb energy during deformation and return it without change in shape, in which emphasis is put on fatigue performance;
ii) Dissipative absorbers, such as bicycle helmets, relying on energy dissipation, possibly by irreversible deformations, in which emphasis is put on minimizing weight and cost whilst maximizing energy dissipation.
The MOAMMM project has contributed toward the following achievements:
i) Using different scale factors to evaluate the minimum cell size in a stochastic manner, helped to adjust machine parameters in order to optimize the AM processes for printing filigree lattice structures and to develop design guidelines for the SLS process.
ii) SEM analysis of cells shows a very irregular surface in which powder particles are not totally sintered. Tomographic analysis has also been performed revealing an actual relative density 20-30% smaller than the design, due to the presence of internal porosity (at least 5% in all the samples) and surface irregularity. The bulk responses of SLS fabricated bulk samples have been experimentally analysed at different length scales using nano-indentation at different strain rates and standard uniaxial tensile and compression tests in different directions with respect to the loading direction and under different strain rates. The tests have shown a marked anisotropy in plastic properties and on failure and fatigue responses.
iii) The mechanical responses of different preliminary cell designs have been studied experimentally. This study includes standard macroscopic compression testing of an array of cells. The results indicate a weaker response of smaller cells due to the larger amount of defects.
iv) A computational homogenisation framework for lattice materials has been developed and different non-linear material models have been implemented including plasticity, visco-elasticity and visco-plasticity. Two computational simulation tools have been considered, FE and FFT. The FFT solver is competitive for relative densities greater than 10% and is especially useful for the direct simulations of tomographic data of a cell including defects. In the case of FE, a technique has been implemented for analysing the instabilities in the collective behaviour of a collection of cells. Low cost time & space homogenization methods are under development for porous visco-elasto-visco-plastic matrix to model the struts behaviour. A surrogate model of the elasto-plastic micro-structure responses has been built from pre-off-line finite element simulations on the randomly loaded micro-structure. After this so-called training step, the surrogate model can be used as the constitutive law of a single-scale simulation, leading to highly efficient simulations while still accounting for the micro-structure of the material. Gains of several orders in terms of computational efficiency are obtained with respect to full-field homogenisation.
From the technological point of view, if the project succeeds, the basis of a new technology will be established in which a high-performance device can be designed and fabricated in a fully personalised way depending on a particular application with particular constraints. This new paradigm paves the way to the design of customised sport equipment, more efficient prostheses for a particular person or again lighter shock absorbers. Socially, extending this new design/fabrication framework to biomechanics would have a strong impact in public health because it would allow a more efficient process for the personalised fabrication of some prostheses, decreasing their cost and making them affordable for the public health systems.

From the scientific point of view, the main outcome is the development of a PSP linkage for printed-metamaterial, in which additional innovations are expected:
i) New and more efficient optimisation and stochastic multi-scale methods relying on surrogate models is still a challenge yet to be solved. The use of surrogate models in multi-scale methods has seen a growing interest to which the MOAMMM project has contributed with a recent publication in the case of irreversible material behaviours.
ii) A rigorous UQ methodology applied to printed metamaterials, with a view to quality control. Indeed, tomographic images of printed cells of reduced sizes show that the real material content significantly differs from that of the initial geometry, inducing variations in the cell responses.
iii) Accurate additive manufacturing process model and optimised process for polymers, with a particular emphasis on the cell-size reduction. Manufacturing process model will allow predicting estimating bulk material properties and in turns optimising the process.
SLS printed cells of different sizes
Data-driven structural properties-micro-structure linkage
Use of trained surrogate models in multi-scale simulations
FFT simulation of a lattice cell with fabrication defects from direct information from tomography