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Final Report Summary - INTERCER2 (Modelling and optimal design of ceramic structures with defects and imperfect interfaces)

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1. Project objectives
The ceramics industry is broadly developed in Europe and is involved in important investments, both in traditional and advanced ceramics. The industrial production of ceramic components faces serious limitations in that it is often based on empirically engineered processes that are poorly understood and difficult to control. This situation is hardly compatible with the quality control standards needed for both advanced and traditional, ceramics. This research project aimed at overcoming these limitations, by addressing an in-depth scientific understanding of production processes with the goal of optimizing them and developing new technological and industrial strategies. These strategies will yield a reduction in the scrap rate of ceramic pieces and therefore leading to reduced waste and energy consumption, crucial in the perspective of sustainable industrial development.
The INTERCER2 network involved three Academic Institutions (the University of Trento, specialized in engineering and Computational Mechanics with a specific expertise in ceramic materials; the University of Liverpool, specialized in Mathematical and Numerical Modelling; and the Aberystwyth University, specialized in Applied Mathematics and Materials Physics) and two Industrial partners (SACMI, a leader in the field of ceramics; covering the entire process of ceramics production and design of machines for production, and Enginsoft, expert in the field of informatics applied to Computer-Aided-Engineering, Virtual Prototyping, process simulation and the optimization of design and production processes).
The Academic partners provided support for the development of new materials testing protocols, mathematical models, and numerical strategies aimed at the simulation of forming processes, analysis of defect criticality, and the improvement of the production technologies.
The industrial partner SACMI provided the experimental data needed for motivating and validating the mathematical models and, more in general, they offered their invaluable experience in ceramics manufacturing. The other industrial partner, Enginsoft, has played a pivotal role in the computer implementation of the developed models, as well as in the numerical simulation of ceramic production processes, involving the forming of ceramic powders.
A research consortium has been created to achieve the following main research targets:
- Modelling and experimental validation of the forming process of ceramics;
- Modelling, design and experimental analysis of innovative ceramic products.
The network partners have collaborated through secondments and recruitment of research fellows. The research targets have been achieved in the following Work Packages:
WP1: Forming ceramics powder;
WP2: Processing of ceramic compounds;
WP3: Enhancing performance of ceramics;
WP4: Modelling of ceramics structures with imperfect interfaces;
WP5: New technological applications.

2. The scientific activity
The modelling and simulation of the forming processes of traditional and advanced ceramics require the development of constitutive models for ceramic powders subjected to progressive mechanical densification. Various yet complementary solutions have been found for these problems, by developing mechanical models based on elastoplasticity and then calibrating and validating them using experimental data. The implementation in a computer code of the mathematical models has been a difficult task, since the yield function, which is the cornerstone of the theory and is tailored to describe the transition from a granular to a fully dense ceramic material, does not allow the use of a standard return mapping integration scheme. This difficulty was successfully overcome by developing several integration schemes, which have all been shown to guarantee convergence. Another problem encountered and solved in the research has been the implementation of a large strain version of the above-mentioned constitutive model, which has never been attempted before, but has been shown to perform excellently.
The development and computer implementation of the model and its calibration using ‘ad hoc’ experiments as part of the research project allowed for the simulation of the forming process of a ceramic object from a granulate. The determination of an 'optimal' model for the description of cold compaction of ceramic powders was obtained through a scrutiny between different possibilities, based on the concept of elastoplastic coupling or on the concept of structured deformation for densification, which is capable of describing the co-existence of loose and dense phases within a granulate.
Considerations of the mechanical effects related to the microstructure of ceramics was pursued through homogenization techniques to define higher-order constitutive models equivalent to heterogeneous materials containing inhomogeneities at low concentration. Non-local modelling improves the description of the mechanical response of materials at the micro-scale and is crucial for the analysis of failure phenomena such as crack propagation, which was also thoroughly analyzed. With the aim of enhancing the mechanical performances of ceramics, especially structural ceramics, analyses of defect criticality were performed. Here 'defect' is meant as a stress raiser, such as voids, inclusions, cracks and notches, so that the dependence of the macroscopic properties of ceramics was analyzed on local parameters as generalised stress intensity factors. New results have been obtained on scattering and dispersion of elastic waves in advanced multi-scale ceramic systems. In particular, an optimal design was pursued for metamaterial geometries that possess remarkable properties, like negative refraction or an exponential localization in a dynamic response. Analytical expressions for the stiffness tensor and scalar density were derived from a non-singular piecewise smooth continuum transformation in which the transformed material properties are finite, continuous, and piecewise smooth. The 'push out' transformation is used in the evaluation of the physical and geometrical parameters required for the reduction of the scattered field.

3. Final results and their potential impact
The chief result obtained in the research project is the full development of a complete numerical simulation tool for the design of industrial items produced through ceramic compaction. This tool has been developed, using a rigorous mechanical approach together with specific experiments, to characterize materials during compaction. The resultant software, now available to the industrial partners, allows the design of ceramic parts through the simulation of powder cold forming, which can realistically describe the state of residual stress/strain, the density distribution inside the ceramic piece, and the spring-back effect. This allows for the production process of traditional or advanced ceramics to be based on a fully engineered approach, which allows a reduction in rejected pieces with the consequent improvement in waste and energy consumption, imperative in the perspective of sustainable development.
Several other outcomes of the project are also available. A new computational algorithm (software freely available online) allows the computer implementation of models similar to that developed for powder compaction, but also useful for the analysis of other materials of engineering interest, such as rock, concrete and soil. Moreover, other results published in several articles (and therefore freely available) are useful in various contexts. They allow for the solution of homogenization problems that trace the evolution of macroscopic properties to the basic ceramic microstructure and its changes. They suggest novel technological applications based on the use of ceramic fillers with piezoelectric properties to realize composite materials for soft dielectric energy harvesting devices. Finally, they allow for the determination of new geometries of materials for wave filtering and scattering, results which can yield ground-breaking ideas with an importance which goes beyond the specific research field of the project.

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