Breakthroughs in materials science and engineering are needed to meet the demands of a sustainable society. Required for this are developments in materials technology for efficient energy applications, such as energy conversion (e.g., high-tech magnets), storage (e.g., batteries, hydrogen tanks), and smart devices.

The functionality and mechanical stability of advanced materials for sustainable energy supply rely on the effective coupling of different physical fields, including electro-magnetic, electro-mechanical, and chemo-mechanical interactions. However, many of the underlying mechanisms in this area have yet to be studied experimentally, and predictive theoretical and numerical models are currently being developed worldwide. Moreover, such mechanisms occur at different time and length scales, which poses another challenge to the data analysis and the design of advanced materials. Of course, sustainability also translates into the need to address the durability of structures and devices, accounting for the specific challenges derived from multi-field effects in materials, such as battery failure for electrolyte cracking or hydrogen embrittlement in steels.

This course delves into essential aspects of materials science and engineering, with a specific focus on modeling multi-field phenomena across various scales. Consequently, several challenges arise, including:

Key topics include:
1. Mathematical modeling of single-phase and multi-phase materials for coupled problems.
2. Scale-bridging techniques, spanning from the nano- to the micro- to the macro-scale.
3. Data analysis and design strategies for multi-field materials customization.
Ariadne’s thread of this course will be the analysis of the energy transfer mechanisms across scales to promote an experimental and in silico material design for a sustainable “Energiewende”. To achieve this, the course will explore experimental, theoretical, and computational methodologies, offering a comprehensive and cross-disciplinary perspective in the field.

Key topics include:
1. Continuum thermodynamics of coupled responses, encompassing thermo-, electro-magneto-, and chemo-mechanical aspects.
2. Numerical approaches for multi-field problems and machine learning technologies for data analysis.
3. Homogenization techniques for complex microstructures and multi-field phenomena.
4. Experimentally study of magnetism on atomic and macroscopic length scales.
5. Understanding the molecular basis of coupled mechanisms, ab initio methods.
6. An exemplary case study on the workflow from experiments to macroscopic characterizations using ab initio methods for hysteresis design aspects of magneto-mechanical coupled materials in high-tech magnets applications.
7. Applications focusing on the coupled response of materials for the green economy, including the study of hydrogen embrittlement in steels, failure of solid electrolyte Li-ion batteries, and multi-responsiveness of functionalized hydrogels.

This course is intended for graduate students and postdoctoral fellows from academia and industry interested in an interdisciplinary perspective of constitutive modeling of multi-physics mechanisms at different scales. A background in engineering or materials science is recommended for participants.