Speaker
Dr
Jean-Paul Pelteret
(Chair of Applied Mechanics, Friedrich-Alexander University Erlangen-Nuremberg)
Description
In recent years there has been a notable growth in research among fields involving coupled media, and in multi-physics problems in general. As the complexity of the physics describing the material loading and response increases, so does the time cost and sophistication of the computational tools used to analyse these problems both in the academic and industrial settings. Associated with this are further challenges, one example being that potential errors in implementation and subsequent numerical instabilities could be misinterpreted as physically plausible material instabilities.
Tools that automate differentiation are one mechanism to tackle the challenges of constitutive law and finite element formulation prototyping, development and validation. In this work we discuss the implementation of frameworks to perform assisted differentiation within the deal.II finite element library. We outline and discuss some of the challenges surrounding the integration of two algorithmic (automatic) and symbolic differentiation libraries within the pre-established tensor and finite element frameworks. Lastly, we discuss applications in the simulation of magnetorheological elastomers; these are smart, field-responsive composite materials that are of increasing interest in numerous industries. We demonstrate and benchmark the current implementation in the context of two problems, namely (i) a rate-dependent magnetic field-response constitutive law and (ii) homogenisation of representative volume element for a rate-independent magneto-rheological elastomer.
Primary author
Dr
Jean-Paul Pelteret
(Chair of Applied Mechanics, Friedrich-Alexander University Erlangen-Nuremberg)
Co-authors
Dr
Andrew McBride
(University of Glasgow)
Mr
Isuru Fernando
(University of Illinois)
Prof.
Paul Steinmann
(Friedrich-Alexander University Erlangen-Nuremberg)
