Configurational Mechanics of Soft Materials: Revolutionising Geometrically Nonlinear Fracture

Project Information

SoftFrac

Grant agreement ID: 101052785

DOI

10.3030/101052785

EC signature date 18 May 2022

Start date 1 January 2023

End date 31 December 2027

Funded under

• European Research Council (ERC)

Total cost

€ 2 494 538,00

EU contribution

€ 2 494 538,00

Coordinated by

FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN-NUERNBERG
Germany

Periodic Reporting for period 1 - SoftFrac (Configurational Mechanics of Soft Materials: Revolutionising Geometrically Nonlinear Fracture)

Reporting period: 2023-01-01 to 2025-06-30

Summary of the context and overall objectives of the project

How do materials fail? Fracture is an every day experience for all of us - sometimes wanted, for example when opening food packages - sometimes dangerous and detrimental, for example when safety relevant constructions collapse and break down. For many materials fracture mechanics is fortunately well-understood, however for the emerging and important complex class of soft materials this is mostly terra incognita. Soft materials are for example underpinning soft robotics, can represent soft biological tissues, constitute various types of sealings, and have many more exciting, oftentimes still upcoming, future applications. Taken together, understanding how various types of soft materials fracture, modelling these intricate processes and eventually being able to simulate soft fracture enables us to either prevent the failure of soft materials or to intentionally exploit fracture of this exiting material class. Imagine for example a future cargo release system based on a kind of bungee rope that fractures precisely at a targeted, extremely large elongation to release its fragile load very gently. Without meticulously mastering the fracturing of soft materials - experimentally, theoretically, and computationally - such imaginative applications will not become a reality.

SoftFrac thus targets the three key aspects of the fracture of soft materials: their experimental investigation, the establishment of a theoretical framework addressing the challenges when modelling soft materials, and a robust and accurate computational setting that enables the prediction and analysis of fracture processes in soft materials. Experimentally investigating soft materials comes with its own challenges due to the difficulties of their handling, the extreme large deformations, which are not easy to control, record and analyse, and their complex interactions with non-mechanical stimuli such as magnetic, electric, optical, and temperature fields. Underpinning our modelling and simulation research is the theory of configurational mechanics, an unconventional approach that allows describing various types of failure processes, and that has been pushed over the past by the applicant. Only the close integration of experiment, modelling, and simulation allows us to jump ahead in the challenging field of fracture of soft materials.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Activities in SoftFrac are grouped in three areas: experiments, modelling, and simulation.

In our experimental work to date we essentially focussed on three types of soft elastomers, i.e. Elastosil, Dowsil and VHB, that vary in their softness and further mechanical properties. Despite conducting uniaxial tests for the material characterisation, we explored their fracturing behaviour under the influence of various types of non-mechanical stimuli. For soft elastomers filled with small hard magnetic particles we found that the magnetic interactions delay fracture onset and propagation. We could also demonstrate how electric-field-induced Coulomb forces exerted laterally on soft elastomers influence the triaxiality close to a crack tip and thus the fracture process. Lately we conducted research into the difficult phenomenon of side-ways cracks where cracks propagate in the direction of loading rather than perpendicular to it. We found that we can influence the transition between perpendicular and side-ways fracture by modulating the cross-linking density of the polymer. Currently we explore the effect of phase transitions in shape memory polymers on their fracturing behaviour.

In our modelling work we addressed two mayor challenges: how to model the complex mechanical behaviour of soft materials based on experimental data and how to analyse the fracture of soft materials based on an unconventional continuum mechanics approach which considers configurational changes such as crack propagations. To this end we established, on the one hand, a novel data-driven approach that adaptively determines a discretised energy storage density based on optical full-field experimental displacement measurements. Based on this new approach we could successfully model the experimentally observed complex behaviour of three types of soft elastomers, i.e. Elastosil, Dowsil and VHB. On the other hand we further developed configurational mechanics so as to exploit it in the fracture analysis of dedicated soft elastomer specimens and, as only seemingly a different field, the fracture-resistant topology optimisation of structures made of soft elastomers.

In our simulation work we pushed forward various computational approaches towards application to soft fracture. We found that the phase field method allows capturing the main features in geometrically nonlinear fracture mechanics, including anisotropy, rate-dependent material response, side-ways cracking, and coupling to various non-mechanical stimuli. However, all these extensions require non-trivial extensions to the plain vanilla version of the phase field method, some that still keep us busy. We furthermore translated the configurational force method into a versatile computational setting in topology optimisation and demonstrated that the resulting algorithm provides fracture-resistant optimal structures. Since elastomers are typically incompressible, we incorporate the concepts of configurational mechanics into various mixed variational methods as the basis of accurate finite element expansions. Last but not least we currently leverage our understanding of crack segmentation in soft materials by analysing recent experimental evidence based on our configurational mechanics approach.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Understanding and controlling when and under which conditions cracks are created, how they propagate and what impacts their geometry and topology, and how these processes can be modulated by external stimuli, all for soft materials, has potentially high impact in various areas of research and technology. Once fully experimentally analysed, novel and/or enhanced/refined modelling approaches that exclusively rely on measured data allow for better capturing the intricate behaviour of soft materials, whereby the model accuracy adaptively increases with more data becoming available.

Our advanced developments in simulation technologies to capture fracture processes in soft materials will likewise have high potential impact in engineering and sciences. We develop improved capabilities of finite element expansions to describe the intricate behaviour of soft materials, thereby exploiting configurational mechanics in discrete settings. Regarding crack propagation, we advance phase field modelling of fracture by extending its realm to large deformations, rate-dependence, coupled problems, side-way cracks, and anisotropy. For finite element formulations, we pursue research into novel mixed mode with a view on increasing the accuracy of discrete configurational force specifically for quasi-incompressible problems.