Many amorphous soft systems exhibit spectacular transitions when subjected to external forces and deformations. One of the more captivating examples is the yielding transition, which unites systems as disparate as gels, glasses, foams, and granular materials [1]: while for small external drives these materials behave substantially elastically, when the driving becomes sufficiently large, they undergo microscopic plastic rearrangements and macroscopic flow. Due to the amorphous nature of these materials, immediate use of theoretical descriptions that work successfully for crystalline solids is prevented. Recent theoretical [2,3], numerical [4,5] and experimental [6,7] approaches have been making progresses to link the emerging macroscopic rheological behavior to the underlying microscopic events [8], however outstanding questions remain and our current understanding of the yielding transition remains incomplete [9].

Quite intriguingly, many living tissues are also subjected to mechanical stresses that, in addition to being external, can also arise from internal physiological processes at the cellular level. As a consequence, one can observe tissue fracture [10], as well as jamming [11] and unjamming [12] transitions that resemble those observed in inert systems, while at the same time playing a key role in physiologically relevant processes such as embryogenesis [13] and cancer growth [14].

The analogies between the rheological behavior of inert and living soft materials is becoming so evident and compelling that cell tissues have been considered as active foams [15], or yield-stress materials [16] that exhibit shear-driven solidification [17] or brittle-to-ductile transitions [18], also accompanied by activation of topological defects [19], just like their inert counterparts. The deeper understanding of the yielding transition, and of its emergence from the relevant microscopic processes, in inert soft matter [1,3,20-22], has therefore important potential implications for the fundamental understanding of living soft materials and tissues. Vice versa, mimicking remedial strategies that are known to work for living soft materials can drive the design of improved artificial materials.

It thus appears timely to bring together leading researchers, early-career researchers and students working in these two communities, and to this aim we propose a 6-week ESI Thematic Program organized around the following keywords: Failure, Yielding, Fracture, Percolation, Jamming, Rigidity, Flocking, Topology, Defects, Memory, Confinement.

A cornerstone of the program is the adoption of a combined theoretical, numerical and experimental perspective that will provide an invaluable overview of the current research and promote the integration of different perspectives. In addition, the proposed program intends to facilitate the exchange of information and results among different communities interested in understanding the rheological behavior of inert and living soft materials, in particular across different length and time scales.

In addition, the program should prompt and facilitate interactions, and ideally identify new fundamental and applied problems, as well as strategic initiatives and directions of research.

Topic 1: Phases, transitions and rheological properties of inert soft materials

Inert soft materials exhibit significant non-linear responses to mechanical solicitations, producing intertwined effects of viscoelasticity, plasticity, and memory [23-25]. Investigating microscopic processes is challenging due to their vast range of time and length scales [21,22,26]. However, advancements in experimental techniques and computer simulations are beginning to offer novel insights [6,9,27-30]. In glass physics, yielding, annealing, avalanches, and memory have been explored [31-35]. Major questions include identifying key microscopic timescales and processes governing yielding, brittleness, ductility, stress relaxation, and overall nonlinear response.

Outstanding questions:

• What are the fundamental microscopic timescales (and length-scales) that govern yielding in soft materials? How can they be extracted experimentally and investigated in simulations or through theoretical predictions?
• Which processes govern the brittleness or ductility of yielding in soft materials? Are there fundamental mechanisms and universal laws?
• How does stress relaxation enter yielding? How is it related to the material aging?
• Which is the (extended) set of material properties that contain truly all the information of the nonlinear response of the material, all the way to the yielding? Does such set exist?
• In amorphous materials, the usual description of elasticity and mechanical response developed for crystalline solids does not hold, and rigidity and mechanics are rather described in terms of constraints. Can concepts derived from this constraint description, such as jamming and rigidity percolation, be relevant and useful when dealing with yielding and rheological behavior? How?

Topic 2: Phases, transitions and rheological properties of living soft materials

Various biological processes hinge on cell rearrangements in tissues. When parameters such as density, motility, cell-cell adhesion, and cortical tension are altered, tissues may undergo transitions from liquid-like to solid-like states [12,-14,36-40]. These transitions impact the tissue's rheological properties [13,15,17,18], though a systematic study correlating rigidity and microscopic dynamics is still needed. Major questions involve rheological characterization at multiple scales, understanding rheology from a multiscale perspective, the sequence of biophysical steps leading to tissue failure [10,41,42], predicting failure based on microscopic precursors, and the applicability of remedial strategies from living materials to inert soft materials.

Outstanding questions:

• How can we perform accurate rheological characterization at the subcellular, cellular, and supracellular scales in a wide frequency range? What theoretical, experimental and numerical techniques can be developed or combined?
• Is it possible to understand the rheology of living soft materials as a multiscale problem starting from the basic components of a single cell? Can we incorporate activity in existing rheological models to achieve a univocal description of living soft materials?
• Can we understand failure in tissues and other cell collectives as a sequence of biochemical/biophysical steps such as cytoskeletal changes, surface adhesion modulation, cell rearrangements/reorientation, etc.?
• Can we predict failure based on the identification and monitoring of microscopic (i.e. subcellular and cellular) precursors?
• What remedial strategies that are available to living materials are applicable to inert soft materials?

Organization of the program

The program will spread over the period Aug. 19, 2024 — Oct. 11, 2024, with two breaks Aug 31 - Sep 8, 2024 and Sep 21 - 29, 2024.

• Week 1 (Aug 19 - Aug 23) and Week 2 (Aug 26 - Aug 30): Summer school Non-equilibrium Processes in Physics and Biology: the training program will offer lectures tailored to the needs of students and postdocs who are interested in the program topics; the target group are PhD students and postdocs, including both local participants and participants from the wider international community. Lectures in the traiditional sense will be primarily in the morning, whereas in the afternoon, a diverse set of activities will take place, including double-talks (e.g. biology&physics, experiments&simulations), journal clubs, hands-on sessions, students flash talks, etc.

Break (Aug 31 - Sep 8)

• Week 3 (Sep 9 - Sep 13): ESI-CECAM joint workshop: “Failure in soft materials: from yielding to fracture”: With this workshop, our objective is to bring together various communities that heavily rely on universal concepts like mechanical response and failure. We firmly believe that there are numerous unresolved questions and ideas that can encourage a fruitful exchange of knowledge between these communities. Consistent with the CECAM tradition, computer simulations are of utmost importance in these fields, serving as both a guiding tool for experiments and a modeling resource when theoretical approaches fall short. Furthermore, in the forthcoming years, the emerging AI/ML paradigm will significantly influence all fields of physics. By inviting experts in this domain, we aim to facilitate an open and comprehensive discussion regarding the impact of such paradigm on the workshop's research themes.
• Week 4 (Sep 16 - Sep 20): Team work of selected researchers toward a roadmap paper, with a soft program of talks (more details will follow)

Break (Sep 21 - Sep 29)

• Week 5 (Sep 30 - Oct 4): Team work of selected researchers toward a roadmap paper, with a soft program of talks (more details will follow)
• Week 6 (Oct 7 - Oct 11): Team work of selected researchers toward a roadmap paper, with a soft program of talks (more details will follow)

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