Generalized multiple peeling theory uploading hyperelasticity and pre-stress

Lyapunov stability of competitive cells dynamics in tumor mechanobiology

“…For these reasons, the study of the effects of solid stress on soft tissue homeostasis has been investigated both theoretically and experimentally, by observing the in vitro growth of confined multicellular spheroids [11][12][13][14] as well as by means of magnetic or mechanical actuators to apply forces on in vivo systems [2,15]. The underlying mechanisms transducing a mechanical cue into a biochemical signal are explained on the basis of some conformational changes and molecular pathways that modify cancer single-cell properties, which exhibit a different cytoskeletal stiffness as well as altered adhesion and motility capabilities [11,[16][17][18][19][20]. Therefore, the understanding of the mechano-responses of cancer systems, from single-cells to entire masses, could actually lead to innovative targeting and therapeutic strategies that, by exploiting the mechanical differences between tumor and host as a selectivity principle, provide the possibility to mechanically attack cancer cells by preserving the healthy surroundings [21][22][23].…”

On the emergence of adhesion in asymptotic analysis of piecewise linear anisotropic elastic bonded joints

“…At the macroscopic scale, adhesion is typically modeled using energetic arguments like Griffith theory or contact laws not invoking any specific theory about the nature of the adhesive material, as for example in Johnson et al (1971), Fremond (1988, Talon and Curnier (2003). At an intermediate level, more refined adhesion models have been proposed, exploiting biological evidence of hierarchy and contact splitting as a strategy to enhance the adhesive properties of natural structures (Berardo and Pugno, 2020;Fraldi et al, 2021). In this paper, another viewpoint arises, attributing the origin of macroscopic adhesion to the mechanical presence of an interposed adhesive layer with piecewise linear elastic anisotropic behavior.…”

Mechanotropism of single cells adhering to elastic substrates subject to exogenous forces

“…For example, processes of mechanotaxis, namely of mechano-driven migration, have been detected, whose most consolidated evidence is represented by the stiffness-guided locomotion mechanism known as durotaxis (Lo et al, 2000;Lazopoulos and Stamenović, 2008). Additionally, (re)orientation and polarization of adherent cells have been largely recognized as influenced by their elastic interactions with the extracellular environment (Schwarz and Safran, 2013;He et al, 2020;Kopfer et al, 2020;Friedrich and Safran, 2012;Lim and Donahue, 2007). In this regard, it has been observed that animal cells, assuming round shapes in suspension, stretch and flatten when adhering to an external surface, some cell types (e.g.…”

“…Motivated by these observations, a number of theoretical approaches have been proposed in the literature for studying the spatial organization and, in particular, the preferential alignments adopted by stationary single-cells as a consequence of the interplay with the network of neighbouring cells or the interaction with externally applied mechanical stimuli, often occurring through elastic media (Schwarz and Safran, 2013;Chen et al, 2015b). In this context, several possible optimization mechanisms have been suggested as underlying the reorientation process, each aimed to the achievement of a specific target, such as the attainment of the lowest strain state (Wang et al, 1995(Wang et al, , 2001De et al, 2008;Ben-Yaakov et al, 2015;Golkov and Shokef, 2017), the retention of a minimal or fixed stress level (De et al, 2007;Tondon and Kaunas, 2014;De et al, 2008;Ben-Yaakov et al, 2015;Golkov and Shokef, 2017), the search for the minimum elastic energy configuration (Schwarz and Safran, 2002;Bischofs and Schwarz, 2003;Livne et al, 2014;Xu et al, 2018) or the stability of the focal adhesions (Chen et al, 2012(Chen et al, , 2015aFraldi et al, 2021). Accordingly, various mechanical descriptions have been provided, which range across different length scales, going from molecular approaches directly involving biochemo-mechanical processes at the level of the focal adhesion complexes to one-and bi-dimensional structural or continuum cellular models.…”