02247nas a2200169 4500008004100000245005800041210005800099490000600157520170300163100001901866700002101885700002301906700001801929700001801947700002301965856008901988 2022 eng d00aMathematical modelling of axonal cortex contractility0 aMathematical modelling of axonal cortex contractility0 v23 a
The axonal cortex is composed of a regular structure of F-actin and spectrin able to contract thanks to myosin II motors. Such an active tension is of fundamental importance in controlling the physiological shape of axons. Recent experiments show that axons modulate the contraction of the cortex when subject to mechanical deformations, exhibiting a non-trivial coupling between the hoop and the axial active tension. However, the underlying mechanisms are still poorly understood. In this paper, we propose a continuum model of the axon based on the active strain theory. By using the Coleman–Noll procedure, we shed light on the coupling between the hoop and the axial active strain through the Mandel stress tensor. We propose a qualitative analysis of the system under the simplifying assumption of incompressibility, showing the existence of a stable equilibrium solution. In particular, our results show that the axon regulates the active contraction to maintain a homeostatic stress state. Finally, we propose numerical simulations of the model, using a more suitable compressible constitutive law. The results are compared with experimental data, showing an excellent quantitative agreement. Statement of Significance The mechanics of cortical contractility in axons is still poorly understood. Unravelling the mechanisms underlying axial and hoop stress generation in the cortex will give insight on the active regulation of axon diameter. The understanding of this phenomenon may shed new light on the physical causes of axonal morphological degeneration as a consequence of neurodegenerative diseases, viral infections, and traumatic brain injuries.

 

1 aAndrini, Dario1 aBalbi, Valentina1 aBevilacqua, Giulia1 aLucci, Giulio1 aPozzi, Giulia1 aRiccobelli, Davide uhttps://math.sissa.it/publication/mathematical-modelling-axonal-cortex-contractility01815nas a2200145 4500008004100000245005800041210005800099300001300157490000800170520135300178100001901531700002201550700002701572856007001599 2022 eng d00aOptimal design of planar shapes with active materials0 aOptimal design of planar shapes with active materials a202202560 v4783 a

Active materials have emerged as valuable candidates for shape morphing applications, where a body reconfiguration is achieved upon triggering its active response. Given a desired shape change, a natural question is to compare different morphing mechanisms to select the most effective one with respect to an optimality criterion. We introduce an optimal control problem to determine the active strains suitable to attain a target equilibrium shape while minimizing the complexity of the activation. Specifically, we discuss the planar morphing of active, hyperelastic bodies in the absence of external forces and exploit the notion of target metric to encompass a broad set of active materials in a unifying approach. For the case of affine shape changes, we derive explicit conditions on the body reference configuration for the optimality of homogeneous target metrics. More complex shape changes are analysed via numerical simulations to explore the impact on optimal solutions of different objective functionals inspired by features of existing materials. We show how stresses arising from incompatibilities contribute to reduce the complexity of the controls. We believe that our approach may be exploited for the optimal design of active systems and may contribute to gather insight into the morphing strategies of biological systems.

1 aAndrini, Dario1 aNoselli, Giovanni1 aLucantonio, Alessandro uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2022.025601464nas a2200157 4500008004100000022001400041245007900055210006900134260000700203490000700210520098300217100001901200700002701219700002201246856003801268 2020 eng d a0021-893600aA Theoretical Study on the Transient Morphing of Linear Poroelastic Plates0 aTheoretical Study on the Transient Morphing of Linear Poroelasti c120 v883 a

Based on their shape-shifting capabilities, soft active materials have enabled new possibilities for the engineering of sensing and actuation devices. While the relation between active strains and emergent equilibrium shapes has been fully characterized, the transient morphing of thin structures is a rather unexplored topic. Here, we focus on polymer gel plates and derive a reduced linear model to study their time-dependent response to changes in the fluid environment. We show that independent control of stretching and bending deformations in stress-free conditions allows to realize spherical shapes with prescribed geometry of the mid-plane. Furthermore, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions compared to the stress-free evolution. We believe that these effects should be considered for the accurate design of smart systems and may contribute to explain the complexity of natural shapes.

1 aAndrini, Dario1 aLucantonio, Alessandro1 aNoselli, Giovanni uhttps://doi.org/10.1115/1.4048806