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Computational morphology and morphogenesis for empowering soft-matter engineering

Morphing soft matter, which is capable of changing its shape and function in response to stimuli, has wide-ranging applications in robotics, medicine and biology. Recently, computational models have accelerated its development. Here, we highlight advances and challenges in developing computational techniques, and explore the potential applications enabled by such models.

Yifan Yang, Fan Xu*

Nature Computational Science, 2024,

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SES 2024 Call for abstract: MS 10.11 Morphing Matters: Inspiration, Mechanics, Computation, Design, Fabrication, and Applications

Dear Colleagues,

We would like to invite you to submit abstracts and attend the minisymposium titled "10.11 Morphing Matters: Inspiration, Mechanics, Computation, Design, Fabrication, and Applications" in the 2024 SES Annual Techinical Meeting, August 20-23, 2024, Hangzhou, China.

Abstract submissions are due April 1, 2024.


10.11 Morphing Matters: Inspiration, Mechanics, Computation, Design, Fabrication, and Applications

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A solid-shell model of hard-magnetic soft materials

Hard-magnetic soft materials (HMSMs) consisting of an elastomer matrix filled with high remnant magnetic particles can exhibit flexible programmability and rapid shape changing under non-contact activation, showing promising potential applications in soft robotics, biomedical devices and flexible electronics. Precise predictions of large deformations of hard-magnetic soft materials would be a key for relevant applications.

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Morphomechanics of growing curled petals and leaves

Petals and leaves are usually curled and exhibit intriguing morphology evolution upon growth, which contributes to their important biological functions. To understand the underlying morphoelastic mechanism and to determine the crucial factors that govern the growth-induced instability patterning in curved petals and leaves, we develop an active thin shell model that can describe variable curvatures and spontaneous growth, within the framework of general differential geometry based on curvilinear coordinates and hyperelastic deformation theory.

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Strain stiffening retards growth instability in residually stressed biological tissues

Soft biological tissues often exhibit notable strain stiffening under increasing stretch, and this can have significant effects on tissue growth and morphological development, such as causing symmetry breaking in growing airways and leading to mucosal folding and airway hyperresponsiveness. To investigate the role of strain stiffening and the multifactorial control in growth and remodeling, we consider a growing tubular structure with strain-stiffening effects caused by increased and tightened collagen.

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Wrinkling of twisted thin films

Thin films usually exhibit instabilities and yield intricate wrinkles when two clamped ends are twisted. Here, we explore the wrinkling behavior and pitch-fork bifurcation of twisted thin films experimentally and theoretically. To quantitatively predict the post-buckling evolution of twist-induced wrinkling morphology, we develop a refined finite-strain plate model derived from 3D field equations and then solve it by using the finite element method with COMSOL. We examine the effects of aspect ratios and pre-tension on the wrinkling profile.

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A 3D hard-magnetic rod model based on co-rotational formulations

Hard-magnetic soft materials have attracted broad interests because of their flexible programmability, non-contact activation and rapid response in various applications such as soft robotics, biomedical devices and flexible electronics. Such multifunctional materials consist of a soft matrix embedded with hard-magnetic particles, and can exhibit large deformations under external magnetic stimuli. Here, we develop a three-dimensional (3D) rod model to predict spatial deformations (extension, bending and twist) of slender hard-magnetic elastica.

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A consistent finite-strain plate model for wrinkling of stretched anisotropic hyperelastic films

Stretch-induced wrinkles usually occur in a thin, clamped-clamped, hyperelastic film and eventually disappear upon excess stretching, with wrinkling direction being perpendicular to the stretching direction within isotropic elasticity framework. Here, we consider in-plane anisotropy induced by infilling fibers in thin films, which significantly affects the orientation and amplitude of wrinkles.

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Competition between Mullins and curvature effects in the wrinkling of stretched soft shells

A highly stretched hyperelastic shell exhibits a coupling behavior of local wrinkling and global bending within the stability boundary, and curvature resists and can even suppress surface wrinkles beyond a critical threshold. Here, we report a novel phenomenon that smooth surface maintains upon stretching a soft shell, while wrinkles emerge upon unloading, which implies a nonlinear interplay between curvature and Mullins (stress softening and residual strain) effects in the entire loading-unloading cycle.

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Buckling of an elastic layer based on implicit constitution: Incremental theory and numerical framework

A general class of implicit bodies was proposed to describe elastic response of solids, which contains the Cauchy–Green tensor as a function of Cauchy stress. Here, we consider the buckling of solids described by such a subclass of implicit constitutive relation. We present a general linear incremental theory and carry out bifurcation analysis of a uniaxially compressed rectangular layer described by an implicit constitution.

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Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory

It was reported both in experiments and computations using some classical plate theories that wrinkles can appear in a uniaxially stretched rectangular hyperelastic film with clamped-clamped boundaries and can be suppressed upon further tension. Here, based on a recently-available consistent finite-strain plate theory, we investigate this complex instability problem with isola-center bifurcation (the nontrivial solution curve begins and ends at two distinct points on the trivial line) in more depth and present an efficient numerical algorithm.

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Mathematically exploring wrinkle evolution

Wrinkling is one of the most important mechanical deformation modes (for example, buckling and crumpling) that are omnipresent in our daily life: for instance, wrinkled fingers after soaking in water for a prolonged time, the folds within the brain, and metal wrinkles after a car collision, to name a few.

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Curvature tunes wrinkling in shells

Transverse wrinkles usually emerge in a uniaxially stretched elastic film and can be suppressed upon further tension, which is an instability-restabilization behavior due to the nonlinear competition between stretching energy and bending energy. Here, we show that curvature can effectively and precisely tune the wrinkling localization and amplitude.

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Nanosleeves: Morphology transitions of infilled carbon nanotubes

Morphology instability of substrate-supported carbon atomic layers can be harnessed to modulate physical properties and functions, which has drawn interesting attention. Curvature would be a critical factor affecting surface morphology and its stability characteristics. Infilled carbon nanotubes, that is to say carbon monolayers with curved geometry and infilled substrates, namely nanosleeves, widely exist in the literature and have many potential applications.

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Special Issue on Instability and Bifurcation in Materials and Structures comes out

Dear Colleagues,

After one-year effort, we are happy to announce that the SI on Instability and Bifurcation in Materials and Structures is now completed and comes out online (

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Oblique wrinkling patterns on liquid crystal polymer core–shell cylinders under thermal load

Smart soft materials, which can flexibly respond to external multi-physics stimuli, have attracted considerable attention over the past few years. Here, we present tunable wrinkling patterns in cylindrical core-shell systems under thermal load via the orientation of director in nematic liquid crystal polymer (LCP). To quantitatively analyze mechanical behavior and morphological evolution of LCP core-shell cylinders, we develop a core-shell model that accounts for director-induced anisotropic spontaneous strains.

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Effect of surface topography on anisotropic friction of graphene layers

Tribological behavior of graphene layers has been a focus of intensive research interest since its crystal lattice structure can be exploited to achieve incommensurate contact, leading to nearly zero friction, namely structural superlubricity. However, wrinkling undulations are omnipresent on graphene and difficult to be completely eliminated, which inevitably resists superlubricity in reality. Here, we explore how the presence of surface wrinkles affects nanotribological behavior of graphene sliding systems.

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Intricate evolutions of multiple-period post-buckling patterns in bilayers

Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling, shape-morphing for camouflaging skins, and micro/nano-scale surface patterning control. However, it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region. Here, we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems.

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A finite strain model predicts oblique wrinkles in stretched anisotropic films

Transverse wrinkles commonly occur in a uniaxially tensile elastic membrane and can vanish upon excess stretching. The wrinkling direction is usually perpendicular to the stretching direction under isotropic elasticity. Here, we show that wrinkles are orientable by material anisotropy, such as in fiber-reinforced or fibrous films, and the wrinkling orientation can be tuned by varying the stiffness and direction of fibers.


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