SOFT-PATTERN

Lead Research Organisation: UNIVERSITY OF OXFORD
Department Name: Mathematical Institute

Abstract

Although pattern formation in soft materials has been studied extensively due to its promising applications in multiple science and
engineering fields, the mechanisms of pattern formation in many cases are still unclear due to the high nonlinearity of the governing
equations induced by large deformations, for instance, localized ridges and complex 3D modes. For stiff thin layer coated to a thick
substrate, an alternative approach is to derive reduced models for the system. However, most existing reduced models are not self*consistent and many nonlinear terms are neglected without proper justifications. This seriously hampers their validity and as a result
the mathematical nature of the above mentioned modes and the effect of additional factors (material inhomogeneity and anisotropy)
are not unveiled.
The project SOFT-PATTERN is to overcome these challenges in an innovative and original way by developing mathematically
consistent and accurate reduced models accounting for material and geometric nonlinearities. The research work will be approached
from theoretical, numerical, and experimental aspects, based on the applicant's and the host laboratory's expertise. The exhaustive
training programme will allow the applicant to grow as a world-class researcher in this field. The proposed research will foster further
development in this direction and contribute to advanced and intelligent technologies of societal importance.
The applicant is a Chinese national, with a solid background in applied mathematics and nonlinear elasticity trained in Hong Kong. He
has published articles in high-impact factor journals, at the frontiers of applied mathematics and other disciplines, and has won two
competitive grants from the National Natural Science Foundation of China, demonstrating independence and leadership in research.
He is requesting funds for two years, to work with Prof. Alain Goriely FRS's team at Oxford. Three secondments at Keele, NUI Galway,
and Cardiff are planned.

Publications

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Liu R (2024) Surface wrinkling of a film coated to a graded substrate in Journal of the Mechanics and Physics of Solids

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Liu Y (2024) Surface wrinkling of a hyperelastic half-space coated by a liquid crystal elastomer film in International Journal of Solids and Structures

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Moulton D (2024) Physique de la morphogenèse des coquilles de mollusques in Reflets de la physique

 
Description Wrinkles are ubiquitous in nature and biological systems. Within the framework of nonlinear elasticity, we systematically investigated the deformation and instability of a stiff film adhered to a compliant substrate, a prototypical mathematical model for studying pattern formation in soft materials. We unravelled the influence of the modulus gradient of substrate and curvature on the onset of surface instability and the resulting patterns in film/substrate bilayers, identifying key parameters that govern the morphogenesis of biological tissues and elephant trunks. Furthermore, we developed a linearized incremental theory for liquid crystal elastomers and discovered that director reorientation can delay surface wrinkling in an elastic substrate coated with a liquid crystal elastomer film.
Exploitation Route Perhaps investigating multi-layered composite materials and more complex geometries could yield deeper insights into biological morphogenesis and inspire innovative applications in soft robotics, flexible electronics, and biomedical devices.
Sectors Education

 
Description Characterizing the nonlinear effects of multiple parameters in regulating pattern formation in soft systems is essential for understanding the morphogenesis of biological tissues and designing bio-inspired devices. We derived analytical formulas to describe the onset of surface wrinkles and the resulting patterns in film/substrate bilayers, identifying the critical parameters that govern pattern formation. These findings provide a fundamental theoretical basis for evaluating the physical properties of soft tissues and controlling surface patterns in flexible structures. Elephant trunks are remarkable for their extraordinary flexibility. A prominent feature of elephant trunks is the widespread distribution of wrinkles, which store additional length and enhance adaptability. We developed a simple mathematical model to study wrinkle formation in elephant trunks, capturing essential characteristics through theoretical predictions. These insights deepen our understanding of the non-uniform wrinkle distribution in elephant trunks.
First Year Of Impact 2024
Sector Education
 
Description Goriely Talk - MathSys forum - University of Warwick 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Guest speaker Lecture title: From neurons, plants, and elephant trunks to actuators and soft robots: The fascinating dynamics of smart active solids.
Year(s) Of Engagement Activity 2025
URL https://warwick.ac.uk/fac/sci/mathsys/forum/abstracts
 
Description Goriely talk - "Nonlinear Elasticity and All That" On the occasion of Giuseppe Saccomandi's 60th birthday 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk title: Elastic Chirality
Year(s) Of Engagement Activity 2024
URL https://neat2024.weebly.com/
 
Description Max Planck Institute of Molecular Cell Biology & Genetics 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Delivered a seminar and listened to graduate presentations: Dynamics and self-organization in the movement of plants and axons: A unified theory of tropism and taxis
Year(s) Of Engagement Activity 2023,2024
 
Description Yang Liu - - 2024 SES Annual Technical Meeting, August 20-23, 2024, Hangzhou, China. 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk Title: Localized instabilities of a residually stressed solid cylinder under stretch.
Year(s) Of Engagement Activity 2024
URL https://www.2024ses.com/index/page.html?id=1015
 
Description Yang Liu - Applied and Computational Mathematics Seminars, Cardiff University, October 1, 2024, Cardiff, UK. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Title: Surface wrinkling in film/substrate bilayers.
Year(s) Of Engagement Activity 2024
 
Description Yang Liu - British Liquid Crystal Society Annual Meeting 2024, April 10-12 2024, Oxford, UK. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk Title: Surface instabilities of a half-space coated by a liquid crystal elastomer film.
Year(s) Of Engagement Activity 2024
 
Description Yang Liu - International Workshop on "The coupled nonlinear continuum theory horizon", July 1-5, 2024, Castro Urdiales, Spain. 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk Title: Surface instabilities of a half-space coated by a liquid crystal elastomer film.
Year(s) Of Engagement Activity 2024
 
Description Yang Liu - Nonlinear Elasticity: Modelling of multi-physics and applications, March 25-28 2024, Edinburgh, UK. 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk Title: Surface wrinkling in film/substrate bilayers: Influence of material inhomogeneity and anisotropy.
Year(s) Of Engagement Activity 2024
URL https://www.icms.org.uk/NonlinearElasticity
 
Description Yang Liu - SES Annual Technical Meeting, August 20-23, 2024, Hangzhou, China 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk Title: Instabilities of film/substrate bilayers.
Year(s) Of Engagement Activity 2024
URL https://www.2024ses.com/index/page.html?id=1015
 
Description Yang Liu talk - "Nonlinear Elasticity and All That" On the occasion of Giuseppe Saccomandi's 60th birthday 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk Title: Buckling and post-buckling of fiber-reinforced tissues.
Year(s) Of Engagement Activity 2024
URL https://neat2024.weebly.com/