Research Studentship in Solid Mechanics

Project: Micromechanics of Soft Materials

Supervisor: Professor Laurence Brassart

Traditional engineering applications mostly use hard materials, such as steel, concrete or fibre-reinforced composites. In contrast, materials found in plant and animal tissues are soft. Softness imparts attractive characteristics to materials, such as the ability to deform in response to external stimuli (force, pH, temperature). Softness is also desirable for applications where materials interact with the human body. Inspired by nature, there has been a fast-growing interest in developing soft materials for emerging applications in engineering and medicine, such as artificial cartilage and soft robots [1,2].

The development of soft materials is currently limited by a lack of understanding of their complex mechanical behaviour in response to various stimuli. Current models are mostly phenomenological, and therefore have limited predictive capability [3,4]. The aim of the Brassart Research Group at Oxford University is to develop new modelling tools at various length scales that can help unravelling the complex structure-property relationships of soft materials.

This project focuses on hydrogels – a broad class of soft materials consisting of a polymer network swollen in water. The mechanical and functional properties of hydrogels depend on microscopic parameters such as the single chain behaviour, network architecture and crosslinking mechanism. The aim of the project is to develop a micromechanical modelling approach to understand the role of microscale parameters on the effective behaviour of hydrogels. This will in turn enable the development of accurate simulation tools (typically using the finite element method) and serve as a guide for the design of new soft materials with superior properties.

In contrast with hard materials, the field of micromechanics applied to soft materials is in its infancy, with many open questions of both fundamental and practical significance. Possible projects are listed below. The specific orientation of the research will be fine-tuned based on the candidate’s interest and background.

1. Mesoscale simulations of polymer networks

The aim of this project is to elucidate the relationships between network parameters and hydrogel mechanical properties using Random Network models previously developed in the group [5]. In this approach, polymer chains are represented by nonlinear springs connected at nodes representing crosslinking points. The project will particularly focus on hydrogel systems in which the crosslinks can be broken and reformed, endowing the gel with rate-dependent properties. The role of network architecture on damage and crack propagation resistance will be assessed. Mesoscale simulations will also serve as reference for the formulation of macroscale “mean-field” estimates useful for large-scale simulations.

2. Modelling viscoplasticity, damage and self-healing in hydrogels

Conventional hydrogels are weak and brittle, which limits their scope of application. Recently, this limitation has been overcome by introducing reversible crosslinking mechanisms in the network, enabling efficient energy dissipation for increased toughness and self-healing properties [6,7]. This project aims at developing a new physics-based constitutive model to describe the viscoplastic behaviour that emerges from the dynamic breaking and reforming of crosslinks at microscale. The model will be developed in a continuum thermodynamics framework at finite strains, and will be implemented as a user subroutine in the Finite Element software ABAQUS. The model will be further extended to simulate damage and self-healing [8], in view of guiding the design of soft structures.

3. Micromechanics of fibre-reinforced hydrogels

Another efficient technique to improve the mechanical strength of hydrogels is to reinforce them with stiff fibres. Indeed, most hydrogels found in natural tissues such as muscles and cartilage contain fibres. Fibres increases the mechanical stiffness and strength, and also induce anisotropy. However, modelling efforts have usually considered isotropic behaviour [3,4] or have a limited physical basis [9]. This project aims to develop a micromechanical approach for fibre-reinforced polymer gels, inspiring from homogenisation techniques previously developed for filled elastomers, e.g. [10]. Mean-field predictions will be validated against full-field simulation results on Representative Volume Element of the microstructure. The effect of fillers on the mechanical and diffusion properties will be investigated.


[1] Calvert, P., 2009. Hydrogels for soft machines. Adv. Mater. 21, 743-756.

[2] Suo, Z., 2012. Mechanics of stretchable electronics and soft machines. MRS Bull. 37, 218-225.

[3] Hong, W., Zhao, X., Suo, Z., 2008. A theory of coupled diffusion and large deformation in polymeric gels. J. Mech. Phys. Solids 56, 1779-1793.

[4] Liu, Z., Toh, W., Ng, T.Y., 2015. Advances in mechanics of soft materials: a review of large deformation behaviour of hydrogels. Int. J. Appl. Mech. 7, 1530001.

[5] Alame, G., Brassart, L., 2019. Relative contributions of chain density and topology to the elasticity of two-dimensional polymer networks. Soft Matter 15, 5703.

[6] Sun, J.-Y., Zhao, X., Illeperuma, W.R.K., Chaudhuri, O., Oh, K.H., Mooney, D.J., Vlassak, J.J., Suo, Z., 2012. Highly stretchable and tough hydrogels. Nature 489, 133.

[7] Zhao, X., 2014. Multi-scale, multi-mechanism design of tough hydrogels: building dissipation into stretchy networks. Soft Matter 10, 672-687.

[8] Yu, K., Xin, A., Wang, Q., 2018. Mechanics of self-healing polymer networks crosslinked by dynamic bonds. J. Mech. Phys. Solids 121, 409-431.

[9] Bosnjak, N., Wang, S., Han, D., Lee, H., Chester, S.A., 2019. Modeling of fiber-reinforced polymeric gels. Mech. Res. Commun. 96, 7-18.

[10] Goudarzi, T., Spring, D.W., Paulino, G.H., Lopez-Pamies, O., 2015. Filled elastomers: A theory of filler reinforcement based on hydrodynamic and interphasial effects. J. Mech. Physics Solids 80, 37-67.


This studentship is funded through the UK Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership and is open to UK students (full award – fees plus stipend). Full details of the EPSRC eligibility requirements can be found here.

Award Value

Course fees are covered at the level set for UK students (c. £7970 p.a.). The stipend (tax-free maintenance grant) is c. £15009 p.a. for the first year, and at least this amount for a further two and a half years.

Candidate Requirements

  • Prospective candidates will be judged according to how well they meet the following criteria:
  • A first class honours degree in Engineering, Physics or Applied Mathematics
  • Excellent English written and spoken communication skills
  • Strong interest for mathematical modelling and numerical simulations in Mechanics of Materials
  • Strong background in Solid Mechanics
  • Good programming skills (e.g. Matlab, Python, C/C++)

The following skills are desirable but not essential:

  • Basic knowledge of polymer physics or soft matter physics
  • Basic knowledge of the Finite Element Method

Application Procedure

Informal enquiries are encouraged and should be addressed to Professor Laurence Brassart.

Candidates must submit a graduate application form and are expected to meet the graduate admissions criteria. Details are available on the course page of the University website.

Please quote 20ENGMM_LB in all correspondence and in your graduate application.

Application Deadline

24 January 2020

Start Date

October 2020