Mechanics of Materials and Structures

Mechanics of Materials and Structures deals with the mechanical behaviour of materials and structures: stiffness, strength and stability.

An important topic is constitutive modelling, where the mechanical behaviour of materials is captured in (phenomenological) constitutive models, which reproduce the observed mechanical behaviour in elementary tests. This is primarily pursued within the subtheme geomechanics and geotechnical engineering.

In the past decade there has been an attempt to simulate the mechanical behaviour of materials from observations at one or several scales below the macroscopic level of observation. Significant work along this line is done in the research division, in particular within the subtheme multi-scale and multi-physics modelling. As is clear from the name of this subtheme, also the increasingly important issue of the interaction of the mechanical behaviour of materials and diffusion phenomena like moisture or thermal flow receive ample attention in this subtheme.

A core strength of the division is the simulation of damage and fracture of materials and structures, which constitutes the third subtheme. Advanced discretisation techniques like extended finite element methods or isogeometric finite elements or isogeometric boundary element analysis are key to capturing non-linear and dynamic phenomena, and are studied in the fourth subtheme: Advanced numerical methods.

Research topics

Multi-scale/multi-physics modelling

Advanced numerical methods

Soil mechanics/geotechnics

Computational damage and fracture mechanics


Prof Chris Pearce  Dr Hean Lee
Prof Simon Wheeler Dr Peter Grassl
Dr Ankush Aggarwal Dr Andrew McBride
Dr Zhiwei Gao Dr Lukasz Kaczmarczyk
Ms Fiona Bradley Mrs Linda Brown
Dr Thomas Shire Dr Prashant Saxena


Multi-scale/multi-physics modelling


Investigations of the mechanical behaviour of materials increasingly account for effects at smaller length scales and for couplings with other physical fields, such as temperature or moisture. The development of computational multi-scale-multi-physics schemes for the characterisation of biological and technical materials is among the most active research fields in the division. Research challenges arise from the formulation of suitable sets of field equations, which together with complex constitutive models capture the interactions between the fields and scales, and from their implementation into advanced computational methods, which are capable of providing robust solutions to the comprehensive problems. The main focus is on enhancing the understanding of structure-function relationships by bridging length and time scales, as well as on developing predictive schemes for engineering and biomedical applications. The computational work is complemented by experimental investigations for model calibration and validation, which are partly carried out in the framework of research collaborations.

A variety of materials is currently being investigated, ranging from fibre-reinforced composites and concrete to bone and wood. Topics covered comprise the understanding of fracture processes and brittleness in heterogeneous materials, the interaction of mass transport and fracture, mechanical properties under extreme conditions, such as high pressure, temperature and severe chemical environments, and the time-dependence of sorption phenomena.



Advanced numerical methods


Most processes in engineering are captured by differential equations. A range of discretization methods is currently available to solve them, for instance finite element methods, finite difference methods, boundary element methods, and finite volume techniques.
For fracture special elements can be needed, for instance hybrid Trefftz elements, as have been developed in the division especially for brittle fracture.

The partition-of-unity property of the Lagrange polynomials commonly used in finite element methods allows for the addition of tailor-made functions to the basis functions (XFEM), thereby allowing for the accurate description of singularities and discontinuities that is free of the underlying discretization. Contributions have been made to cohesive crack propagation, fracture in porous media, and delamination in composite shells.

Recently, Lagrange polynomials have been replaced by spline functions, which are commonly used in Computer Aided Design, also for analysis purposes. This not only holds for finite elements, but also for boundary elements, where we have shown that the improved description of the geometry has shown spectacular improvements, for instance in acoustic wave propagation around spheres (isogeometric boundary element analysis). And in isogeometric finite element analysis we have shown that the higher-order continuity of the interpolants leads to a superior prediction of stresses and other derived quantities, like the relative fluid flow in porous media, where the local mass balance is now automatically satisfied. Furthermore, elegant procedures have been developed to describe damage and fracture using isogeometric analysis.

Phase-field models have recently become en vogue as a mathematically sound continuum method to capture discontinuities. The limitations for brittle fracture have been pointed out, and an extension to cohesive fracture has been made.

Soil mechanics / geotechnics

Staff: Prof Simon Wheeler, Dr Peter GrasslDr Zhiwei Gao

One particular area of long-standing activity is the behaviour of unsaturated soils, including coupling of mechanical behaviour and water retention behaviour. The group has specialised laboratory facilities for suction-controlled testing and has made important contributions in the development of constitutive models for unsaturated soils, having published a number of seminal papers in the field. Applications of the research include: foundations in arid, semi-arid and tropical regions; impact of climate change on embankments for road, rail and flood defences; and performance of bentonite clay barriers for underground disposal of nuclear waste.

Other areas of research include the evolution of both fabric anisotropy and inter-particle bonding during plastic straining, and the influence of this evolution of soil microstructure on mechanical behaviour. This has considerable importance in geotechnical applications involving a wide range of soils, from natural soft clays to granular materials. Other topics of interest include performance and modelling of fibre-reinforced sands and temperature effects on soil behaviour (relevant to ground source heating, thermal piles, impact of climate change and underground disposal of nuclear waste).

Computational damage and fracture mechanics


Computational modelling of damage and fracture in materials and structures has been a main research field of the division for a long time. The main challenge is to develop constitutive models, which describe damage and fracture processes accurately, and are independent of the numerical discretisation.

Constitutive models based on damage mechanics, plasticity theory, and linear and non-linear fracture mechanics have been implemented in a wide range of continuum and discontinuum methods. In brittle fracture, configurational forces have been applied to drive fracture propagation. In quasi-brittle and ductile fracture, the widely used cohesive-surface approach has been extended to include phenomena like in-plane stretching and mass transport. As alternative to continuum methods, lattice models – a prototypical discontinuum method – have been extended to include mass transport. Contributions have also been made to the regularisation of plasticity and damage models at incipient failure, i.e. by non-local averaging, or by including strain gradients in the constitutive model.
The models have been applied to a variety of structures made of materials ranging from fibre-reinforced composites and concrete to bone and wood. Applications include understanding fracture processes and brittleness in heterogeneous materials, the interaction of mass transport and fracture, prediction of fracture induced size effects on strength and the modelling of dynamic fracture.