Modelling Localisation and Spatial Scaling of Constitutive Behaviour: a Kinematically Enriched Continuum Approach

It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.Comment: Proceedings of Asian-Pacific Conference on Fracture and Strength 2014 and the International Conference on Structural Integrity and Failure, 9-12 December, Sydney, Australi

Geometrically-exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

We develop an Optimal Transportation Meshfree (OTM) particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler-Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method.Comment: 19 pages, 8 figure

Parallelized Hybrid Monte Carlo Simulation of Stress-Induced Texture Evolution

A parallelized hybrid Monte Carlo (HMC) methodology is devised to quantify the microstructural evolution of polycrystalline material under elastic loading. The approach combines a time explicit material point method (MPM) for the mechanical stresses with a calibrated Monte Carlo (cMC) model for grain boundary kinetics. The computed elastic stress generates an additional driving force for grain boundary migration. The paradigm is developed, tested, and subsequently used to quantify the effect of elastic stress on the evolution of texture in nickel polycrystals. As expected, elastic loading favors grains which appear softer with respect to the loading direction. The rate of texture evolution is also quantified, and an internal variable rate equation is constructed which predicts the time evolution of the distribution of orientations.Comment: 20 pages, 8 figure

Physically-based data assimilation

Ideally, a validation and assimilation scheme should maintain the physical principles embodied in the model and be able to evaluate and assimilate lower dimensional features (e.g., discontinuities) contained within a bulk simulation, even when these features are not directly observed or represented by model variables. We present such a scheme and suggest its potential to resolve or alleviate some outstanding problems that stem from making and applying required, yet often non-physical, assumptions and procedures in common operational data assimilation. As proof of concept, we use a sea-ice model with remotely sensed observations of leads in a one-step assimilation cycle. Using the new scheme in a sixteen day simulation experiment introduces model skill (against persistence) several days earlier than in the control run, improves the overall model skill and delays its drop off at later stages of the simulation. The potential and requirements to extend this scheme to different applications, and to both empirical and statistical multivariate and full cycle data assimilation schemes, are discussed.G. Levy, M. Coon, G. Nguyen, and D. Sulsk

Modelling Screwpile Installation Using the MPM

Screwpiles are, as the name suggests, piled foundations which are screwed into the ground. They provide restraint to both upwards and downward loading directions and are commonly used for light structures subject to overturning or wind loading, such as sign gantries at the sides of motorways. An EPSRC-funded project led by University of Dundee has recently started, with Durham and Southampton as partners, in which the use of screwpiles (individual or in groups) for offshore foundations is under investigation. At Durham, a numerical modelling framework based on the material point method (MPM) is being developed for the installation phase of a screwpile. The aim is to use the model to provide an accurate representation of the in situ ground conditions once the pile is installed, as during installation the ground is disturbed and any model that “wishes in place” a screwpile may not provide representative long-term performance predictions. Following modelling of installation, the soil state will be transferred to a standard finite element package for the subsequent modelling of in-service performance (the MPM being considered unnecessary and computationally expensive for this phase of the life of a screwpile). In this preliminary work, we present the development of features of this numerical tool to simulate the screwpile installation. These features include a moving mesh concept (both translation and rotation) and interface elements. The effectiveness of the algorithm is illustrated through simple examples

Shear deformation in granular materials

An investigation into the properties of granular materials is undertaken via numerical simulation. These simulations highlight that frictional contact, a defining characteristic of dry granular materials, and interfacial debonding, an expected deformation mode in plastic bonded explosives, must be properly modeled. Frictional contact and debonding algorithms have been implemented into FLIP, a particle in cell code, and are described. Frictionless and frictional contact are simulated, with attention paid to energy and momentum conservation. Debonding is simulated, with attention paid to the interfacial debonding speed. A first step toward calculations of shear deformation in plastic bonded explosives is made. Simulations are performed on the scale of the grains where experimental data is difficult to obtain. Two characteristics of deformation are found, namely the intermittent binding of grains when rotation and translation are insufficient to accommodate deformation, and the role of the binder as a lubricant in force chains

MPM based simulation for various solid deformation

Solid materials are responsible for many interesting phenomena. There are various types of them such as deformable objects and granular materials. In this paper, we present an MPM based framework to simulate the wide range of solid materials. In this framework, solid mechanics is based on the elastoplastic model, where we use von Mises criterion for deformable objects, and the Drucker-Prager model with non-associated plastic flow rules for granular materials. As a result, we can simulate different kinds of deformation of deformable objects and sloping failure for granular materials