An implicit high-order material point method.

The material point method (MPM) is a version of the particle-in-cell (PIC) which has substantial advantages over pure Lagrangian or Eulerian methods in numerical simulations of problems involving large deformations. The MPM helps to avoid mesh distortion and tangling problems related to Lagrangian methods and as well as the advection errors associated with Eulerian methods. Despite the MPM being promoted for its ability to solve large deformation problems the method suffers from instabilities when material points cross between elements. These instabilities are due to the lack of smoothness of the grid basis functions used for mapping information between the material points and the background grid. In this paper a novel high-order MPM is developed to eliminate the cell-crossing instability and improve the accuracy of the MPM method

Gradient elasto-plasticity with the generalised interpolation material point method.

The modelling of geomechanics problems can require a method that allows large deformations and non-linear material behaviour, in this respect the Generalised Material Point Method (GIMPM) is ideal. A fully implicit version of GIMPM has recently been developed for geomechanics problems and some aspects of its implementation are described here. An area that has received less attention in material point methods is that conventional analysis techniques constructed in terms of stress and strain are unable to resolve structural instabilities such as shear banding. This is because they do not contain any measure of the length of the microstructure of the material analysed, such as molecule size or grain structure. Gradient theories provide extensions of the classical equations with additional higher-order terms. The use of length scales makes it possible to model a finite thickness shear band which is not possible with traditional methods. Much work has been done on using gradient theories to include the effect of microstructure in the finite element method (and other numerical analysis techniques) however this yet to be combined with material point methods. In this paper the key equations that are required to extend the implicit GIMPM method to include gradient elasto-plasticity are detailed

Two Types of Planning in Neighborhoods

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68338/2/10.1177_0739456X8400300209.pd

An implicit high-order material point method

The material point method (MPM) is a version of the particle-in-cell (PIC) which has substantial advantages over pure Lagrangian or Eulerian methods in numerical simulations of problems involving large deformations. The MPM helps to avoid mesh distortion and tangling problems related to Lagrangian methods and as well as the advection errors associated with Eulerian methods. Despite the MPM being promoted for its ability to solve large deformation problems the method suffers from instabilities when material points cross between elements. These instabilities are due to the lack of smoothness of the grid basis functions used for mapping information between the material points and the background grid. In this paper a novel high-order MPM is developed to eliminate the cell-crossing instability and improve the accuracy of the MPM method

Gradient elasto-plasticity with the generalised interpolation material point method

The modelling of geomechanics problems can require a method that allows large deformations and non-linear material behaviour, in this respect the Generalised Material Point Method (GIMPM) is ideal. A fully implicit version of GIMPM has recently been developed for geomechanics problems and some aspects of its implementation are described here. An area that has received less attention in material point methods is that conventional analysis techniques constructed in terms of stress and strain are unable to resolve structural instabilities such as shear banding. This is because they do not contain any measure of the length of the microstructure of the material analysed, such as molecule size or grain structure. Gradient theories provide extensions of the classical equations with additional higher-order terms. The use of length scales makes it possible to model a finite thickness shear band which is not possible with traditional methods. Much work has been done on using gradient theories to include the effect of microstructure in the finite element method (and other numerical analysis techniques) however this yet to be combined with material point methods. In this paper the key equations that are required to extend the implicit GIMPM method to include gradient elasto-plasticity are detailed

Modelling seabed ploughing using the material point method

Ploughing of the seabed is needed for the installation of cables and pipelines and is an area of construction likely to increase given plans in the UK and elsewhere for offshore marine energy (wind and tidal). Seabed ploughing is an expensive and sometimes risky operation for which there are limited guidelines as to what the tow force and speed is for an expected trenching profile within a specified ground condition. Most ploughing schemes are designed using semi-empirical approaches, with very few computational tools able to take into account the geometric and material nonlinearity inherited by the ploughing problem. In this paper we describe how the Material Point Method (MPM) is being used as a numerical tool to model seabed ploughing with the aim of providing an improved predictive tool for the future, via an EPSRC-funded research project at Durham and Dundee Universities. Various issues are discussed in the paper including the means of modelling moving essential boundaries and the choice of basis functions, and this new method in MPM is demonstrated on a simple ploughing problem

Do Europeans View their Homes as Castles? Homeownership and Poverty Perception throughout Europe

The paper investigates the notion that homeownership affects poverty perception. This is investigated by utilising a logit model to analyse various characteristics of homeowners in 11 different European nations. Overall, the analysis fails to reject the notion that homeowners throughout Europe are less likely to perceive themselves as living in poverty, but no evidence is found that homeownership is more valued in nations with high owner-occupancy rates. However, support is found for the notion that homeownership is used as a form of security in countries that experience greater income inequality

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