On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity

The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being dened based on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satises equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specic focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, dierent domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation elds. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former

An efficient and locking-free material point method for three dimensional analysis with simplex elements

The Material Point Method is a relative newcomer to the world of solid mechanicsmodelling. Its key advantage is the ability to model problems having large defor-mations while being relatively close to standard nite element methods, howeverits use for realistic engineering applications will happen only if the material pointcan be shown to be both ecient and accurate (compared to standard nite elementmethods), when modelling complex geometries with a range of material models. Inthis paper we present developments of the standard material point method aimed atrealising these goals. The key contribution provided here is the development of amaterial point method that avoids volumetric locking (arising from elastic or elasto-plastic material behaviour) whilst using low order tetrahedral nite elements forthe background computational mesh, hence allowing unstructured background gridsto be used for complex geometries. We also show that these developments can beeectively parallelised to improve computational ecienc

Persistent Place-Making in Prehistory: the Creation, Maintenance, and Transformation of an Epipalaeolithic Landscape

Most archaeological projects today integrate, at least to some degree, how past people engaged with their surroundings, including both how they strategized resource use, organized technological production, or scheduled movements within a physical environment, as well as how they constructed cosmologies around or created symbolic connections to places in the landscape. However, there are a multitude of ways in which archaeologists approach the creation, maintenance, and transformation of human-landscape interrelationships. This paper explores some of these approaches for reconstructing the Epipalaeolithic (ca. 23,000–11,500 years BP) landscape of Southwest Asia, using macro- and microscale geoarchaeological approaches to examine how everyday practices leave traces of human-landscape interactions in northern and eastern Jordan. The case studies presented here demonstrate that these Epipalaeolithic groups engaged in complex and far-reaching social landscapes. Examination of the Early and Middle Epipalaeolithic (EP) highlights that the notion of “Neolithization” is somewhat misleading as many of the features we use to define this transition were already well-established patterns of behavior by the Neolithic. Instead, these features and practices were enacted within a hunter-gatherer world and worldview

There is no such thing as ‘undisturbed’ soil and sediment sampling: sampler-induced deformation of salt marsh sediments revealed by 3D X-ray computed tomography

Purpose: Within most environmental contexts, the collection of 'undisturbed' samples is widely relied-upon in studies of soil and sediment properties and structure. However, the impact of sampler-induced disturbance is rarely acknowledged, despite the potential significance of modification to sediment structure for the robustness of data interpretation. In this study, 3D-computed X-ray microtomography (μCT) is used to evaluate and compare the disturbance imparted by four commonly-used sediment sampling methods within a coastal salt-marsh. Materials and methods: Paired sediment core samples from a restored salt-marsh at Orplands Farm, Essex, UK were collected using four common sampling methods (push, cut, hammer and gouge methods). Sampling using two different area-ratio cores resulted in a total of 16 cores that were scanned using 3D X-Ray computed tomography, to identify and evaluate sediment structural properties of samples that can be attributed to sampling method. Results and discussion: 3D qualitative analysis identifies a suite of sampling-disturbance structures including gross-scale changes to sediment integrity and substantial modification of pore-space, structure and distribution, independent of sediment strength and stiffness. Quantitative assessment of changes to pore-space and sediment density arising from the four sampling methods offer a means of direct comparison between the impact of depth-sampling methods. Considerable disturbance to samples result from use of push, hammer and auguring samplers, whilst least disturbance is found in samples recovered by cutting and advanced trimming approaches. Conclusions: It is evident that with the small-bore tubes and samplers commonly used in environmental studies, all techniques result in disturbance to sediment structure to a far greater extent than previously reported, revealed by μCT. This work identifies and evaluates for the first time the full nature, extent and significance of internal sediment disturbance arising from common sampling methods