arXiv subjects

Giuliano Pretti

Publications and source records attributed to Giuliano Pretti.

5 recordsLinked to original sources

arXiv2026

An implicit octree-based adaptive Material Point Method

The Material Point Method provides an effective approach for modelling the large deformations that often arise from contact interactions between rigid structures and surrounding continua. However, solving these problems requires accurate representation of the continuum-structure interface, which necessitates high resolution background mesh and material point discretisations. This requirement, combined with evolving continuum-structure interfaces and the fact that most Material Point Method implementations are dependent on structured meshes, can result in large numerical systems and long run times especially when modelling problems in three-dimensions. Motivated by this issue, this paper provides the first octree-based implicit Material Point Method for efficient solution of large deformation continuum-structure interaction problems. The octree background mesh provides a natural way to automatically adapt both the computational mesh and the material point discretisation based on the position of the interaction between the structure and continuum. The new approach is demonstrated on a number of large deformation benchmark and continuum-structure interaction problems, where up to a 5.5-times speed up and a consequent 21-times CO2 saving is achieved when running on a HPC compared to results obtained using a conforming mesh.

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arXiv2026

Caveats on formulating finite elasto-plasticity in curvilinear coordinates

Tensor analysis provides a frame-invariant foundation for continuum mechanics, yet numerical implementations rely on matrix representations expressed in user-selected bases. When these bases are non-Cartesian and non-orthonormal, additional terms arise that are normally absent or implicit in Cartesian formulations. Using cavity expansion as an initial model problem, this paper clarifies the roles of the deformation gradient, Jacobian, and shifter in finite-strain kinematics under axisymmetry. These quantities, typically straightforward in Cartesian frames, require more careful treatment in curvilinear coordinates, particularly in applications involving large deformations where axisymmetric reductions provide substantial computational savings. The formulation is further complicated when anelastic effects are included: the elastic and anelastic components of the deformation gradient and Jacobian must be distinguished, and the Cauchy stress depends on configuration changes beyond the current elastic state. This increases the complexity of the consistent linearisation required for finite element implementation. The paper provides a clear, step-by-step procedure for handling these contributions. The focus is practical rather than geometric. Instead of adopting a differential-geometric manifold framework, we work within standard Cartesian representations and use explicit changes of basis to obtain the required curvilinear forms. The resulting methodology enables robust finite element analysis of axisymmetric elasto-plastic problems undergoing finite strains.

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arXiv2025

Three-dimensional modelling of drag anchor penetration using the material point method

Drag embedment anchors are a key threat to buried subsea linear infrastructure, such as power/data cables and pipelines. For cables, selecting a burial depth is a compromise between protecting the cable from anchor strike and the increased cost of deeper installation. This presents an efficient large deformation, elasto-plastic Material Point Method-based soil-structure interaction predictive tool for the estimation of anchor penetration based on Cone Penetration Test (CPT) site investigation data. The tool builds on earlier work by the authors supplemented by three developments: modelling assemblies of rigid bodies (necessary for articulated anchors), a partitioned domain approach to enable accurate and efficient modelling of long anchor pulls and an improved means of modelling rotational inertia. The tool is validated against scaled physical tests conducted in a geotechnical centrifuge on sands with a range of relative densities with good agreement across the tested conditions. Numerical simulations identify key issues with the UK Cable Burial Risk Assessment (CBRA) approach for estimating anchor penetration and reveal the potentially non-conservatism of the CBRA framework for sandy seabeds. The numerical model enables site-specific anchor-penetration assessment along cable routes and can be used to evaluate the performance of different anchor designs and sizes in varied soil conditions.

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arXiv2024

A dynamic implicit 3D material point-to-rigid body contact approach for large deformation analysis

Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. The numerical challenges come from several non-linear sources: large deformation mechanics, history dependent material behaviour and slip/stick frictional contact. In this paper the Material Point Method (MPM) is adopted to represent the deformable material, combined with a discretised rigid body which provides an accurate representation of the contact surface. The three dimensional interaction between the bodies is detected though the use of domains associated with each material point. This provides a general and consistent representation of the extent of the deformable body without introducing boundary representation in the material point method. The dynamic governing equations allows the trajectory of the rigid body to evolve based on the interaction with the deformable body and the governing equations are solved within an efficient implicit framework. The performance of the method is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.

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arXiv2024

A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation

The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formulations for poro-mechanics can be affected by two major sources of instability. Firstly, inf-sup condition violation can arise when the spaces for the displacement and pressure fields are not chosen correctly, resulting in an unstable pressure field. Secondly, the intrinsic nature of particle-based discretisation makes the MPM an unfitted mesh-based method, which can affect the system's condition number and solvability, particularly when background mesh elements are poorly populated. This work proposes a solution to both problems. The inf-sup condition is avoided using two overlapping meshes, a coarser one for the pressure and a finer one for the displacement. This approach does not require stabilisation of the primary equations since it is stable by design and is particularly valuable for low-order shape functions. As for the system's poor condition number, a face ghost penalisation method is added to both the primary equations, which constitutes a novelty in the context of MPM mixed formulations. This study frequently makes use of the theories of functional analysis or the unfitted Finite Element Method (FEM). Although these theories may not directly apply to the MPM, they provide a robust and logical basis for the research. These rationales are further supported by three numerical examples, which encompass both elastic and elasto-plastic cases and drained and undrained conditions.

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