Recent development trends in metal forming

It has been 25 years since Sulsky and her coworkers developed the first version of the material point method (MPM): a quasi particle method to solve continuum mechanics problems. In the MPM, the continua are discretized by Lagrangian particles moving over a fixed Eulerian background grid. As a result, large deformation and contact can be treated effortlessly. Since then, many improved instances of the MPM have been developed and the MPM has found applications in many fields from geoengineering to movie industry. As the MPM has now been matured and a large body of literature on it exists, it is a good time to ponder and reflect on the developments of the method to date. To this end, this manuscript provides a concise introduction to the MPM, covering theory, implementation, and applications. All the algorithms required to have a working MPM implementation for the simulations of solids, fluids, and their interactions are provided. We have coded these algorithms in in-house open source programs and used them to study the performance of different MPM variants for large deformation solid mechanics problems. These problems exhibit large plastic deformation, fractures and contacts. Convergence of different MPMs (CPDI, GIMP, B-splines, total Lagrangian MPM, improved MPMs) are studied. Furthermore, MPM formulations for fluids/gases and heat conduction are also covered. Potential areas for improvement on the method have been identified. The paper is the first review of the MPM and presents a state of the art of the current MPM literature covering 339 references.

Material point method after 25 years: Theory, implementation, and applications

3D regularized μ(I)-rheology for granular flows simulation

Landslide is a uniquely dynamic large-deformation process that can present serious threat to human lives and infrastructures. The natural soil properties often exhibit inherent spatial variability, which affects the landslide behavior significantly. This paper focuses on combined Monte Carlo simulation and three-dimensional (3D) dynamic large-deformation finite-element (LDFE) analysis using the coupled Eulerian-Lagrangian method to investigate the whole runout process of landslide induced by the earthquake in spatially varying soil. The results from LDFE analysis show that the mean value of runout distance in spatially varying soil is significantly higher than that of the deterministic value obtained from a homogeneous slope due to the slope failure developed along the weakest path in soils. The mean runout distance increases and converges with increasing slope length in 3D-LDFE stochastic analysis. The advantages and necessities of 3D-LDFE analysis were illustrated by comparing it with two-dimensional (2D) LDFE analysis of landslide in spatially varying soil. The results show that the calculated mean runout distance using 3D-LDFE method is at least 16.1% higher than that calculated using 2D-LDFE analysis. Finally, a linear regression formula was established to estimate the mean runout distance of landslide due to horizontal inertia acceleration. Such a formula may facilitate the risk assessment of landslide in practical engineering.

A three-dimensional large-deformation random finite-element study of landslide runout considering spatially varying soil

In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.

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A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from “standard” Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.

Zhiming Guo

Papers

Comparison of a Material Point Method and a Galerkin Meshfree Method for the Simulation of Cohesive-Frictional Materials.