Shift boundary material point method: an image-to-simulation workflow for solids of complex geometries undergoing large deformation

  • Chuanqi Liu
  • WaiChing SunEmail author


We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries in the geometrically nonlinear regime. While the material point method is used to circumvent the mesh distortion issues commonly exhibited in Lagrangian meshes, a shifted domain technique originated from Main and Scovazzi (J Comput Phys 372:972–995, 2018) is used to represent the boundary conditions implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometric need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifferent results. Meanwhile, simulations using micro-CT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details.


Material point method Shift domain Image-based simulations Nonlocal damage Granular materials 



This paper is dedicated to Professor Jiun-Shyan Chen on the occasion of his 60th birthday. This work is supported by the Earth Materials and Processes program from the US Army Research Office under grant contract W911NF-18-2-0306, the Dynamic Materials and Interactions Program from the Air Force Office of Scientific Research under grant contract FA9550-17-1-0169, the nuclear energy university program from Department of Energy under grant contract DE-NE0008534 and the Mechanics of Material program at National Science Foundation under grant contract CMMI-1462760. These supports are gratefully acknowledged. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsors, including the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein.


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© OWZ 2019

Authors and Affiliations

  1. 1.Department of Civil Engineering and Engineering MechanicsColumbia UniversityNew YorkUSA

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