TY - JOUR
T1 - Deriving a lattice model for neo-Hookean solids from finite element methods
AU - Zhang, Teng
N1 - Funding Information:
The simulations were performed at the Triton Shared Computing Cluster (TSCC) at SDSC and Comet cluster at SDSC in XSEDE (No. TGMSS170004 ) supported by NSF, USA .
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2019/1
Y1 - 2019/1
N2 - Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adaptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.
AB - Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adaptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.
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U2 - 10.1016/j.eml.2018.11.007
DO - 10.1016/j.eml.2018.11.007
M3 - Article
AN - SCOPUS:85058245550
SN - 2352-4316
VL - 26
SP - 40
EP - 45
JO - Extreme Mechanics Letters
JF - Extreme Mechanics Letters
ER -