Large deformation analysis of a gel using the complex variable element-free Galerkin method

Li, D.M.; Tian, Li-Rui

doi:10.1016/j.apm.2018.04.004

Cited by 16 publications

(2 citation statements)

References 24 publications

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“…35,36 The element-free Galerkin method and element-free IMLS-Ritz method were also implemented for the coupled large deformation and diffusion of gels. 34,37,38 The material point method (MPM), which is a continuum-based particle method proposed by Sulsky et al, 39 is a hybrid Lagrangian and Eulerian method that combines the advantages of both kinds of spatial descriptions. In the MPM, material points (particles) are discretized from the continuum body as the Lagrangian description, while the Eulerian background grid that is independent of the body is utilized to solve the governing differential equations.…”

Section: Introductionmentioning

confidence: 99%

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A total‐Lagrangian material point method for coupled growth and massive deformation of incompressible soft materials

Zhang

Pan

Wang

et al. 2021

Numerical Meth Engineering

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A total-Lagrangian material point method (TLMPM) with a mixed formulation is proposed in this article for the mechanical analysis of incompressible soft materials coupling the mass growth and massive deformation. In this work, the growth-induced large deformation behavior is handled within the framework of the material point method (MPM) based on the multiplicative decomposition of deformation gradient. To overcome the volumetric locking caused by the incompressibility of soft materials, a weak-form equation for hydrostatic pressure is implemented into a mixed MPM framework. To deal with the massive deformation caused by growth, the total-Lagrangian formulation is further introduced into the mixed MPM. The TLMPM discretized via the B-spline basis functions is then developed in the proposed solution procedure. The efficiency and accuracy of the proposed method are demonstrated by several representative two-and three-dimensional numerical examples with large deformation such as the free growth of blocks and constrained growth of rings. The challenging problems including the volumetric growth of bilayers with complex geometry and the strain-driven growth of skin are further investigated using the proposed TLMPM to illustrate its ability for evaluating the growth phenomena and behaviors as observed in nature and engineering.

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Section: Introductionmentioning

confidence: 99%

“…For example, the meshless Hermite–Cloud method was used for the one‐dimensional steady‐state analysis of hydrogels according to a multiphase mixture theory 35,36 . The element‐free Galerkin method and element‐free IMLS‐Ritz method were also implemented for the coupled large deformation and diffusion of gels 34,37,38 …”

Section: Introductionmentioning

confidence: 99%