The Generalized Interpolation Material Point Method

By Scott Bardenhagen, E. Kober. 2004

861 citations recorded by the source corpus.

Subfields: Computational Mechanics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1bb783a80321369ed45b805915b6d7acb28d7fdf

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In Computational Mechanics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

An Eulerian-Lagrangian approach for simulating explosions of energetic devices (2007, background): “Traditionally, standard tri-linear shape functions are used, but recently smoother interpolants, as described in [13], have yielded improved results.”
A COUPLED MPM-FDM ANALYSIS METHOD FOR MULTI-PHASE ELASTO-PLASTIC SOILS (2010, methodology): “It is worth noting that it is possible to improve the numerical solutions by employing the newer algorithms (e.g., Sulsky et al., 1995; Nairn, 2003) and the other discretization scheme (e.g., Bardenhagen and Kober, 2004).”
Examination and Analysis of Implementation Choices within the Material Point Method (MPM) (2008, methodology): “More recently, Bardenhagen and Kober (2004) generalized the development that gives rise to MPM and showed that MPM can be considered a subset of their “Generalized InterpolationMaterial Point” (GIMP) method.”
Second‐order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces (2013, methodology): “Incidentally, noting that generic particle data Gp are mapped to nodes by using Gi D P p S ipGp , the approximate C 0 description of a generic field G.x/ is given by G.x/D X p GpYp.x/, where Yp.x/D X i S ipS i .x/, (26) Bardenhagen and Kober [15] used the symbol p to denote what we have written as Y”
Enhancement of the material point method using B‐spline basis functions (2018, neutral): “The derivative of Ni , p(ξ) can be also computed by a recursive formula, 23,24 ie, dNi;p ξð Þ dξ ¼ p ξ iþp−ξ i Ni;p−1 ξð Þ− pξ iþpþ1−ξ iþ1 Niþ1;p−1 ξð Þ (13) The B‐spline basis functions constructed from an open knot vector are interpolatory at the end knots of ξ1 and ξn+ p+ 1, but generally not int”
A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations (2011, methodology): “In the GIMP method, the effective averages of the basis function and its gradient over the particle domain were generalized by Bardenhagen and Kober [3] as i p ≡ Sip = 1 Vp ∫ p(x−xp)Si (x)dx (16) ∇ i p ≡ ∇Sip = 1 Vp ∫ p(x−xp)∇Si (x)dx (17) where p(x) is the particle characteristic function and denot”
Dark, Beyond Deep: A Paradigm Shift to Cognitive AI with Humanlike Common Sense (2020, methodology): “with the original MPM formulation, researchers have proposed different variations of the MPM, including the generalized interpolation material point (GIMP) method [434, 435], the convected particle domain interpolation (CPDI) method [436], and the dual domain material point (DDMP) method [437].”
Continuum modelling and simulation of granular flows through their many phases (2014, methodology): “We use the same notation as in Bardenhagen & Kober (2004).”
Formulation of a dynamic material point method (MPM) for geomechanical problems (2013, methodology): “Generalized interpolation MPM In 2004, Bardenhagen and Kober [8] generalized the MPM solution procedure by applying a Petrov-Galerkin discretization scheme.”
Modeling Imperfect Interfaces in the Material PointMethod using Multimaterial Methods (2013, background): “where Gip are generalized shape function gradients (Bardenhagen and Kober [2004]).”
Material Point Method Calculations with Explicit Cracks (2003, methodology): “Although MPM uses a background grid and is frequently compared to finite element methods, a new derivation or MPM [Bardenhagen and Kober (2003)] presents it as a Petrov-Galerkin method that has similarities with meshless methods such as Element-Free Galerkin (EFG) methods [Belytschko, Lu, and Gu…”
Material point method with enriched shape function for crack problems (2017, methodology): “Later, the generalized interpolation material point (GIMP) method was proposed by Bardenhagen et al. [19] using a Petrov–Galerkin formulation to alleviate the cell crossing noise.”
B-spline based boundary conditions in the material point method (2019, methodology): “Major improvements of the MPM include the development of the generalised interpolation material point (GIMP) method [8], the convected particle domain interpolation (CPDI) method [9] and the second-order convected particle domain interpolation (CPDI2) method [10].”
Meshfree Methods: Progress Made after 20 Years (2017, positive): “The generalization of MPM (Bardenhagen and Kober 2004) to the generalized interpolation material point (GIMP) method avoids the cell-crossing instability due to rough interpolation functions in MPM by employing particle functions that smooth the grid approximation.”
iGIMP: An implicit generalised interpolation material point method for large deformations (2017, methodology): “These errors have been investigated in [56] and there are a selection of methods that have been proposed to address this issue and improve the MPM including CPDI [57,58], DDMP [59] and the Generalised Interpolation Material Point (GIMP) method [60].”