Implicit dynamics in the material-point method

By Deborah Sulsky, A. Kaul. 2004

138 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8731dd3c5eb6b8ba553857aa27cd5740c5e812f3

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, methodology): “For a state-of-the-art summary of meshless methods, see [23–40].”
Comparison study of MPM and SPH in modeling hypervelocity impact problems (2009, methodology): “The critical time step is determined by the smallest smoothing length [42] in SPH, and determined by the background mesh size [44] in MPM.”
An energy‐consistent material‐point method for dynamic finite deformation plasticity (2006, methodology): “solids, thus extending the work in [26], [30], [58].”
Development of an implicit material point method for geotechnical applications (2016, methodology): “the time that it takes for a wave to traverse the disk [17].”
Examination and Analysis of Implementation Choices within the Material Point Method (MPM) (2008, methodology): “1 represents the mass-lumped version of what Sulsky and Kaul (2004) describe as the consistent mass matrix Mi j = ∑p φipφ jpmp.”
Decoupling and balancing of space and time errors in the material point method (MPM) (2010, methodology): “Implicit time-stepping schemes exist for MPM [16, 20, 21]; however, we choose to use the explicit Euler-Forward time discretization presented within the original MPM algorithm, which has the following expression for the update of velocity: vk+1 i =vi +ai!t .”
Formulation of a dynamic material point method (MPM) for geomechanical problems (2013, methodology): “In contrast to references [52] and [159], Guilkey and Weiss [72] explicitly formed the tangent stiffness matrix and used Newton’s method together with Newmark integration scheme to solve the equilibrium equations in time.”
A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations (2011, background): “Also, their basic algorithms and formulations have been studied by a number of authors such as [17–29].”