A new solution procedure for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics

Laursen, Tod A.; Meng, X.N.

doi:10.1016/s0045-7825(01)00257-2

Cited by 53 publications

(46 citation statements)

References 15 publications

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“…The original construction of S pt for general models of hyperelasticity can be found in [40], and is elaborated upon in [30]. However, a more convenient form is from references [21], [22] and is given as…”

Section: The Lagrangian Mesh Dynamicsmentioning

confidence: 99%

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An unconditionally stable, energy–momentum consistent implementation of the material-point method

Love

Sulsky

2006

Computer Methods in Applied Mechanics and Engineering

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The Center for High Performance Computing (HPC@UNM) provides a focus for high performance computing and communication at the University of New Mexico (UNM). HPC@UNM is committed to innovative research in computational and computer science with emphasis on both algorithm development and application. As part of this commitment, HPC@UNM sponsors this technical report series. The technical reports are subject to internal review by HPC@UNM. However, the material, as presented, does not necessarily reflect any position of HPC@UNM. Further, neither UNM, nor the HPC, makes any warranty or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information contained in this report. Abstract Conservation of linear and angular momenta, and conservation of energy are examined for the material-point method (MPM). It is shown that MPM can be formulated with implicit energy and momentum conserving mesh dynamics for hyperelastic materials. With a consistent mass matrix the resulting overall numerical method preserves the conservative properties of the mesh solution. Energy dissipation and angular momentum errors are also quantified for a lumped mass formulation. Properties of the method are illustrated in numerical examples.

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Section: The Lagrangian Mesh Dynamicsmentioning

confidence: 99%

“…Unfortunately, a consistent linearization of equations (29) - (31), with the stress defined as in (54), produces an unsymmetric tangent matrix [21], [30], [40].…”

Section: It Is Not Necessary To Use a Midpoint-based Energy Conservinmentioning

confidence: 99%

An unconditionally stable, energy–momentum consistent implementation of the material-point method

Love

Sulsky

2006

Computer Methods in Applied Mechanics and Engineering

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“…Such observation has motivated the development of energy conserving schemes. Following the pioneering work by Simo and Tarnow [40], many studies extended this conserving algorithm to general hyperelastic materials [24,33,35,16] and arbitrary geometric nonlinearities [38,39]. Other work focused on applying these algorithms to specific finite element formulations (beam and shell elements) [41,42,15,48] and multi-body systems [7,10,28].…”

Section: Introductionmentioning

confidence: 99%

A robust composite time integration scheme for snap-through problems

et al. 2015

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A robust time integration scheme for snapthrough buckling of shallow arches is proposed. The algorithm is a composite method that consists of three sub-steps. Numerical damping is introduced to the system by employing an algorithm similar to the backward differentiation formulas (BDF) method in the last substep. Optimal algorithmic parameters are established based on stability criteria and minimization of numerical damping. The proposed method is accurate, numerically stable, and efficient as demonstrated through several examples involving loss of stability, large deformation, large displacements and large rotations.

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“…It consists in a mid-point scheme with an adequate evaluation of the internal forces, and was derived for a Saint Venant-Kirchhoff hyperelastic material. Laursen [2] generalized this approach to other hyperelastic models. His method involves resolving iteratively a new equation for each material point in order to compute the adequate Piola-Kirchhoff stress tensor.…”

Section: Introductionmentioning

confidence: 99%

A new formulation of internal forces for non-linear hypoelastic constitutive models verifying conservation laws

Noels¹,

Stainier²,

Ponthot³

et al. 2003

Computational Fluid and Solid Mechanics 2003

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A new solution procedure for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics

Cited by 53 publications

References 15 publications

An unconditionally stable, energy–momentum consistent implementation of the material-point method

An unconditionally stable, energy–momentum consistent implementation of the material-point method

A robust composite time integration scheme for snap-through problems

A new formulation of internal forces for non-linear hypoelastic constitutive models verifying conservation laws

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