scholarly journals An investigation of stress inaccuracies and proposed solution in the material point method

2019 ◽  
Vol 65 (2) ◽  
pp. 555-581 ◽  
Author(s):  
José Leόn González Acosta ◽  
Philip J. Vardon ◽  
Guido Remmerswaal ◽  
Michael A. Hicks
Keyword(s):  
Shape Function ◽  
Time Integration ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Implicit Time ◽  
Integration Scheme ◽  
Time Integration Scheme

AbstractStress inaccuracies (oscillations) are one of the main problems in the material point method (MPM), especially when advanced constitutive models are used. The origins of such oscillations are a combination of poor force and stiffness integration, stress recovery inaccuracies, and cell crossing problems. These are caused mainly by the use of shape function gradients and the use of material points for integration in MPM. The most common techniques developed to reduce stress oscillations consider adapting the shape function gradients so that they are continuous at the nodes. These techniques improve MPM, but problems remain, particularly in two and three dimensional cases. In this paper, the stress inaccuracies are investigated in detail, with particular reference to an implicit time integration scheme. Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations.

scholarly journals IMPACT: an implicit time integration scheme for chemical species and families

2000 ◽  
Vol 18 (3) ◽  
pp. 337-346 ◽  
Author(s):  
G. D. Carver ◽  
P. A. Stott
Keyword(s):  
Middle Atmosphere ◽  
Time Integration ◽  
Three Dimensional ◽  
Chemical Species ◽  
Atmospheric Composition ◽  
Implicit Time ◽  
Integration Scheme ◽  
Implicit Time Integration ◽  
Time Integration Scheme ◽  
Complex Chemistry

Abstract. The implicit time integration scheme of Stott and Harwood (1993) was proposed as an efficient scheme for use in three-dimensional chemical models of the atmosphere. The scheme was designed for chemistry schemes using `chemical families', in which species with short lifetimes are grouped into longer-lived families. Further study with more complex chemistry, more species and reactions showed the scheme to be non-convergent and unstable under certain conditions; particularly for the perturbed chemical scenarios of polar stratospheric winters. In this work the scheme has been improved by revising the treatment of families and the convergence properties of the scheme. The new scheme has been named IMPACT (IMPlicit Algorithm for Chemical Time-stepping). It remains easy to implement and produces simulations that compare well with integrations using more accurate higher order schemes.Key words: Atmospheric composition and structure (middle atmosphere - composition and chemistry; lioposphere - composition and chemistry; instruments and techniques)

Axisymmetric Generalized Interpolation Material Point Method for Fully Coupled Thermomechanical Evaluation of Transient Responses

2019 ◽  
Vol 17 (04) ◽  
pp. 1950003
Author(s):  
Jun Tao ◽  
Yonggang Zheng ◽  
Hongwu Zhang ◽  
Zhen Chen
Keyword(s):  
Time Integration ◽  
Three Dimensional ◽  
Material Point Method ◽  
Coupled System ◽  
Thermomechanical Analysis ◽  
Solution Procedure ◽  
Material Point ◽  
Point Method ◽  
Transient Responses ◽  
Fully Coupled

In this paper, an axisymmetric generalized interpolation material point method for fully coupled thermomechanical analysis (AxiCTGIMP) is developed for evaluating the transient responses, where both the thermoelastic and thermoplastic effects are taken into account. The generalized interpolation material point method (GIMP) discretization in space for the coupled governing equations is described in detail. A staggered solution scheme is designed to split the coupled system into the parts related to the temperature and displacement fields, respectively, which are then solved individually with explicit time integration. The AxiCTGIMP is then verified and validated with two benchmark examples: the thick-walled cylinder and the Taylor-bar impact test. The simulation results show good agreements with available analytical solutions, experimental data and other numerical results. In addition, the results indicate that the proposed solution procedure is more accurate than the original MPM while it is much more efficient than the fully three-dimensional simulation for the axisymmetric thermomechanical problems.

Modeling of 3D Magnetostrictive Systems with Application to Galfenol and Terfenol-D Actuators

2012 ◽  
Vol 77 ◽  
pp. 11-28
Author(s):  
Marcelo J. Dapino ◽  
Suryarghya Chakrabarti
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Three Dimensional ◽  
Nonlinear Dynamic System ◽  
Element Model ◽  
Implicit Time ◽  
Integration Scheme ◽  
Modeling Framework ◽  
Time Integration Scheme ◽  
Parametric Analyses

This work presents a unified approach to model three dimensional magnetostrictive transducers. Generalized procedures are developed for incorporating nonlinear coupled constitutive behavior of magnetostrictive materials into an electro-magneto-mechanical finite element modeling framework. The finite element model is based on weak forms of Maxwell's equations for electromagnetics and Navier's equations for mechanical systems. An implicit time integration scheme is implemented to obtain nonlinear dynamic system responses. The model is implemented into a finite element (FE) solver and applied to two case studies, a Galfenol unimorph actuator and a magnetohydraulic Terfenol-D actuator for active engine mounts. Model results are compared with experiments, and parametric analyses are conducted which provide guidelines for optimization of actuator design.

Three-dimensional face stability analysis of shallow tunnels using numerical limit analysis and material point method

2021 ◽  
Vol 112 ◽  
pp. 103904
Author(s):  
Fabricio Fernández ◽  
Jhonatan E.G. Rojas ◽  
Eurípedes A. Vargas ◽  
Raquel Q. Velloso ◽  
Daniel Dias
Keyword(s):  
Stability Analysis ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Face Stability ◽  
Shallow Tunnels ◽  
Dimensional Face

Numerical Analysis of Solute Segregation in Directional Solidification under Static Magnetic Field

2011 ◽  
Vol 312-315 ◽  
pp. 253-258 ◽  
Author(s):  
Sabrina Nouri ◽  
Mouhamed Benzeghiba ◽  
Ahmed Benzaoui
Keyword(s):  
Magnetic Field ◽  
Static Magnetic Field ◽  
Time Integration ◽  
Magnetic Field Effect ◽  
Computer Code ◽  
Thermosolutal Convection ◽  
Implicit Time ◽  
Integration Scheme ◽  
Dimensional Solution ◽  
Time Integration Scheme

This paper addresses the effect of thermosolutal convection in the formation of defects in directionally solidified alloys. The numerical model is based on a bi-dimensional solution consisting of an implicit time integration scheme to couple thermal and solutal fields, which is supported by a finite volume numerical modeling technique. In this article, the macrosegregation phenomenon under a static magnetic field effect is analyzed numerically by a computer code developed and validated with experimental data. The numerically obtained results have been widely discussed in dependence of the characteristic parameters of the studied problem.

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