Thermomechanical total Lagrangian SPH formulation for solid mechanics in large deformation problems

Ba, Kadiata; Gakwaya, A.

doi:10.1016/j.cma.2018.07.038

Cited by 44 publications

(21 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The governing equations are derived following a Lagrangian variational principle leading to a Hamiltonian system of particles (energy-based) [12,[17][18][19] where the motion of each particle is given by the classical Lagrange equations. Therefore, as explained by Bonet et al [18], constants of the motion such as linear and angular momentum are conserved.…”

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

“…For each particle, the physical quantities are calculated through interpolation over neighbor particles. Every particle is considered as a moving thermodynamic subsystem [12]. The volume of each particle is given by [15] and (b) seen in the space of a B-spline [16].…”

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

“…With dissipative effects such as plasticity, the equations of motion of the system of particles representing the continuum can be evaluated following the classical Lagrangian formalism. For more details, readers can refer to Ba and Gakwaya [12]:…”

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

“…In this paper, a Hamiltonian formulation is proposed for dynamic and steady-state problem simulation focusing on numerical efficiency such as accuracy and simulation time. The governing equations are derived following a Lagrangian variational principle leading to a Hamiltonian system of particles [12][13][14]. With the Hamiltonian SPH formulation, local conservation of momentum between particles is respected, and they remain locally ordered during the process as wanted in solid mechanic problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hot Compression Tests Using Total Lagrangian SPH Formulation in Energy-Based Framework

Ba¹

2020

Progress in Relativity

Self Cite

View full text Add to dashboard Cite

Limitations of the finite element method (FEM) in some cases involving large deformations as in forging or high compression tests are overcome nowadays by meshless methods such as the smoothed particle hydrodynamic (SPH) method. This paper presents a corrected total Lagrangian SPH formulation for problems encountering large deformations in solid mechanics. The continuum is modeled as a Hamiltonian system of particles (energy-based framework). The total Lagrangian formulation proposed overcomes some problems faced by standard SPH in simulating solid mechanic problems such as tensile instability. Numerical applications compared with experimental results are presented to show the capabilities of this novel formulation.

show abstract

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

Section: Discrete Equations Of Motion From Energy-based Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hot Compression Tests Using Total Lagrangian SPH Formulation in Energy-Based Framework

Ba¹

2020

Progress in Relativity

Self Cite

View full text Add to dashboard Cite

show abstract

“…The SPH was developed independently by both Lucy and Gingold and Monaghan in 1977 for astrophysical simulations. Since then, its range of applications has expanded to include many different fields, including free surface flows, solid mechanics, reactive systems, and multiphase systems, the details of which can be found in several review papers . Although continuum level governing equations are solved, the mesh‐free aspect of SPH makes its implementation, formulation, strengths, and weaknesses different from other fluid modeling approaches.…”

Section: Introductionmentioning

confidence: 99%

Simulating bubble dynamics in a buoyant system

Arai

Villafranco

Grace

et al. 2019

Numerical Methods in Fluids

View full text Add to dashboard Cite

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid-based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge. KEYWORDS bubble dynamics, buoyant systems, multiphase flows, rising bubble dynamics, smoothed particle hydrodynamics (SPH), volume of fluid (VOF) Re = vL ,

show abstract

The Process of Progressive Limiting State and Determination of the Residual Strain Energy of a Structure Based on the Force Method

Stupishin,

Nikitin,

Moshkevich

2024

Lecture Notes in Civil Engineering

View full text Add to dashboard Cite

Thermomechanical total Lagrangian SPH formulation for solid mechanics in large deformation problems

Cited by 44 publications

References 17 publications

Hot Compression Tests Using Total Lagrangian SPH Formulation in Energy-Based Framework

Hot Compression Tests Using Total Lagrangian SPH Formulation in Energy-Based Framework

Simulating bubble dynamics in a buoyant system

The Process of Progressive Limiting State and Determination of the Residual Strain Energy of a Structure Based on the Force Method

Contact Info

Product

Resources

About