Numerical Modeling of Thermo-Mechanically Induced Stress in Substrates for Droplet-Based Additive Manufacturing Processes

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Chang Yoon Park ◽  
Tarek I. Zohdi
Keyword(s):  
Additive Manufacturing ◽  
Mechanical Response ◽  
Fe Model ◽  
Simulation Framework ◽  
Order Accuracy ◽  
Free Surfaces ◽  
Flat Substrate ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Laplacian Operators

Within the scope of additive manufacturing (AM) methods, a large number of popular fabrication techniques involve high-temperature droplets being targeted to a substrate for deposition. In such methods, an “ink” to be deposited is tailor-made to fit the desired application. Concentrated stresses are induced on the substrate in such procedures. A numerical simulation framework that can return quantitative and qualitative insights regarding the mechanical response of the substrate is proposed in this paper. A combined smoothed particle hydrodynamics (SPH)-finite element (FE) model is developed to solve the governing coupled thermo-mechanical equations, for the case of Newtonian inks. We also highlight the usage of consistent SPH formulations in order to recover first-order accuracy for the gradient and Laplacian operators. This allows one to solve the heat-equation more accurately in the presence of free-surfaces. The proposed framework is then utilized to simulate a hot droplet impacting a flat substrate.

scholarly journals Mathematical modeling of the electron-beam wire deposition additive manufacturing by the smoothed particle hydrodynamics method

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Dmitriy Nikolayevich Trushnikov ◽  
Elena Georgieva Koleva ◽  
Roman Pozolovich Davlyatshin ◽  
Roman Mikhailovich Gerasimov ◽  
Yuriy Vitalievich Bayandin
Keyword(s):  
Numerical Simulation ◽  
Mass Transfer ◽  
Electron Beam ◽  
Additive Manufacturing ◽  
Heat And Mass Transfer ◽  
Smoothed Particle Hydrodynamics ◽  
Lagrangian Description ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Smoothed Particle Hydrodynamics Method

Abstract Background The actual problem for calculating a shape of free surface of the melt when analyzing the processes of wire-based electron-beam surfacing on the substrate, being introduced into additive manufacturing, is the development of adequate mathematical models of heat and mass transfer. The paper proposed a formulation of the problem of melt motion in the framework of the Lagrangian description. The mathematical statement includes the balance equations for mass, momentum and energy, and physical equations for describing heat and mass transfer. Methods The smoothed particle hydrodynamics method was used for numerical simulation of the process of wire-based electron-beam surfacing on the substrate made from same materials (titanium or steel). A finite-difference analog of the equations is given and the algorithm for solving the problem is implemented. To integrate the discretized equations Verlet method was utilized. Algorithms are implemented in the open software package LAMMPS. Results The numerical simulation results allow the estimation of non-stationary volume temperature distributions, melt flow velocities and pressures, and characteristics of process. Conclusion The possibility of applying the developed mathematical model to describe additive production is shown. The comparison of numerical calculations with experimental studies showed good agreement.

A Comparison of Smoothed Particle Hydrodynamics (SPH) and Coupled SPH-FEM Methods for Modeling Machining

2020 ◽  
Author(s):  
Nishant Ojal ◽  
Harish P. Cherukuri ◽  
Tony L. Schmitz ◽  
Adam W. Jaycox
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Solid Mechanics ◽  
Large Deformations ◽  
Computational Time ◽  
Depth Of Cut ◽  
Fe Model ◽  
Sph Method ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Smoothed Particle

Abstract Smoothed Particle Hydrodynamics (SPH), a particle-based, meshless method originally developed for modeling astrophysical problems, is being increasingly used for modeling fluid mechanics and solid mechanics problems. Due to its advantages over grid-based methods in the handling of large deformations and crack formation, the method is increasingly being applied to model material removal processes. However, SPH method is computationally expensive. One way to reduce the computational time is to partition the domain into two parts where, the SPH method is used in one segment undergoing large deformations and material separation and in the second segment, the conventional finite element (FE) mesh is used. In this work, the accuracy of this SPH-FEM approach is investigated in the context of orthogonal cutting. The high deformation zone (where chips form and curl) is meshed with the SPH method, while the rest of the workpiece is modeled using the FE method. At the interface, SPH particles are coupled with FE mesh for smooth transfer of stress and displacement. The boundary conditions are applied to tool and FE zone of the workpiece. For comparison purposes, a fully-SPH model (workpiece fully discretized by SPH) is also developed. This is followed by a comparison of the results from the coupled SPH-FE model with the SPH model. A comparison of the chip profile, the cutting force, the von Mises stress and the damage parameter show that the coupled SPH-FE model reproduces the SPH model results accurately. However, the SPH-FE model takes almost 40% less time to run, a significant gain over the SPH model. Similar reduction in computation time is observed for in a micro-cutting application (depth of cut of 300 nm). Based on these results, it is concluded that coupling SPH with FEM in machining models decreases simulation time significantly while still producing accurate results. This observation suggests that three-dimensional machining problems can be modeled using the combined SPH-FEM approach without sacrificing accuracies.

scholarly journals A Discrete Multi-Physics Model to Simulate Fluid Structure Interaction and Breakage of Capsules Filled with Liquid under Coaxial Load

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 354
Author(s):  
Ignacio Nilo Ruiz-Riancho ◽  
Alessio Alexiadis ◽  
Zhibing Zhang ◽  
Alvaro Garcia Hernandez
Keyword(s):  
Mechanical Response ◽  
Experimental Tests ◽  
Elastic Membrane ◽  
Core Shell ◽  
Displacement Curve ◽  
Lattice Spring Model ◽  
Proposed Model ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Physics Model

This paper investigated the mechanical response (including breakage and release of the internal liquid) of single core–shell capsules under compression by means of discrete multi-physics. The model combined Smoothed Particle Hydrodynamics for modelling the fluid and the Lattice Spring Model for the elastic membrane. Thanks to the meshless nature of discrete multi-physics, the model can easily account for the fracture of the capsule’s shell and the interactions between the internal liquid and the solid shell. The simulations replicated a parallel plate compression test of a single core–shell capsule. The inputs of the model were the size of the capsule, the thickness of the shell, the geometry of the internal structure, the Young’s modulus of the shell material, and the fluid’s density and viscosity. The outputs of the model were the fracture type, the maximum force needed for the fracture, and the force–displacement curve. The data were validated by reproducing equivalent experimental tests in the laboratory. The simulations accurately reproduced the breakage of capsules with different mechanical properties. The proposed model can be used as a tool for designing capsules that, under stress, break and release their internal liquid at a specific time.

scholarly journals Animating multiple interacting miscible and immiscible fluids based on particle simulation

2013 ◽  
Vol 9 (2) ◽  
pp. 73-86
Author(s):  
Juraj Onderik ◽  
Michal Chládek ◽  
Roman Ďurikovič
Keyword(s):  
Immiscible Fluids ◽  
Particle Simulation ◽  
Advection Equation ◽  
Miscible Fluids ◽  
Particle Sedimentation ◽  
Free Surfaces ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
The Common ◽  
Usual Problem

Abstract We present a particle-based approach for animating multiple interacting liquids that can handle number of immiscible fluids as well as number of miscible fluids in our simulation framework. We solve the usual problem of robust interface tracking, between immiscible fluids, by reconstructing the zero level set of our novel composite implicit function, see Fig. 1 left and center. It’s recurrent formulation handles directly interfaces between any number of liquids including the free surfaces. We model the miscible fluids by tracking concentrations of dissolved materials in the vicinity of each particle. Flick’s law is applied for the Laplacian-based diffusion of concentrations, see Fig. 1 right. Particle sedimentation is achieved by directional advection along the settling velocity. The diffusion-advection equation is discretized by particles using the Lagrangian formulation. The proposed improvements can be easily implemented into the common Smoothed Particle Hydrodynamics (SPH) simulations framework

Stress Evaluation of Articular Cartilage Chondrocyte Cell by Using Multi-Scale Finite Element Method and Smoothed Particle Hydrodynamics Method

2016 ◽  
Author(s):  
Kaito Nakahara ◽  
Yusuke Morita ◽  
Yoshihiro Tomita ◽  
Eiji Nakamachi
Keyword(s):  
Finite Element ◽  
Surface Layer ◽  
Articular Cartilage ◽  
Smoothed Particle Hydrodynamics ◽  
Cartilage Tissue ◽  
Fe Model ◽  
Stress Evaluation ◽  
Multi Scale ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

The morphology and function of articular cartilage tissue is regenerated through the metabolic activity of cells stimulated by the mechanical loading. In this study, a biphasic multi-scale analyses scheme is adopted for stress evaluation occurred in the chondrocyte cell. The dynamic-explicit finite element (FE) method was employed for the solid phase and the smoothed particle hydrodynamics (SPH) method was used for the fluid phase. A macro-scale 3D human knee joint FE model was constructed based on magnetic resonance (MR) cross sectional images. Further, we derived the Representative volume element (RVE) based on the Multiphoton microscopy (MPM) observation to build a micro-scale FE model of cartilage tissue. We characterized three layers in the articular cartilage tissue. Parameters of the visco-anisotropic hyperelastic constitutive law and SPH models were determined using experimental results. Biphasic multi-scale FE and SPH analyses were carried out under the maximum loading condition in the normal walking motion. As a result, large flow velocity was observed around chondrocyte in the surface layer. The highest hydrostatic and shear stress occurred on chondrocyte in the surface layer. Numerical results shows a good agreement with experimental results.

scholarly journals An Application of the Cahn-Hilliard Approach to Smoothed Particle Hydrodynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. Hirschler ◽  
M. Huber ◽  
W. Säckel ◽  
P. Kunz ◽  
U. Nieken
Keyword(s):  
Phase Separation ◽  
Boundary Conditions ◽  
Smoothed Particle Hydrodynamics ◽  
Sph Method ◽  
Free Surfaces ◽  
Diffusion Controlled ◽  
Universal Power Law ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Solid Walls

The development of a methodology for the simulation of structure forming processes is highly desirable. The smoothed particle hydrodynamics (SPH) approach provides a respective framework for modeling the self-structuring of complex geometries. In this paper, we describe a diffusion-controlled phase separation process based on the Cahn-Hilliard approach using the SPH method. As a novelty for SPH method, we derive an approximation for a fourth-order derivative and validate it. Since boundary conditions strongly affect the solution of the phase separation model, we apply boundary conditions at free surfaces and solid walls. The results are in good agreement with the universal power law of coarsening and physical theory. It is possible to combine the presented model with existing SPH models.

scholarly journals Numerical study of mechanisms to minimize failure in a metal with soft backing under plane shock loading

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150285
Author(s):  
A. V. S. Siva Prasad ◽  
Sumit Basu
Keyword(s):  
Numerical Study ◽  
Void Nucleation ◽  
Experimental Studies ◽  
Blast Waves ◽  
Plane Shock ◽  
Metallic Structures ◽  
Free Surfaces ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Plate Geometry

In recent times, several experimental studies have reported improved ballistic penetration resistance and blast survivability of metallic structures to which an external coating of a soft elastomeric material has been applied. This work is aimed at understanding, through numerical simulations on a simple metal/elastomer flat plate geometry subjected to planar blast waves, the detailed mechanics of wave propagation, damage evolution and mitigation in a bilayer system. Void nucleation, growth and coalescence is assumed to be the damaging mechanism in the metal. A meshless technique based on smoothed particle hydrodynamics is used within the framework of large deformation elasto-viscoplasticity in the metal and nonlinear elasticity in the elastomer. We show that the thickness of the elastomer plays an important role in shielding void activity in the metal, by creating a sequence of closely spaced pulses that reflect from the interface and free surfaces to maintain non-tensile or weakly tensile states of stress. Moreover, a fictitious material that is capable of undergoing a transformation to a harder material under pressure is studied that proves to be an ideal candidate for damage mitigation.

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