Residual stresses in gas tungsten arc welding: a novel phase-field thermo-elastoplasticity modeling and parameter treatment framework

Proc Appl Math and Mech

Sun

2023

Self Cite

Nowadays, supervised machine learning (ML) via artificial neural network (ANN) is increasingly applied within multiscale material modeling and homogenization to generate data‐based, physics‐informed material models as an alternative to conventional material models. This application is associated with many benefits, such as increasing of computational efficiency and accuracy. However, the establishment of a reliable data‐based or ML‐based material model requires the availability of a proper and sufficiently large database from small‐scale simulations and appropriate processing of these data as part of the model building steps. In this connection, this contribution discusses the method to generate ML‐based material models, which strictly fulfill a number of restrictions, such as objectivity (or material frame‐indifference) and thermodynamic consistency (second‐law of thermodynamics) for an elasto‐plastic material response. While focusing in this contribution on anisotropic crystal plasticity, the two aforementioned restrictions can be fulfilled via the utilization of informed‐graph NN and the application of data representation in spectral form. The numerical results show that learning the ML model to explicitly predict the plastic strain as an intermediate step not only enhances the fulfillment of thermodynamic consistency but also improves the accuracy of the final prediction.

Section: Informed Directed Graph Representation and Objectivity Enhan...mentioning

confidence: 99%

Objectivity and accuracy enhancement within ANN‐based multiscale material modeling

Proc Appl Math and Mech

Sun

2023

Self Cite

“…Moreover, b and r represent the mass-specific body force and the heat generation source. For the elastoplastic response of metals within the small strains assumption, we consider J2 theory with a linear isotropic strain hardening law as detailed in [5,9]. On the other hand, by the dissipative terms in the entropy inequality, the evolution equation for the phase-field variable can be expressed as…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…In the following, the formulations of the coupled phase-field thermomechanical model are briefly presented. For the detailed derivation steps, the interested reader is referred to [9]. The governing partial differential equations for balance of linear momentum and energy balance as well as the evolution equation for phase-field variable.…”

Section: Mathematical Modellingmentioning

confidence: 99%

Modeling the thermomechanical processes and residual stresses in additive manufacturing of metallic components

Ali

Proc Appl Math and Mech

Markert

2023

Self Cite

In additive manufacturing of metallic components and fusion welding, undesirable deformations and residual stresses are common drawbacks, which directly influence the performance and functionality of the manufactured components. In this work, a thermomechanical continuum model is developed by using the phase‐field method to track the evolution of the melting/remelting‐solidification occurring due to the incident of localized heat input sources, e.g, by means of a laser heat source. The result of the thermal analysis is then employed for the mechanical analysis to predict the residual stresses. In the thermal and mechanical analysis, the thermomechanical properties are considered to evolve with the phase‐field variable. In addition, a scalar‐valued history variable is introduced to distinguish between consolidated and loose powder materials. This enables single‐track additive manufacturing simulations with a possible extension to multi‐layer and multi‐track simulations. To verify and validate the modeling approach, the coupled system of equations is implemented in the open‐source FEniCS project and a numerical example for additive manufacturing is solved and compared qualitatively and quantitatively with reference results from the literature.

“…The energetic phase-field method (PFM), which is widely applied in the modeling of phase change evolution of phasechange materials, see, for example, [16][17][18][19][20][21] has witnessed in recent years increasing popularity in the application of simulating crack propagation.…”

Section: Introductionmentioning

confidence: 99%

A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media

Chaaban

Num Anal Meth Geomechanics

Markert

2022

Self Cite

In this paper, we present a reliable micro-to-macroscale framework to model multiphase fluid flow through fractured porous media. This is based on utilizing the capabilities of the lattice Boltzmann method (LBM) within the phase-field modeling (PFM) of fractures in multiphase porous media. In this, we propose new physically motivated phase-field-dependent relationships for the residual saturation, the intrinsic as well as relative permeabilities. In addition, an anisotropic, phase-field-dependent intrinsic permeability tensor for the fractured porous domains is formulated, which relies on the single-and multiphasic LBM flow simulations. Based on these results, new relationships for the variation of the macroscopic theory of porous media (TPM)-PFM model parameters in the transition zone are proposed. Whereby, a multiscale concept for the coupling between the multiphasic flow through the crack on one hand and the porous ambient, on the other hand, is achieved. The hybrid model is numerically applied on a real microgeometry of fractured porous media, extracted via X-ray microcomputed tomography data of fractured Berea Sandstone. Moreover, the model is utilized for the calculation of the fluid leak-off from the crack to the intact zones. Additionally, the effects of the depth of the transition zone and the orientation of the crack channels on the amount of leakage flow rates are studied. The outcomes of the numerical model proved the reliability of the multiscale model to simulate multiphasic fluid flow through fractured porous media.