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At least 19 records

Computational solid mechanics (finite elements and boundary elements) - Present status and future directions

Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.

Atluri, S. N.↗

OptimiSM v.0.0.1

SAND2021-15062 O OptimiSM is a library for solving solid mechanics problems and for rapid prototyping of computational solid mechanics research ideas. It was originally created to facilitate research and development of algorithms for contact mechanics. It is a realization of a philosophy that problems can be represented with variational least-action principles, even when there is history-dependent material behavior and contact. This opens the door to using powerful methods from non-convex optimization for solutions. The code was successful in its original purpose, but along the way, the authors realized that it could be of general use to the computational solid mechanics research community as an R&D platform. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Talamini, Brandon↗

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Abstract Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multiphysics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multiphysics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Computer Science↗

Latent Pitfalls in Microstructure-Based Modeling for Thermally Aged 9Cr-1Mo-V Steel (Grade 91)

A case study was conducted on a mechanistic model development that predicted tensile strength deterioration with thermal aging of 9Cr-1Mo-V steel in supporting the 60-year design life expected for advanced nuclear reactors. For property prediction beyond practical testing times, mechanistic modeling is highly desired, as it taps into the physics of structure–property relationships and therefore can generate reliable results for extrapolation. Meanwhile, as mechanistic models are often complicated, reflecting the intricacy of microstructure and strengthening mechanisms, pitfalls that are difficult to detect often exist. Here, this paper discusses latent pitfalls that are common in mechanistic modeling or specific in this 9Cr-1Mo-V case development through using the American Society of Mechanical Engineers verification and validation in computational solid mechanics (ASME V&V 10) standard for evaluating credibility of modeling in materials engineering. Suggestions are also made for enhancing reliability of microstructure-based modeling.

36 MATERIALS SCIENCE↗

Advances in computational structural and solid mechanics; Proceedings of the First World Congress on Computational Mechanics, University of Texas, Austin, Sept. 22-26, 1986

Papers are presented on the nonlinear dynamic analysis of quasi-symmetric anisotropic structures, the analysis of large deformations of membrane shells by the generalized finite difference method, the vibration of shear-deformable laminated plate structures by the finite strip method, and Coon's surface method for the formulation of finite elements for plates and shells. Other topics include an evaluation of higher-order modal methods for calculating the transient structural response, a nonlinear dynamic analysis of frame structures, and a nonlinear analysis of a truss by energy minimization. Also considered are an incremental Galerkin method for plates and stiffened plates, a comparison of the postbuckling behavior of plates and shells, and a general solution of bending in a cylindrical shell.

Noor, Ahmed K.↗

Mechanical Erosion Modeling of TPS Materials

This work describes the development of a model that accounts for the additional surface recession in Thermal Protection Systems (TPS) materials as a result of mechanical erosion due to high shear conditions during atmospheric entry. A computational solid mechanics module was integrated within the Porous material Analysis Toolbox (PATO) based on OpenFOAM. The mechanical erosion was modeled in three steps: first, the implemented stress analysis solver computes the stress and the displacement fields for orthotropic materials using the wall shear stress tensor as a boundary condition; then, regions on the surface where the stress meets the failure criteria are identified; and last, the mesh is moved accordingly to remove the failed material. The outcome is a model capable to predict the total recession of the material due to surface chemistry and mechanical erosion. Results will be included in the final paper after verifying and completing the study.

Stress Analysis↗

Mechanical Erosion Modeling of TPS Materials

This work describes the development of a model that accounts for the additional surface recession in Thermal Protection Systems (TPS) materials as a result of mechanical erosion due to high shear conditions during atmospheric entry. A computational solid mechanics module was integrated within the Porous material Analysis Toolbox (PATO) based on OpenFOAM. The mechanical erosion was modeled in three steps: first, the implemented stress analysis solver computes the stress and the displacement fields for orthotropic materials using the wall shear stress tensor as a boundary condition; then, regions on the surface where the stress meets the failure criteria are identified; and last, the mesh is moved accordingly to remove the failed material. The outcome is a model capable to predict the total recession of the material due to surface chemistry and mechanical erosion. Results will be included in the final paper after verifying and completing the study.

Stress Analysis↗

Mechanical Erosion Modeling of TPS Materials

This work describes the development of a model that accounts for the additional total surface recession in Thermal Protection Systems materials as a result of mechanical erosion due to high shear conditions during atmospheric entry. A computational solid mechanics capability module was integrated within the Porous material Analysis Toolbox based on OpenFOAM, PATO. The mechanical erosion was modeled in three steps: first, the implemented stress analysis solver module computes the stress and the displacement fields for orthotropic materials using the wall shear stress tensor as a boundary condition; then, regions on the surface where the stress meets the failure criteria are identified; and last, the mesh is moved accordingly to remove the failed material. The outcome is a model of the total recession of the material due to surface chemistry and mechanical erosion. Results will be included in the final paper after verifying and completing the study.

Stress Analysis↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

Modular machine learning-based elastoplasticity: Generalization in the context of limited data

The development of highly accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. This ability to extrapolate from limited data was the main reason for the early and continued success of phenomenological models and the main shortcoming in machine learning-enabled constitutive modeling approaches. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

42 ENGINEERING↗

Material Response Modeling of Ablative Thermal Protection Systems using PATO

Developing thermal protection systems (TPS) for future space vehicles involves an extensive design and test cycle. A key component of the cycle is determining margins for a safe design that rely on confidence in the performance of the TPS. Predicting the complicated multiphysics phenomena that occur during atmospheric entry requires high-fidelity modeling tools. To this end, the Porous-material Analysis Toolbox based on OpenFOAM (PATO) has been developed. PATO is an open-source software for computing material response of reactive porous materials submitted to high-temperature environments. Recent applications of PATO include computation of the full heatshield 3D material response from the Mars Science Laboratory atmospheric entry and ablation during arc jet testing. Current efforts are underway to loosely couple PATO with other discipline specialized codes including hypersonic computational fluid dynamics (CFD) to assess the effects of pyrolysis-gas blowing into the boundary layer and computational solid mechanics to address modeling of mechanical erosion. Surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation are also being added.

Thermal Protection Systems↗

Material Response Modeling of Ablative Thermal Protection Systems using PATO

Developing thermal protection systems (TPS) for future space vehicles involves an extensive design and test cycle. A key component of the cycle is determining margins for a safe design that rely on confidence in the performance of the TPS. Predicting the complicated multiphysics phenomena that occur during atmospheric entry requires high-fidelity modeling tools. To this end, the Porous-material Analysis Toolbox based on OpenFOAM (PATO) has been developed. PATO is an open-source software for computing material response of reactive porous materials submitted to high-temperature environments. Recent applications of PATO include computation of the full heatshield 3D material response from the Mars Science Laboratory atmospheric entry and ablation during arc jet testing. Current efforts are underway to loosely couple PATO with other discipline specialized codes including hypersonic computational fluid dynamics (CFD) to assess the effects of pyrolysis-gas blowing into the boundary layer and computational solid mechanics to address modeling of mechanical erosion. Surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation are also being added.

Thermal Protection Systems↗

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Predicting mechanical responses of heterogeneous materials across scales remains a significant challenge. Traditional computational methods often struggle with complex and multiscale nature of these materials, limiting their effectiveness in real-world applications. Here, in this paper, we introduce Micrometer, a vision transformer based deep learning model designed to predict full field mechanical responses of heterogeneous materials, bridging the gap between computer vision and solid mechanics problems. We show that Micrometer, trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of material properties and loading conditions. Our model demonstrates accuracy and computational efficiency in applications such as computational homogenization and multiscale modeling, reducing computational time by up to two orders of magnitude compared to conventional numerical solvers while maintaining less than 1 % errors in predicting macroscale stress fields. Furthermore, we showcase Micrometer’s adaptability through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in computational solid mechanics. These results represent a significant step towards AI-driven innovation in materials science, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Composite materials↗

HOSS: Hybrid Optimization Software Suite

HOSS software, developed at LANL, is a powerful, flexible, and parallelized package that enables the user to predict deformation and failure of materials in a variety of situations. LANL’s HOSS software is an R&D 100 finalist that integrates solid mechanics and computational fluid dynamics into a multi-physics platform able to handle millions of interacting and fracturing solids and/or particle systems. This nextgeneration simulation software integrates solid mechanics and computational fluid dynamics into a multi-physics platform able to provide state-of-the-art simulation solutions for a wide field of applications including oil and gas, construction, mining, defense, material sciences, and biomechanics.

36 MATERIALS SCIENCE↗

Parallel computation using boundary elements in solid mechanics

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

Chien, L. S.↗

Computational Design of Alloys for Energy Technologies

Advanced materials that maintain their mechanical performance under elevated temperatures, corrosive environments, and a range of static and evolving stresses are needed to improve the efficiency and reduce the environmental impact of a wide spectrum of energy technologies. For instance, cost-efficient alloys that can withstand high temperatures (e.g., 700 °C) have a critical role in improving the efficiency and economics of power generation to support decarbonization of the energy sector; such is true of both the nuclear and fossil energy sectors. Considering both the threats of the energy crisis, namely soaring costs of greenhouse gas emission-producing energy and climate change, it is essential to increase the pace of material discovery and enable rapid paths for material qualification to advance clean energy technologies. Conventionally, alloy development has followed a slow Edisonian process that uses repeated cycles of making, characterizing, and modifying to arrive at optimum composition and processing conditions to achieve the desired component performance. This optimization is followed by the necessary stepwise materials qualification. Furthermore, the increasing adoption of sound data management and physics-informed machine learning represents the next step in the acceleration of materials design and development. In the integrated computational materials engineering (ICME) approach, computational modeling and simulation data from different length and time scales can be combined with complex microstructural details from multimodal experimental characterization and selective property testing to close the design loop for rapid alloy development.

Computational Design Of Materials↗