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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

42 ENGINEERING↗
DOE OSTI2023

Hexagonal Distributed Embedded Energy Converter (HexDEEC)

Hexagonal Distributed Embedded Energy Converters are relatively small, centimeter scale, energy transducers that leverage variable capacitance to generate electricity when their hyperelastic structure is dynamically deformed. A multitude of HexDEECs can be woven to form construction materials that can be used to build complete energy conversion structures, such as ocean wave energy converters.

BFSF↗
DOE OSTI2026

Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D

The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger overpressure magnitudes (𝒪⁡(1⁢0 2 )⁢kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪⁡(1⁢0 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.

42 ENGINEERING↗
DOE OSTI2023

Stress‐constrained topology optimization of structures subjected to nonproportional loading

Abstract This work considers the topology optimization of hyperelastic structures for maximum stiffness (minimum compliance) subject to constraints on their volume and maximum stress. In contrast to almost all previous works, we subject the structures to nonproportional loading, wherein the maximum stress does not necessarily occur at the final load step. As such, the stress is constrained at each load step. The augmented Lagrangian method is used to formulate the optimization problem with its many constraints. In numerical examples, we investigate different load trajectories for the same terminal load and compare the optimized designs and their performances. The results show the importance of considering the entire load trajectory as the load history significantly influences the optimized designs.

42 ENGINEERING↗
DOE OSTI2025

Toward Standardized Microscale Tensile Testing for Two‐Photon Polymerization‐Fabricated Materials in Liquid

Two-photon polymerization (TPP) enables the fabrication of intricate 3D microstructures with submicron precision, offering significant potential in biomedical applications like tissue engineering. In such applications, to print materials and structures with defined mechanics, it is crucial to understand how TPP printing parameters impact the material properties in a physiologically relevant liquid environment. Herein, an experimental approach utilizing microscale tensile testing (μTT) for the systematic measurement of TPP-fabricated microfibers submerged in liquid as a function of printing parameters is introduced. Using a diurethane dimethacrylate-based resin, the influence of printing parameters on microfiber geometry is first explored, demonstrating cross-sectional areas ranging from 1 to 36 μm 2 . Tensile testing reveals Young's moduli between 0.5 and 1.5 GPa and yield strengths from 10 to 60 MPa. The experimental data show an excellent fit with the Ogden hyperelastic polymer model, which enables a detailed analysis of how variations in writing speed, laser power, and printing path influence the mechanical properties of TPP microfibers. The μTT method is also showcased for evaluating multiple commercial resins and for performing cyclic loading experiments. Collectively, this study builds a foundation toward a standardized microscale tensile testing framework to characterize the mechanical properties of TPP printed structures.

mechanical characterization↗
DOE OSTI2026

Input specific neural networks

Neural networks have emerged as powerful tools for mapping between inputs and outputs. However, their black-box nature limits the ability to encode or impose specific structural relationships between inputs and outputs. Many scientific and engineering problems, such as constitutive modeling in solid mechanics, require networks that can enforce convexity, monotonicity, or other structural constraints to ensure physical consistency. Here, we introduce the Input Specific Neural Network (ISNN), a new architecture that enables multiple, distinct constraints to be imposed on different input subsets for scalar-valued outputs. This framework unifies convex, monotone–convex, monotone, and arbitrary mappings within a single network for the first time. Two ISNN architectures with analytical first- and second-order derivatives are developed. We demonstrate the performance on synthetic toy problems, inverse problems in isotropic hyperelasticity, and finite element simulations. ISNNs achieve improved extrapolation behavior, require fewer invariant inputs than standard input convex networks for polyconvex potentials, and enable significant computational savings via manual differentiation. We also show how ISNNs can be used to learn structural relationships between inputs and outputs via a binary gating mechanism. Particularly, ISNNs are employed to model a homogenized anisotropic free energy potential in a decoupled multiscale setting. The network learns whether or not the potential should be modeled as polyconvex and retains only the relevant layers while using the minimum number of inputs. ISNNs provide a flexible foundation for embedding structural priors into neural networks, enhancing both interpretability and stability. They are broadly applicable across computational mechanics and other scientific domains requiring constrained functional relationships.

Jadoon, Asghar A. [Univ. of Texas, Austin, TX (Uni↗
DOE OSTI2023

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simultaneous shape and topology optimization of inflatable soft robots

Simultaneous shape and topology optimization is used to design pressure-activated inflatable soft robots. The pressure loaded boundary is meshed conformingly and shape optimized, while the morphology of the robot is topology optimized. The design objective is to exert maximum force on an object, i.e. to produce soft “grippers”. The robot’s motion is modeled using nearly incompressible finite deformation hyperelasticity. To ensure stability of the robot, the buckling load factors obtained via linearized buckling analyses are constrained. The finite element method is used to evaluate the optimization cost and constraint functions and the adjoint method is employed to compute their sensitivities. The numerical examples produce pressure-driven soft robots with varying complexity. We also compare our simultaneous optimization results to those obtained via sequential topology and then shape optimization.

42 ENGINEERING↗
DOE OSTI2024

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.

Data-driven constitutive models↗
DOE OSTI2026

Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. In this work, we propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

42 ENGINEERING↗
DOE OSTI2025

Physics augmented machine learning discovery of composition-dependent constitutive laws for 3D printed digital materials

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. Here, this work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply $L_0$ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

Constitutive modeling↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
DOE OSTI2023

A diffusion–deformation model with damage for polymer undergoing rapid decompression failure

Green hydrogen is emerging as one of the most promising alternatives to replace fossil fuels. While hydrogen gas has a good energy density by weight, its poor energy density by volume requires it to be stored under high pressure for commercial use. The hydrogen infrastructure developed to handle this high pressure hydrogen contains multiple components made of polymers as sealing agents. Although polymers do not react chemically with hydrogen gas, they undergo a mechanical failure when high pressure hydrogen gas is suddenly depressurized. This phenomenon known as 'rapid decompression failure' occurs due to the diffusion of hydrogen through polymer and getting trapped inside pre-existing cavities or voids. Here, in this paper, a continuum mechanics-based coupled diffusion-deformation-damage model was developed to predict the hydrogen distribution, stress distribution, and damage propagation inside the polymer while it undergoes rapid decompression failure. The polymer was modeled as a hyperelastic material because it represents the nonlinear material response observed in uniaxial tensile tests perfectly. The effects of hydrogen diffusivity, pre-existing cavity size, cavity location, applied hydrogen pressure, and depressurization rate on damage initiation were studied. It was found that the coefficient of diffusion plays an important role in damage initiation and damage was mostly concentrated in the inside areas rather than near the surface. Experiments were conducted with EPDM polymer which agreed well with the predicted trends using the given model. The effect of adding carbon black and silica filler particles and plasticizer to the pure EPDM polymer was also studied. It was found that damage during RDF decreases with the addition of fillers, but increases with the addition of the plasticizer. Finally, the damage evolution in the presence of two cavities was also studied, and was found that the interaction of stress fields around the cavities alters the damage occurring during RDF.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants ( l, m and n ) are given for common metals. Further, the TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m . The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ~ 35°C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

42 ENGINEERING↗
DOE OSTI2022

Enhancing high-fidelity nonlinear solver with reduced order model

Abstract We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM’s prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards’ equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM’s accuracy while speeding up nonlinear solver by 18–73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM’s prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM’s accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A new woven composite constitutive model validated by shock wave experiments

In this paper, we present results of plate impact simulations of shock compressed woven glass fiber-reinforced plastic (GRP) performed using the Arbitrary Lagrangian–Eulerian three-dimensional finite element code. A hyperelastic large-strain-based empirical Continuum Damage Mechanics (CDM) formulation is employed to describe damage initiation and growth in the shock-compressed GRP. The model parameters calibration scheme utilizes the Velocity Interferometer System for Any Reflector normal particle velocity measurements at the free surface of the GRP target plates. The impact velocity in the experiments ranged from 8.5 to 418 m/s. The finite element model considered planar 0°/90° bidirectional plies with an individual ply thickness of 0.68 mm, stacked to reach a total laminate thickness of 6.8 mm. The anisotropic elastic strains were estimated from the experimentally determined tetragonal symmetry stiffness matrix for the GRP. The strain-based damage model captures several salient features observed in the measured free surface particle wave profiles, including the shock rise time, onset of Elastic—Elastic Cracking, and the shape of the nonlinear portion of the experimental particle velocity profiles. Furthermore, the CDM model predicts the dominant damage mode to be matrix microcracking due to shear and the associated bulk expansion (bulking) under the global compressive loading in the plate impact configuration.

42 ENGINEERING↗
DOE OSTI2024

The Role of Unit-Cell Topology in Modulating the Compaction Response of Additively Manufactured Cellular Materials using Simulations and Validation Experiments

Additive manufacturing has enabled a transformational ability to create cellular structures (or foams) with tailored topology. Compared to their monolithic polymer counterparts, cellular structures are potentially suitable for systems requiring materials with high specific energy-absorbing capability to provide enhanced damping. In this work, we demonstrate the utility of controlling unit-cell topology with the intent of obtaining a desired stress–strain response and energy density. Using mesoscale simulations that resolve the unit-cell sub-structures, we validate the role of unit-cell topology in selectively activating a buckling mode and thereby modulating the characteristic stress–strain response. Simulations incorporate a linear viscoelastic constitutive model and a hyperelastic model for simulating large deformation of the polymer under both tension and compression. Simulated results for nine different cellular structures are compared with experimental data to gain insights into three different modes of buckling and the corresponding stress–strain response.

36 MATERIALS SCIENCE↗