SEARCH · Engineering Papers

Results for “viscoelasticity”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Tailoring the rheological properties of high protein suspension by thermal-mechanical treatment

The viscoelasticity of concentrated protein suspensions associates closely with the mixing efficiency and cleaning frequency of facility during high-protein food development. This study investigated the effects of thermal-mechanical treatment on the viscoelasticity of milk protein isolate (MPI) suspensions and their underlying mechanisms to develop protein ingredient with low viscoelasticity. MPI suspensions (20%) were treated at 25, 50 and 85°C for 10-60 min under constant shear (100 s -1 ), followed by storage at 4°C. The viscosity (η) of MPI suspension treated at 50°C and 85°C was similar to 1-10% as those treated at 25 ° C. After four days of storage at 4°C, η showed the least value in 50°C-treated samples compared to those at 25 ° C and 85 ° C. The η and storage modulus (G') was decreased with prolonged treatment at 25 and 50°C, whereas opposite trend was found in 85°C treated samples. Differential scanning calorimetry found proteins in 50°C treated samples had smaller enthalpy than those in the control and 25°C treated samples. Protein surface hydrophobicity was increased slightly from 25°C to 50°C, but remarkably in 85°C treated samples. Ultra-small angle x-ray scattering showed the radius of gyration (R-g) of casein micelle was similar to 38 nm at 25°C and 50°C treated samples but increased to similar to 44 nm 85°C treated samples with reduced compactness. A new sphere-like structure with R-g of 18 nm was generated in 85°C treated samples. These findings suggested modulating temperature during thermal-mechanical treatment is essential to alter protein structures and morphology for desirable rheological properties.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Revealing the unusual rate-dependent mechanical behaviors of nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and enhanced energy dissipation with rate dependency. They are potentially transformative materials for applications in mechanical impact mitigation and vibration isolation. However, previous studies have primarily focused on the mechanics of LCEs under equilibrium and quasistatic loading conditions. Critical knowledge gaps exist in understanding their rate-dependent behaviors, which are a complex mixture of traditional network viscoelasticity and the soft elastic behaviors with changes in the mesogen orientation and order parameter. Together, these inelastic mechanisms lead to unusual rate-dependent energy absorption responses of LCEs. In this work, we developed a viscoelastic constitutive theory for monodomain nematic LCEs to investigate how multiple underlying sources of inelasticity manifest in the rate-dependent and dissipative behaviors of monodomain LCEs. Here, the theoretical modeling framework combines the neo-classical network theory with evolution rules for the mesogen orientation and order parameter with conventional viscoelasticity. The model is calibrated with uniaxial tension and compression data spanning six decades of strain rates. The established 3D constitutive model enables general loading predictions taking the initial mesogen orientation and order parameter as inputs. Additionally, parametric studies were performed to further understand the rate dependence of monodomain LCEs in relation to their energy absorption characteristics. Based on the parametric studies, particularly loading scenarios are identified as conditions where LCEs outperform conventional elastomers regarding energy absorption.

42 ENGINEERING↗

DOE OSTI2021

The 3D printing and modeling of functionally graded Kelvin foams for controlling crushing performance

Mechanical impact protection is an important consideration in many applications, ranging from product transportation to sports. Cellular materials are typically used due to their desirable energy absorption properties and light weight. However, their large deformation and rate dependent responses (especially of polymer foams) are challenging to consider in design. Additionally, the use of foams with uniform properties, such as uniform density and uniform stiffness, often restricts the designed foams to only be suitable for a narrow range of mechanical impact conditions whereas real applications commonly face unpredictable situations. 3D printing offers fabrication flexibility and thus opens the door to create foams with tailored properties. In this work, we investigate the feasibility of using 3D printing for functionally graded foams (FGFs) that are optimal over a broad range of mechanical environments. The foams are fabricated by the recently developed grayscale digital light processing (g-DLP) method which can print parts with locally designed properties. These foams are tested under drop test conditions and with slower displacement control. We also model the large deformation behavior of FGFs using finite element analysis in which we account for the different viscoelastic behaviors of the distinct grayscale regions. We then use the model to examine the impact mitigation capabilities of FGFs in different loading scenarios. Finally, we show how FGFs can be used to satisfy real-world design goals using the case study of a motorcycle helmet. In contrast to prior work, we investigate continuous, functionally graded foams of a single density that differ in their viscoelastic responses. This work provides further insight into the benefits of viscoelastic properties and modulus graded foams and presents a manufacturing approach that can be used to produce the next generation of flexible lattice foams as mechanical absorbers.

3D printing↗

DOE OSTI2021

Microstructure homogenization of concrete used in nuclear power plants

Almost all nuclear power plants in the United States are operating past their intended lifetimes or are requesting lifetime extensions. Therefore, understanding changes to the concrete containment structure over time is crucial to evaluate the structure’s continued viability. Concrete materials are heterogeneous particulate composites that exhibit viscoelastic material properties, which can lead to slow deformation over time, causing stress redistribution and the potential for creep cracking. A code to generate random, three dimensional (3D) concrete microstructures has been developed and paired with finite element analysis to predict the long-term viscoelastic properties of concrete. Data from these simulations are used to develop constitutive equations for the viscoelastic behavior of the homogenized concrete. The codes in this work are used to virtualize laboratory experiments, to obtain long-term creep data in a faster, cheaper manner. To validate this work, the simulated creep behavior of concrete is compared to 800 d of experimental data that has been extended to 27 y of data using the Time-Temperature superposition (TTS) principal. Excellent agreement between the simulation results and experimental data is seen.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Critical Role of the Interfacial Layer in Associating Polymers with Microphase Separation

Polymers with dynamic (transient) bonds, often called associating polymers, have been attracting significant attention in recent years due to their unique viscoelastic properties, self-healing ability, and recyclability. Nevertheless, understanding the mechanisms and the factors controlling their macroscopic properties remains limited due to the higher complexity introduced by the dynamic bonds. Here in this study, small-angle X-ray scattering (SAXS), broadband dielectric spectroscopy (BDS), and rheology were applied to unravel the structure and dynamics of telechelic associating polymers with different molecular weights. SAXS measurements revealed phase separation of the functional end groups with an average cluster size of ~2–3 nm and the distance between clusters controlled by the chain length. Borrowing the interfacial layer model analysis of BDS data from the polymer nanocomposite field, we demonstrated the presence of an interfacial polymer layer with a thickness of ~0.7–0.9 nm surrounding these clusters. Rheological measurements showed quantitatively that the presence of the interfacial layer significantly alters the viscoelastic behavior of these materials, indicating the crucial role of the interfacial layer in defining the macroscopic mechanical properties of the studied telechelic materials. The presented results emphasize that phase separation of the functional groups in associating polymers leads to very significant changes of the viscoelastic properties, opening a promising avenue in the design of novel functional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Egg yolk as a model for gelation: From rheometry to flow physics

Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.

Marsh, Maxwell C. [Department of Mechanical Scienc↗

DOE OSTI2020

Collaborative Research: Polymer Macrocycles: A novel topology to control dynamics of rubbery materials

Understanding the dynamics of polymers of different topologies is an important field of study and one of the most important unanswered questions in this field is "how do circular polymers move," particularly in the melt state. New information suggests that molecular topology, specifically circular rings, impacts the response of materials in nanometer- scale confinement. The work performed here tackles these subjects through a collaboration in which specialists in polymer synthesis, polymer rheology and scattering methods, and in the physics of nanoconfinement work together to investigate the thermophysical behavior of circular macromolecules. The project goals are to use a novel synthesis method of "green" oxidative polymerization to produce high purity macrocycles and to investigate their linear viscoelastic behavior in order to fully characterize the dynamics of circular macromolecules to sizes that correspond to linear molecule entanglement densities higher than previously obtainable with synthetic polymers. Chemical chain end characterization and critical edge fractionation coupled with direct visualization of the prepared polymers through the use of polymer amplification methods are proposed in order to quantify the numbers of circular and linear molecules in each sample. The study of the linear viscoelastic response of blends of linear and circular molecules is also to be undertaken in the project. Nonlinear viscoelastic measurements, including extensional viscosity, are to be made. Strong differences in behavior between linear chains and circular ones also provides an important opportunity for new technology to break the "magic triangle" for tires: it is believed that improving one of the three key attributes - traction, wear, rolling resistance - necessarily sacrifices at least one of the others. Rubber made from cyclic polymers has the potential to break out of this triangle by reducing the so-called Payne effect in reinforced rubbers because circular macromolecules are less sensitive to nanoconfinement than their linear counterparts. The work has as one objective to characterize the impact of nanoconfinement on the behavior of large circular macromolecules. In addition, the dynamics of carbon black filled circular macromolecules are to be studied to test the hypothesis that the resulting rubbery materials will exhibit a reduced Payne effect.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Modeling and Measuring the Stress Distribution in Soft Magnetic Cores due to Epoxy Impregnation and Curing

Understanding the effects of viscoelastic relaxation of stresses is critical in electric motor and inductor applications, where the magnetic material is fully or partially comprised of an amorphous phase and impregnated in an epoxy. Magnetic Amorphous Nanocomposites (MANCs) are a class of recently developed high-frequency magnetic materials that exhibit low magnetic hysteresis, high saturation flux density and very low AC magnetic losses. MANCs are formed as long, thin ribbons, a shape factor that minimizes eddy current-induced self-heating. This feature, in addition to their 1 GPa strength, and makes them attractive candidates for high-speed, high-power density, electric motors. MANCs are used in the form of tape-wound cores (TWCs). During the manufacturing process, the cores are impregnated with liquid epoxy between each layer of ribbon. Validated knowledge of the stresses imposed by the manufacturing process and during operation is necessary to understand motor performance limitations with respect to strength. Magnetostriction, the strain imposed by reversal of the magnetic field, also affects performance. When the epoxy cures, it contracts volumetrically by 8%, imposing radial and circumferential stresses that vary along the radial direction. To date, these stresses have received little attention in the literature. Here, we model the stress distribution throughout a TWC due to epoxy curing. Strain gauge measurements reported here indicate substantially lower tangential strain than model values, which is beneficial and which we attribute to viscoelastic relaxation of the epoxy layers. We will incorporate a constitutive model of this viscoelastic relaxation, and conduct more detailed strain measurements to understand how this takes

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Resolving glacial isostatic adjustment (GIA) in response to modern and future ice loss at marine grounding lines in West Antarctica

Accurate glacial isostatic adjustment (GIA) modelling in the cryosphere is required for interpreting satellite, geophysical and geological records and for assessing the feedbacks of Earth deformation and sea-level change on marine ice-sheet grounding lines. GIA modelling in areas of active ice loss in West Antarctica is particularly challenging because the ice is underlain by laterally varying mantle viscosities that are up to several orders of magnitude lower than the global average, leading to a faster and more localised response of the solid Earth to ongoing and future ice-sheet retreat and necessitating GIA models that incorporate 3-D viscoelastic Earth structure. Improvements to GIA models allow for computation of the viscoelastic response of the Earth to surface ice loading at sub-kilometre resolution, and ice-sheet models and observational products now provide the inputs to GIA models at comparably unprecedented detail. However, the resolution required to accurately capture GIA in models remains poorly understood, and high-resolution calculations come at heavy computational expense. We adopt a 3-D GIA model with a range of Earth structure models based on recent seismic tomography and geodetic data to perform a comprehensive analysis of the influence of grid resolution on predictions of GIA in the Amundsen Sea Embayment (ASE) in West Antarctica. Through idealised sensitivity testing down to sub-kilometre resolution with spatially isolated ice loading changes, we find that a grid resolution of ~$\frac{1}{3}$ of the radius of the load or higher is required to accurately capture the elastic response of the Earth. However, when we consider more realistic, spatially coherent ice loss scenarios based on modern observational records and future ice-sheet model projections and adopt a viscoelastic Earth, we find that predicted deformation and sea-level change along the grounding line converge to within 5 % with grid resolutions of 7.5 km or higher, and to within 2% for grid resolutions of 3.75 km and higher, even when the input ice model is on a 1 km grid. Furthermore, we show that low mantle viscosities beneath the ASE lead to viscous deformation that contributes to the instrumental record on decadal timescales and equals or dominates over elastic effects by the end of the 21st century. Our findings suggest that for the range of resolutions of 1.9–15 km that we considered, the error due to adopting a coarser grid in this region is negligible compared to the effect of neglecting viscous effects and the uncertainty in the adopted mantle viscosity structure.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Phase-field modeling of rate-dependent fluid-driven fracture initiation and propagation

The rate-dependent behavior associated with deformation and fracturing of materials, such as natural rocks, poses significant challenges for modeling. In addition to the complications of the viscoelastic response, the speed of fracture propagation reflects micromechanical mechanisms in the fracture process zone(FPZ). In order to represent these complicated behaviors, a thermodynamically consistent, rate-dependent fracture model is required. Based on rigorous thermodynamic principles, we derive a rate-dependent phase-field mechanical model coupled with single-phase fluid flow in both the matrix and the fracture. The model is guaranteed to satisfy energy conservation during fracture propagation. Here, the system of equations is solved using the introduced solution procedure and a novel preconditioner that accounts for the complex fluid-structure interaction. The proposed phase-field model is tested against several benchmark problems on solid-fluid coupling, fluid-driven fracture propagation and rate-dependent viscoelastic deformation. The model serves as a strong basis for investigating rate-dependent fracturing experiments and for making predictions of material behaviors under new conditions.

42 ENGINEERING↗

DOE OSTI2021

Flow visualisation in real-size optical injectors of conventional, additised, and renewable gasoline blends

Research on renewable and alternative fuels is crucial for improving the energy and environmental efficiency of modern gasoline internal combustion engines. To highlight the influence of fuel rheological and thermodynamic properties on phase change and atomisation processes, three types of gasoline blends were tested. More specifically, the campaign comprised a reference gasoline, an ethanol/gasoline blend (10% v/v) representative of renewable fuels, and an additised gasoline sample treated with viscoelasticity-inducing agents. High-speed imaging of the transient two-phase flow field arising in the internal geometry and the near-nozzle spray region of gasoline injectors was performed employing Diffuse Backlight Illumination. The metallic body of a commercial injector was modified to fit transparent tips realising two nozzle layouts, namely a two-hole real size model resembling the Engine Combustion Network spray G injector and an enraged replica with an offset hole. Experiments were conducted at realistic operating conditions comprising an injection pressure of 100 bar and ambient pressures in the range of 0.1–6.0 bar to cover the entire range of chamber pressures prevailing in Gasoline Direct Injection engines. The action of viscoelastic additives was verified to have a suppressive effect on in-nozzle cavitation (6% reduction in cavitation extent) , while also enhancing spray atomisation at flash-boing conditions, in a manner resembling the more volatile gasoline/ethanol blends. Finally, persisting liquid ligaments were found to form after the end of injection for the additised sample, owing to the surfactant nature of the additives.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2021

A constitutive model for glass–ceramic materials

Glass–ceramics have received recent attention for use in glass–ceramic to metal hermetic seals. Due to their heterogeneous microstructure, these materials exhibit a number of advantageous responses over conventional glass based seals. Key amongst them is the possibility of a controllable thermal strain response and apparent coefficient of thermal expansion which may be used to minimize thermally induced residual stresses for aforementioned seals. Furthermore, these behaviors result from an inorganic glass matrix and variety of crystalline ceramic phases including silica polymorph(s) that may undergo reversible solid-to-solid transformations with associated inelastic strain. Correspondingly, these materials exhibit complex thermomechanical responses associated with multiple inelastic mechanisms (viscoelasticity and phase transformation). While modeling these behaviors is essential for developing and analyzing the corresponding applications, no such model exists. Therefore, in this work a three-dimensional continuum constitutive model for glass–ceramic materials combining these various inelastic mechanisms is developed via an internal state variable approach. A corresponding fully implicit three dimensional numerical formulation is also proposed and implemented. The model is used to simulate existing experiments and validate the proposed formalism. As an example, the simple seal problem of a glass–ceramic seal inside a concentric metal shell is explored. Finally, the impact of the cooling rates, viscoelastic shift factors, and inelastic strain on final residual stress state are all investigated and the differing contributions highlighted.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Soft sample deformation, damage and induced electromechanical property changes in contact- and tapping-mode atomic force microscopy

Probe-induced soft sample damage in atomic force microscopy (AFM), as well as the resulting alteration of local mechanical and electrical properties of the material are explored, specifically comparing contact-mode and intermittent-contact-mode imaging methods. In our experiments, performed on conductive polymer films, induced changes are present in contact-mode imaging while they are negligible or absent in tapping-mode imaging. Here, to understand this result, a viscoelastic parameter extraction is performed, which suggests that permanent sample deformation can readily occur for tip-sample interactions with a duration on the timescale of contact-mode interactions. Using the extracted viscoelastic parameters, a dynamic AFM simulation is conducted, which suggests that the material responds more elastically with reduced or absent sample damage in tapping-mode AFM, due to the higher rate of mechanical deformation and shorter timescales.

42 ENGINEERING↗

DOE OSTI2022

Application of Multiharmonic QCM-D for Detection of Plasmin at Hydrophobic Surfaces Modified by β-Casein

Plasmin protease plays an important role in many processes in living systems, including milk. Monitoring plasmin activity is important for control of the nutritional quality of milk and other dairy products. We designed a biosensor to detect the proteolytic activity of plasmin, using multiharmonic quartz crystal microbalance with dissipation (QCM-D). The β-casein immobilized on the hydrophobic surface of 1-dodecanethiol on the AT-cut quartz crystal was used to monitor plasmin activity. We demonstrated detection of plasmin in a concentration range of 0.1–20 nM, with the limit of detection about 0.13 ± 0.01 nM. The analysis of viscoelastic properties of the β-casein layer showed rapid changes of shear elasticity modulus, μ, and coefficient of viscosity, η, at plasmin sub-nanomolar concentrations, followed by modest changes at nanomolar concentrations, indicating multilayer architecture β-casein. A comparative analysis of viscoelastic properties of β-casein layers following plasmin and trypsin cleavage showed that the higher effect of trypsin was due to larger potential cleavage sites of β-casein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Two-dimensional glass transition–like behavior of Janus particle–laden interface

Abstract Understanding the interactive behavior of Janus particles (JPs) is a growing field of research. The enhancement in binding energy, in comparison to homogenous particles, and the dual characteristic of JPs open up new possibilities for novel applications. In many such applications, interfacial materials become subjected to flows that produce dilational and shear stresses. Therefore, it is important to understand the impact that the Janus character brings to interfaces. In this work, we study the microstructure of two-dimensional (2D) JP monolayers formed at the air–water interface and examine the shear viscoelasticity with an interface rheometer that was adapted for in situ surface pressure control via a Langmuir trough. We extend concepts from bulk rheology to data obtained from interfacial rheology as a tool to understand and predict the monolayer’s viscoelastic behavior. Finally, by calculating the time relaxation spectrum from the measured 2D dynamic moduli, we conclude that a phenomenon similar to glass transition is taking place by analogy.

42 ENGINEERING↗

DOE OSTI2023

Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks

Abstract Anticipating qualitative changes in the rheological response of complex fluids (e.g., a gelation or vitrification transition) is an important capability for processing operations that utilize such materials in real-world environments. One class of complex fluids that exhibits distinct rheological states are soft glassy materials such as colloidal gels and clay dispersions, which can be well characterized by the soft glassy rheology (SGR) model. We first solve the model equations for the time-dependent, weakly nonlinear response of the SGR model. With this analytical solution, we show that the weak nonlinearities measured via medium amplitude parallel superposition (MAPS) rheology can be used to anticipate the rheological aging transitions in the linear response of soft glassy materials. This is a rheological version of a technique called structural health monitoring used widely in civil and aerospace engineering. We design and train artificial neural networks (ANNs) that are capable of quickly inferring the parameters of the SGR model from the results of sequential MAPS experiments. The combination of these data-rich experiments and machine learning tools to provide a surrogate for computationally expensive viscoelastic constitutive equations allows for rapid experimental characterization of the rheological state of soft glassy materials. We apply this technique to an aging dispersion of Laponite ® clay particles approaching the gel point and demonstrate that a trained ANN can provide real-time detection of transitions in the nonlinear response well in advance of incipient changes in the linear viscoelastic response of the system.

Lennon, Kyle R. (ORCID:0000000212515461)↗

DOE OSTI2022

Dynamic stability of a crude oil/brine interface: Effect of anion type

The chemical composition of the aqueous phase plays an essential role in water-based enhanced-oil recovery processes. The aqueous phase ionic profile affects the snap-off response of a crude oil-brine system by linking it to the brine-crude oil interfacial rheology. In this work, we focus on the effect of the anion on the snap-off response. To this end, a sample of crude oil from the Minnelusa Sandstone formation in Wyoming was selected, and several aqueous solutions were prepared with salts containing sodium cation and different anions (chlorides, sulfates, and phosphates) at two ionic strength values, 0.6 M and 6 mM, as cases of high- and low-salinity water. Interfacial tension, interfacial viscoelasticity and interface stability were analyzed as functions of aging time using pendant drop, dilatational rheology, and liquid bridge techniques, respectively. Here the results show that solutions with higher ionic strength led to the formation of more rigid interfaces, i.e. higher elastic modulus, and faster formation kinetics. In the low-salinity regime, solutions with polyvalent anions produce more viscoelastic interfaces at faster rates than solutions with monovalent anions. Finally, an excellent correlation (R 2 greater than 0.97) between the relative stability of the interfacial film, predicted in liquid bridge tests, and the ratio of interfacial tension and interfacial elastic modulus was found.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗