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Results for “continuum mechanics of solids”

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 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2020

Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypo-elastoplastic mechanical model, and develop a projection method to enforce quasi-static equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Size dependent lattice pseudosymmetry for frustrated decahedral nanoparticles

Geometric frustration—where geometry prevents simultaneous satisfaction of local interactions—generates pseudosymmetry and emergent behaviors across physical and biological systems. At the nanoscale, pseudosymmetric features in crystalline materials manifest as local strain and distortion, but how they depend on particle size and control structural stability remains unclear. Here, we report the first study of a size-dependent crossover in pseudosymmetry in multi-twinned gold nanoparticles (NPs), combining four-dimensional scanning transmission electron microscopy with nanoscale strain mapping grounded in continuum solid mechanics. Analysis of more than 20 decahedral NPs (20–55 nm) reveals pronounced heterogeneity in multiple modes of in-plane strain and displacement field in small NPs as five tetrahedral grains close the geometric gap, without extended defects. With increasing particle size, strain fields homogenize across grains and local phases shift from predominantly low-symmetry body-centered tetragonal motifs at small sizes to face-centered cubic character approaching the bulk limit. We identify a crossover particle size of ~35 nm, well below bulk, correlating with a transition from modified-Wulff shapes to pentagonal bipyramids, consistent with finite element predictions. This quantitative framework for mapping size-dependent strain and pseudosymmetry enables precise design and control of functional crystalline solids and phase transformation for catalysis, photonics, electronics, and energy storage.

Lin, Oliver [University of Illinois at Urbana-Cham↗
DOE OSTI2025

Green's function fast multipole method for continuum mechanics (SM-FMM)

Solid Mechanics Fast Multipole Method based on elastic Green's function and accelerated using FFTs The code calculates the mechanical fields (stress and strain) for a heterogeneous elasto-plastic material unit cell under quasi-static conditions (no dynamic effects). The fields are calculated using a Green's function method, where the strain field is given by a discrete convolution of Green's operator with an auxiliary stress field. The convolution is calculated using the fast multipole method.

Zecevic, Miroslav↗
DOE OSTI2023

Multiphysics Modeling Framework for Soft PVC Gel Sensors with Experimental Comparisons

Polyvinyl chloride (PVC) gels have recently been found to exhibit mechanoelectrical transduction or sensing capabilities under compressive loading applications. This phenomenon is not wholly understood but has been characterized as an adsorption-like phenomena under varying amounts and types of plasticizers. A different polymer lattice structure has also been tested, thermoplastic polyurethane, which showed similar sensing characteristics. This study examines mechanical and electrical properties of these gel sensors and proposes a mathematical framework of the underlying mechanisms of mechanoelectrical transduction. COMSOL Multiphysics is used to show solid mechanics characteristics, electrostatic properties, and transport of interstitial plasticizer under compressive loading applications. The solid mechanics takes a continuum mechanics approach and includes a highly compressive Storakers material model for compressive loading applications. The electrostatics and transport properties include charge conservation and a Langmuir adsorption migration model with variable diffusion properties based on plasticizer properties. Results show both plasticizer concentration gradient as well as expected voltage response under varying amounts and types of plasticizers. Experimental work is also completed to show agreeance with the modeling results.

42 ENGINEERING↗
DOE OSTI2022

An Eulerian crystal plasticity framework for modeling large anisotropic deformations in energetic materials under shocks

Here, this paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response.

42 ENGINEERING↗
DOE OSTI2021

Peridynamic Model for Microballistic Perforation of Multilayer Graphene

The peridynamic theory of solid mechanics is applied to the continuum modeling of the impact of small, high-velocity silica spheres on multilayer graphene targets. The model treats the laminate as a brittle elastic membrane. The material model includes separate failure criteria for the initial rupture of the membrane and for propagating cracks. Material variability is incorporated by assigning random variations in elastic properties within Voronoi cells. Here, the computational model is shown to reproduce the primary aspects of the response observed in experiments, including the growth of a family of radial cracks from the point of impact.

42 ENGINEERING↗
DOE OSTI2020

Computational Model for Microballistic Perforation of Multilayer Graphene

The peridynamic theory of solid mechanics is applied to the continuum modeling of the impact of small, high-velocity silica spheres on multilayer graphene targets. The model treats the laminate as a brittle elastic membrane. The material model includes separate failure criteria for the initial rupture of the membrane and for propagating cracks. Material variability is incorporated by assigning random variations in elastic properties within Voronoi cells. The computational model is shown to reproduce the primary aspects of the response observed in experiments, including the growth of a family of radial cracks from the point of impact.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

Towards the design of nature-inspired materials: Impact of complex pore morphologies via higher-order homogenization

Even though the development of novel materials that mimic nature is widely used in a variety of engineering and scientific fields, the relationship between effective material properties and underlying, often complex pore morphology is still not fully understood. To address this knowledge gap and accelerate the development of novel nature-inspired materials, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we create unique pore morphologies with varying levels of complexity that serve as a more realistic representation of natural materials. Here, we then use the second-order homogenization method to capture the role of pore size, shape, orientation, and distribution on effective properties. By creating different pore morphologies, we systematically studied the relationship between morphology and effective mechanical properties. The results highlight the necessity of higher-order parameters to fully capture the role of realistic pore morphologies on effective mechanical properties and provide a path forward in the design of nature-inspired materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Mechanical analysis of heterogeneous materials with higher-order parameters

Abstract Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

42 ENGINEERING↗
DOE OSTI2023

Continuum-Level Modeling of Li-Ion Battery SEI by Upscaling Atomistically Informed Reaction Mechanisms

Understanding and controlling solid-electrolyte interphase (SEI) formation to stabilize cell performance is a significant challenge for next-generation Li-ion battery technologies. In recent years, computational modeling has become an essential tool in providing fundamental insights into SEI properties and dynamics. However, neither atomistic nor continuum-level approaches alone can capture the complexities of SEI chemistry across all relevant length and time scales. In this work, a continuum-level model is developed that is informed by reaction mechanisms obtained from first-principle calculations. The atomistically informed continuum-level model is used to understand electrolyte degradation, including the decomposition of ethylene carbonate (EC), ethyl methyl carbonate (EMC), and fluoroethylene carbonate (FEC). The model presented here is the most chemically complex continuum-level SEI model in the literature to date. The SEI model is calibrated against experimental irreversible leakage currents and shows qualitative agreement with expected SEI growth trends. The model framework is expected to accelerate fundamental understanding of SEI formation, facilitate mechanism development feedback, and dynamically interact with experimental insights.

continuum-level model↗
DOE OSTI2020

Derived crystal structure of martensitic materials by solid–solid phase transformation

A mathematical description of crystal structure is proposed consisting of two parts: the underlying translational periodicity and the distinct atomic positions up to the symmetry operations in the unit cell, consistent with the International Tables for Crystallography. By the Cauchy–Born hypothesis, such a description can be integrated with the theory of continuum mechanics to calculate a derived crystal structure produced by solid–solid phase transformation. In addition, the expressions for the orientation relationship between the parent lattice and the derived lattice are generalized. Additionally, the derived structure rationalizes the lattice parameters and the general equivalent atomic positions that assist the indexing process of X-ray diffraction analysis for low-symmetry martensitic materials undergoing phase transformation. The analysis is demonstrated in a CuAlMn shape memory alloy. From its austenite phase (L2 1 face-centered cubic structure), it is identified that the derived martensitic structure has orthorhombic symmetry Pmmn with the derived lattice parameters a d = 4.36491, b d = 5.40865 and c d = 4.2402 Å, by which the complicated X-ray Laue diffraction pattern can be well indexed, and the orientation relationship can be verified.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Nondissipative Martensitic Phase Transformation after Multimillion Superelastic Cycles

Superelastic alloys used for stents, biomedical implants, and solid-state cooling devices rely on their reversible stress-induced martensitic transformations. These applications require the alloy to sustain high deformability over millions of cycles without failure. Here, we report an alloy capable of enduring 10 × 10 7 tensile stress-induced phase transformations while still exhibiting over 2% recoverable elastic strains. After millions of cycles, the alloy is highly reversible with zero stress hysteresis. We show that the major martensite variant is reversible even after multimillions of cycles under tensile loadings with a highly coherent $(1\bar{1}0)_A$ interface. Finally, this discovery provides new insights into martensitic transformation, and may guide the development of superelastic alloys for multimillion cycling applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The Microscopic Mechanism of Lithiation and Delithiation in the Ag/C Buffer Layer for Anode‐Free Solid‐State Batteries

Abstract Lithium metal solid‐state batteries (LMSSBs) have demonstrated their high energy density and cycling performance at high current densities in an anode‐free architecture, featuring a thin Ag/C composite buffer layer (BL) between the current collector (CC) and the solid electrolyte (SE). This study explains the microscopic mechanism of the Ag/C BL by using first‐principles atomistic and continuum modeling. It is shown that Ag effectively acts as a homogeneous solid‐solution beyond AgLi 2.32 and maintains a positive potential even at AgLi 25 during lithiation. Key factors underlying the working of the Ag/C BL include lower interfacial resistance at the BL/CC interface than at the BL/SE interface, leading to predominant Li deposition on BL/CC, and substantial Ag–Li volume expansion during lithiation. This, combined with stronger BL/SE adhesion, causes BL/SE separation and Ag–Li extrusion toward the CC side. During delithiation, Ag re‐precipitates as nanoparticles uniformly on the CC, with its positive lithiation potential homogenizing Li currents in subsequent cycles. Other metals are less effective due to their relatively large overpotential, premature lithiation termination, and limited volume expansions hindering movement toward the CC. The study aids the BL design, focusing on metal choice and optimization material and microstructural properties, such as the Li‐ion conductivity and interfacial resistance.

25 ENERGY STORAGE↗
DOE OSTI2025

Modeling the formation of Sedan Crater using the FLAG and HOSS codes

Numerical modeling of explosion crater formation requires accounting for complex physical processes. Numerical validation of explosion cratering is an important step in modeling and requires experimental data for comparison. Models using discrete elements and continuum models have both benefits and drawbacks to their approaches. In this work, we consider both an arbitrary Lagrangian–Eulerian (ALE) hydrocode and a finite discrete element method (FDEM) approach to modeling the formation of the Sedan crater, the largest human-made crater in the United States. The Sedan crater formed from an underground nuclear detonation in the Nevada desert as part of Project Plowshare. Our models show that the continuum approach of the hydrocode matched well compared to early test time prior to the mound rupture and subsequent fireball venting, when most of the alluvium exhibited fluid behavior. Our FDEM approach matched the final crater dimensions well, after material had settled back into the crater, when material strength and solid mechanics play key roles. Our work shows how leveraging the benefits of multiple numerical approaches can lead to better understanding of complex physical problems, especially problems with limited experimental data. By using a continuum approach to early-time hydrodynamics and an FDEM approach to later-time solid mechanics, we can better understand the different physical regimes of explosion crater formation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Selective mass scaling for single-layer thick shell elements in DYNA3D

Hexahedral elements can be adapted to model thin and moderately thick structures by neglecting the coupling of through-thickness stress, resulting in a fully three-dimensional, but simplified, state of stress. These specialized elements, often referred to as “thick” or “solid” shells, are generally employed to model thin-walled structures using continuum mechanics-based material models. In explicit dynamics simulations, where computational speed is important, these elements are integrated with a single quadrature point and a set of anti-hourglassing (stabilizing) forces. Thick shells, by definition, have a thickness dimension smaller than their in-plane dimensions, and this small thickness often determines the stable time step size in simulations, despite the mechanics being approximated. To alleviate this limitation while retaining the relevant dynamics of thin-walled structures, selective mass scaling (SMS), or selective mass “augmentation,” has been proposed in the literature. In this technical report, we explore the application of SMS to single-layer thick shells in the simulation software DYNA3D.

42 ENGINEERING↗