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At least 73 records · Page 4

Marmot V2

MARMOT is a robust numerical tool for mesoscale modeling of fuel performance developed under the NEAMS Fuels technical area to predict the coevolution of microstructure and properties in fuel and cladding materials. MARMOT accomplishes this using the phase field method coupled with finite strain mechanics and heat conduction. MARMOT is based on the open source Multiphysics Object-Oriented Simulation Environment (MOOSE) and solves the coupled partial differential equations defining the physics using the finite element method. MARMOT is being developed in order to facilitate the development of improved materials models for fuel performance, but it is also being developed as a powerful tool in and of itself for the simulation of mesoscale fuel performance.

Aagesen, LarryK.↗

Modeling low cycle fatigue (LCF) of additively manufactured Hastelloy X using An accelerated crystal plasticity fatigue damage model

This paper presents a microstructure-based model for low cycle fatigue (LCF) behavior and life of Nickel-based alloy Hastelloy X manufactured using laser-powder bed fusion (L-PBF) additive manufacturing (AM). AM Hastelloy X, a solution-strengthened alloy, is tested at elevated temperature under fully reversed LCF conditions at different strain levels. A generalized plane strain finite element model is generated from electron backscatter diffraction (EBSD) characterization. The constitutive behavior of the material under fatigue is modeled using crystal plasticity and calibrated with both monotonic tensile and cyclic stress–strain data. The fatigue micro-crack initiation and propagation in the microstructure is modeled using a modified Chaboche fatigue damage model. An embedded boundary condition with a homogenous medium is used to apply the cyclic deformation and prevent numerically introduced over-constraints during fatigue simulation. A ‘cycle-jump’ method is used to accelerate the fatigue simulation and reduce the computational cost. The simulation results are compared to LCF experiments, showing satisfactory matches in cyclic stress behavior and number of cycles to macro-crack initiation for all applied strain ranges. In addition, the model illustrates the potential for quantifying microscale fatigue life impacting factors such as microstructure and surface roughness, which is needed to accurately quantify the reliability of AM components in service.

36 MATERIALS SCIENCE↗

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗

Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites

The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.

Finite element analysis↗

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗

Testing and Analysis of Composite Skin/Stringer Debonding Under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from skin. In a second step, a two dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location, Hence. Unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

Testing and Analysis of Composite Skin/Stringer Debonding under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from the skin. In a second step, a two-dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location. Hence, unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

A variational justification of the assumed natural strain formulation of finite elements. I - Variational principles. II - The C(0) four-node plate element

The assumed natural strain formulation of finite elements is interpreted from a variational standpoint. The approach is based on hybrid extensions of the Reissner-type functional which uses the strains and displacements as independent fields. Consideration is restricted to linear elasticity. The four-node C(0) plate-bending quadrilateral is used as a specific example to illustrate the application of the present interpretation. A key finding is that any change in the strain-displacement interpolation from the variationally consistent interpolation must be associated in some way to the addition of incompatible displacement modes.

Militello, Carmelo↗

A fully-integrated lattice Boltzmann method for fluid–structure interaction

Here we present a fully-integrated lattice Boltzmann (LB) method for fluid–structure interaction (FSI) simulations that efficiently models deformable solids in complex suspensions and active systems. Our Eulerian method (LBRMT) couples finite-strain solids to the LB fluid on the same fixed computational grid with the reference map technique (RMT). An integral part of the LBRMT is a new LB boundary condition for moving deformable interfaces across different densities. With this fully Eulerian solid–fluid coupling, the LBRMT is well-suited for parallelization and simulating multi-body contact without remeshing or extra meshes. We validate its accuracy via a benchmark of a deformable solid in a lid-driven cavity, then showcase its versatility through examples of soft solids rotating and settling. The LBRMT achieves a spatial convergence rate between first-order and second-order for FSI simulations and is designed for low to intermediate Reynolds number flows with finite inertia at small Mach numbers. With simulations of complex suspensions mixing, we highlight the potential of the LBRMT for studying collective behavior in soft matter and biofluid dynamics.

97 MATHEMATICS AND COMPUTING↗

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗

Inelastic equation of state for solids

In this study, a complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem.

42 ENGINEERING↗

Simulations of crack extensions in arc-shaped tension specimens of uncharged and hydrogen-charged 21-6-9 austenitic stainless steels using cohesive zone modeling with varying cohesive parameters

Crack extensions in uncharged and hydrogen-charged side-grooved A(T) specimens of conventionally forged 21-6-9 austenitic stainless steels are simulated using the cohesive zone modeling approach. Two-dimensional plane strain finite element analyses with fixed cohesive parameters are first conducted to fit the experimental load-displacement curves. Similar analyses using varying cohesive parameters as functions of the crack extension are then conducted to fit the experimental load-crack extension and crack extension-displacement curves. The computational results with varying cohesive parameters can fit very well the experimental data. The computational results also indicate that the average cohesive energy for the hydrogen-charged A(T) specimen is lower than that for the uncharged A(T) specimen.

42 ENGINEERING↗

Anomalous elastic behavior of tantalum at high pressures: Experimental and theoretical studies

Elastic wave velocities of polycrystalline tantalum have been measured up to 13.6 GPa at room temperature using ultrasonic interferometry technique in a multi-anvil apparatus. The bulk and shear moduli, as well as their pressure derivatives are obtained using Eulerian 3rd order finite strain equations, yielding K S0 = 193.9(29) GPa, G 0 = 69.3(10) GPa, K S0' = 3.18(5) and G 0' = 0.88(1). Here the Steinberg-Guinan yield stress model is examined using the current shear modulus and its pressure derivative, where a slightly lower A 0 = 0.0127 GPa –1 compared to previous studies is obtained. First-principles calculations on the elasticity of tantalum have also been performed up to 200 GPa. Anomalous softening of the elastic shear constant C 44 and shear wave velocity V S is observed between 80– 180 GPa, whereas the anisotropy shows a softening-stiffening behavior with increasing pressure and reaches a minimum at around 150 GPa. Such anomalies might commonly originate from the nesting of Fermi surface for Group VB metals.

36 MATERIALS SCIENCE↗

Crystal plasticity including a phase-field deformation twinning model for the high-rate deformation of cyclotetramethylene tetranitramine

A new finite strain thermomechanical model for the high-rate deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) has been developed and applied to simulations of plate impact experiments. The crystal plasticity model is based on a model developed previously for RDX (Luscher et al. 2017), which is extended to incorporate deformation twinning. Twinning during normal plate impacts is simulated with a phase-field twin model. First, material parameters governing the kinetics of dislocation slip are calibrated on the subset of simulations which had negative Schmid factors for the twin system. Second, a parametric study of the twin material parameters was performed to find suitable values. Overall, the results of the simulations with the phase-field twinning model are reported for impacts on several crystal orientations. We find that the twin growth decreases with increasing distance from the impact surface because of dissipation of the shock front via dislocation-mediated plasticity, and that the simulated interface velocity with and without phase-field twinning do not show appreciable differences. These modeling results suggest that the significance of twinning in β-HMX cannot be determined with traditional loading configurations and diagnostics.

36 MATERIALS SCIENCE↗

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗

Implications of Sound Velocities of Natural Topaz on the Seismic L–Discontinuity

Compressional and shear wave velocities of topaz have been measured by ultrasonic interferometry in a multi-anvil apparatus up to 13 GPa at room temperature. By fitting the measured velocities under pressure to finite strain equations, the elastic moduli of topaz and their pressure derivatives were obtained, yielding K S0 = 165.5 (25) GPa, K S ' = 2.9 (1), G 0 = 116.5 (17) GPa, and G' = 1.0 (1). Modeling of the velocity profiles of subducted sediments suggests that at 8 GPa (~240 km depth) the P- and S- wave velocities of the subducted sediments exhibit a first order increase of 10% and 11%, respectively. Furthermore, the comparison between seismic observations and velocity contrasts of sediment + MORB model at 240 km shows dehydration of a 1.5–3.9 km thick sediment layer can potentially contribute to the seismically observed Lehmann discontinuity in Tonga, Japan, Philippine Sea, South America, Indonesia, and South Shetland subduction zones.

36 MATERIALS SCIENCE↗

Seismic Visibility of Eclogite in the Earth’s Upper Mantle—Implications From High Pressure‐Temperature Single‐Crystal Elastic Properties of Omphacite

Abstract Identifying and locating the geochemical and geophysical heterogeneities in the Earth’s interior is one of the most important and challenging tasks for the deep Earth scientists. Subducted oceanic crust metamorphizes into the dense eclogite in the upper mantle and is considered as a major cause of geochemical and geophysical heterogeneities in the deep Earth. In order to detect eclogitic materials inside the Earth, precise measurements of the high pressure‐temperature single‐crystal elasticity of major minerals in eclogite are thus exceedingly important. Omphacite, a Na,Al‐bearing clinopyroxene, constitutes up to 75 vol% of eclogite. In the present study, we performed the first high pressure‐temperature single‐crystal elasticity measurements of omphacite using Brillouin spectroscopy. Utilizing the finite‐strain approach, we obtained the following thermoelastic parameters for omphacite: K S0 ’ = 4.5(1), G 0 ’ = 1.53(5), ∂K S0 /∂ T = −0.029(5) GPa/K, ∂G 0 /∂ T = −0.013(5) GPa/K, with K S0 = 123(3) GPa, G 0 = 74(2) GPa, and ρ 0 = 3.34(1) g/cm 3 . We found that the seismic velocities of undeformed eclogite are similar to pyrolite at the depths of 200–300 and 410–500 km, thus eclogite is seismically invisible at these depths. Combined with the lattice‐preferred orientations of the omphacite in naturally deformed eclogites, we also modeled seismic anisotropy of eclogite at various pressure‐temperature conditions. A 10 km thick subducted eclogitic crust can result in ∼0.2 s shear wave splitting in the Earth’s upper mantle.

Hao, Ming↗