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NASA NTRS2012

Simulating the Response of a Composite Honeycomb Energy Absorber: Dynamic Crushing of Components and Multi-Terrain Impacts - Part 1

This paper describes the experimental and analytical evaluation of an externally deployable composite honeycomb structure that is designed to attenuate impact energy during helicopter crashes. The concept, designated the Deployable Energy Absorber (DEA), utilizes an expandable Kevlar (Registered Trademark) honeycomb to dissipate kinetic energy through crushing. The DEA incorporates a unique flexible hinge design that allows the honeycomb to be packaged and stowed until needed for deployment. Experimental evaluation of the DEA included dynamic crush tests of multi-cell components and vertical drop tests of a composite fuselage section, retrofitted with DEA blocks, onto multi-terrain. Finite element models of the test articles were developed and simulations were performed using the transient dynamic code, LSDYNA (Registered Trademark). In each simulation, the DEA was represented using shell elements assigned two different material properties: Mat 24, an isotropic piecewise linear plasticity model, and Mat 58, a continuum damage mechanics model used to represent laminated composite fabrics. DEA model development and test-analysis comparisons are presented.

Jackson, Karen E.↗

NASA NTRS2018

Determination of Ballistic Limit for IM7/8552 Using LS-DYNA MAT 261

The goal of the NASA ACC High Energy Dynamic Impact Project is to determine the state of the art of dynamic fracture simulations for high velocity impact for composite fuselage shielding applications. Using a building block approach, several computational models considered under NASA ACC are being validated against test data, starting at unconfigured panels and progressing to configured panels under combined out-of-plane and in-plane loading due to ballistic impact. The computational models being evaluated in this project include MAT 162, MAT 213, MAT 261, SPG, and Peridynamics. In this paper, the simulation results using LS-Dyna Material MAT 261 are presented. In particular, a series of blind predictions for unconfigured panels were performed to determine the ballistic limit or V50 velocity. MAT 261 employs failure approach that is generally physically-based using fracture toughness criteria. The overall material model relies on typical ply-level stiffness properties, similar to MAT 162 and other composite continuum damage material models. The fracture toughness values are based on standard tests, and thus are not subject to extensive calibration. This approach is more efficient than performing extensive optimization studies for calibration of parameters. Also, this approach of relying on physical properties reduces the uncertainty of results, as questions concerning the quality and extent of the calibration studies is no longer relevant. However, it was found that carefully controlled coupon-level tests are needed to accurately obtain the required fracture toughness values. Additionally, it should be noted that there is one significant parameter in MAT 261 that does appear to require calibration, and that is the overall failure strain. This is the strain at which the element is deleted, and is not the same as the strain at which damage begins to accumulate. This failure strain is termed EFS (Effective Failure Strain), and is the maximum effective stain for element failure. Simulations have shown that this value will significantly affect impact response and failure. The paper presents the effect of this element failure strain parameter, along with possible uncertainties in fracture toughness values. With an adjusted appropriate value for EFS, it is seen that simulation results compare well with impact test data for predicted penetration velocity.

Byar, Alan↗

NASA NTRS2018

Modeling Fiber Kinking at the Microscale and Mesoscale

A computational micromechanics (CMM) model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking. The CMM model considers an individually discretized three dimensional fiber and surrounding matrix accounting for nonlinearity in the fiber, matrix plasticity, fiber/matrix interface debonding, and geometric nonlinearity. Key parameters of the CMM model were measured through experiments. In particular, a novel experimental technique to characterize the in situ longitudinal compressive strength of carbon fibers through indentation of micropillars is presented. The CDM model is formulated on the basis of Budiansky's fiber kinking theory (FKT) with a constitutive deformation-decomposition approach to alleviate mesh size sensitivity. In contrast to conventional mesoscale CDM models that prescribe a constitutive response directly, the response of the proposed model is an outcome of material nonlinearity and large rotations of the fiber direction following FKT. Comparison of the predictions from the CMM and CDM models shows remarkable correlation in strength, post-peak residual stress, and fiber rotation, with less than 10% difference between the two models in most cases. Additional comparisons are made with several fiber kinking models proposed in the literature to highlight the efficacy of the two models. Finally, the CMM model is exercised in parametric studies to explore opportunities to improve the longitudinal compression strength of a ply through the use of nonconventional microstructures.

Herraez, Miguel↗

NASA NTRS2018

Validation of a Mesoscale Fiber Kinking Model Through Test and Analysis of Double Edge Notch Compression Specimens

Tests and analyses were conducted on a series of geometrically-scaled double edge notch compression specimens to validate the capability of the fiber-kinking model in the NASA continuum damage mechanics code for progressive damage analysis, CompDam. The tests and analyses focused on the fiber-kinking damage mechanism, which is of critical importance for predicting accurately longitudinal compression failure in carbon fiber reinforced polymer laminates. The fiber-kinking model in CompDam was augmented with a new capability to represent a hardening response once a kink band has fully formed, enabling prediction of band broadening. Correlation of the test and analysis results showed agreement in stiffness and strength with less than 10% error. The analysis predicts the same sequence of events leading to ultimate failure that was found in the test. The overall excellent correlation in terms of stiffness, strength, and failure process validates the capability of the model for predicting longitudinal compression failure in notched laminates with cross-ply layups.

Bergan, Andrew C.↗

NASA NTRSDate not supplied

New Developments in the CompDam Fiber Kinking Model for the Interaction of Kinking and Splitting Cracks with Application to Open Hole Compression Specimens

This paper describes two new additions to the NASA fiber kinking model: 1) A failure index for fiber kinking is developed to facilitate interaction between kinking and matrix cracking and 2) A criterion for fiber rupture is introduced to account for fiber breakage before or after fiber kinking. The model formulation is described with the aid of graphical Considered constructions to elucidate the behavior. Verification studies are conducted with single element models to show the behavior of the model in light of the new developments and to evaluate the effect of numerical parameters of the model. The model is used to analyze open hole compression specimens with soft, quasi-isotropic, and hard layups. Analysis results are shown for a conventional continuum damage mechanics model as well as the proposed model to highlight the differences between the two. Comparison with test data highlights the capabilities and remaining gaps in the quantitative prediction of damage evolution in open hole compression. Overall, the results show that the proposed model is capable of representing the kinematics of fiber kinking, and specifically the role of fiber kinking in open hole compression.

Andrew Cole Bergan↗

NASA NTRSDate not supplied

New Developments in the CompDam Fiber Kinking Model for the Interaction

This paper describes two new additions to the CompDam fiber kinking model: 1) a failure index for fiber kinking to facilitate interaction between kinking and matrix cracking and 2) a strain-based criterion for fiber rupture to account for fiber breakage before or after fiber kinking. The model formulation is described with the aid of the graphical Considère construction, which is used to determine the conditions for fiber kinking. Verification studies are conducted with single element models to show the behavior of the model in light of the new developments and to evaluate the effect of numerical parameters of the model. The model is used to analyze open hole compression (OHC) specimens with soft, quasi-isotropic, and hard layups. Analysis results are shown for a conventional continuum damage mechanics model using a trilinear constitutive law for fiber damage and for the proposed model to highlight the differences between the two. Comparison with test data highlights the capabilities and remaining gaps in the quantitative prediction of the damage and failure response. While both models can predict many features of the OHC response, accurate prediction of kinking onset in the OHC specimens remains elusive. The results suggest that it is necessary to predict the combined effects of compression and shear loading as well as the structural effects (e.g., ply thickness, strain gradient effect) accurately to match the experimental observations of fiber kinking onset in the three OHC laminates.

Andrew C. Bergan↗

DOE OSTI2021

Modeling Lithium Diffusion in Battery Cathodes Considering Chemo-Mechanically Induced Damage

This talk will present a 3D, continuum-level damage model for simulating Lithium diffusion within generated Li_{x}Ni_{0.5}Mn_{0.3}Co_{0.2} (NMC 532) secondary cathode particles. The primary motivation of the particle-level model is to inform cathode-particle design and determine charging profiles that reduce cathode fracture. The model considers NMC 532 secondary particles containing an agglomeration of anisotropic, randomly oriented grains. The model predicts that secondary-particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. The model predicts that small secondary-particles with large grains develop significantly less damage than larger secondary particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first high-rate cycles. This chemo-mechanical “damage saturation” effect indicates that initial secondary-particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

A unified finite strain gradient-enhanced micropolar continuum approach for modeling quasi-brittle failure of cohesive-frictional materials

Here, in this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials like concrete, mortar, rock, tough ceramics, energetic materials, but also granular materials like sands or powders in terms of a unified continuum approach is proposed. It is based on a combination of the gradient-enhanced continuum with gradients of internal variables for representing quasi-brittle cracking, and the micropolar continuum, accounting for the deformation of the microstructure. For developing the gradient-enhanced micropolar framework, the set of balance equations and the kinematic relations are derived, and the constitutive relations are established in a general manner. The framework is formulated in a geometrically exact setting, based on the thermodynamically sound theory of hyperelasto-plasticity, and the numerical implementation by means of the finite element method is discussed. For assessing the approach, realizations of this new approach in terms of constitutive models for particular materials are developed. They are applied to numerical benchmark examples, investigating various loading conditions, and the obtained results are validated by means of a comparison with experiments from the literature.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗

DOE OSTI2022

Simulating ice-shelf extent using damage mechanics

Abstract Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2019

A Three-Dimensional Thermodynamically Based Function for the Progressive Failure of Unidirectional Composites

A thermodynamically-based work potential theory for modeling progressive damage for laminated, unidirectional composites assuming plane stress (2D Schaperystheory) is extended to three dimensioanl (3D). An internal state variable, S, is defined to account for the dissipated energy due to damage evolution in the form of microstructure changes in the matrix. With the stationary of the total work potential with respect to the internal state variable, a thermodynamically-consistent set of evolution equationsis derived. The internal state variable is related to the transverse and shear modulithrough microdamage functions. In the first part of this work, coupon specimensare prepared to conduct experiments to characterize the relations between the internalstate variable and the transverse modulus as well as shear modulus. The informationis subsequent used for the prediction of three point bending test. In the second partof this work, objectivity is studied. Three separate methods utilizing different definitions of a reduced internal state variable or of the order of the polynomials are used to represent the matrix micro-damage functions are employed. The three methods are implemented in a user defined subroutine within a commercial finite element method software package. Results from numerical simulations of a center-notched composites panel are compared. The agreement in the maximum stress predictions among the three methods indicates that objectivity, with respect to the functional form of themicrodamage functions, is satisfied.

carbon fiber reinforced polymer composites↗

DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A smeared crack modeling framework accommodating multi-directional fracture at finite strains

A generic smeared crack modeling framework predicated on the deformation gradient decomposition (DGD) approach is proposed for use in dynamic fracture problems at finite strains, accommodating failure along multiple mutually orthogonal fracture planes embedded within an independently defined bulk material model. Within this constitutive framework, the traction equilibrium conditions imposed at each failure surface are used to determine the associated crack displacements stored as internal state variables. In general, the enforcement of interfacial equilibrium entails the implicit solution of a non-linear system of equations within the constitutive update procedure. However, if inertial effects arising due to the relative motion of the fractured material are incorporated within the model, the traction equilibrium conditions are shown to give rise to corresponding dynamic equations of motion governing the time-evolution of the crack opening displacements. For dynamic problems, an explicit time-integration procedure is devised to efficiently update the material state, subject to a set of internal frictionless contact constraints to prevent material inversion. Finally, the efficacy of the proposed modeling framework is investigated through several benchmark dynamic fracture problems run within the explicit finite element code DYNA3D.

42 ENGINEERING↗

DOE OSTI2020

A novel framework for elastoplastic behaviour of anisotropic solids

A general framework for developing nonlinear hyperelastic/plastic constitutive laws for anisotropic solids experiencing large strains and strain rates has been developed. The proposed framework does not rely on the “a priori” known strain energy function, but instead introduces a physical decomposition of the material element into seven physically independent stress bearing mechanisms, each of which has a constitutive law in terms of internal moments described by a scalar function of a single variable. Furthermore, the model has been encoded into a combined finite-discrete element method and tested against static geomechanical test data. The numerical validation experiments show the model can reproduce plastic anisotropic behavior in both biaxial and uniaxial loading of a geomaterial.

58 GEOSCIENCES↗

NASA NTRS2013

Numerical Predictions of Damage and Failure in Carbon Fiber Reinforced Laminates Using a Thermodynamically-Based Work Potential Theory

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Consistent characteristic lengths are introduced into the formulation to govern the evolution of the failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented into a commercial finite element code. The model is verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.

composite materials↗

NASA NTRS1994

A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum based fatigue damage model for unidirectional metal matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress which fully couples the fatigue damage calculations with the finite element deformation solution. An axisymmetric stress analysis was performed on a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. The composite core behavior was represented using Hill's anisotropic continuum based plasticity model, and similarly, the matrix cladding was represented by an isotropic plasticity model. Results are presented in the form of S-N curves and damage distribution plots.

Wilt, Thomas E.↗

NASA NTRS1997

A Coupled/Uncoupled Computational Scheme for Deformation and Fatigue Damage Analysis of Unidirectional Metal-Matrix Composites

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum-based fatigue damage model for unidirectional metal-matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress that fully couples the fatigue damage calculations with the finite element deformation solution. Two applications using the fatigue damage algorithm are presented. First, an axisymmetric stress analysis of a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. Second, a micromechanics analysis of a fiber/matrix unit cell using both the finite element method and the generalized method of cells (GMC). Results are presented in the form of S-N curves and damage distribution plots.

Wilt, Thomas E.↗

NASA NTRSDate not supplied

An Automated Meshing Framework for Progressive Damage Analysis of Fabrics Using CompDam

A meshing and model construction framework for progressive damage analysis of fabric composites is proposed. A mesoscale idealization is used such that the fiber tows are considered homogeneous and transversely isotropic continua, and the matrix is a homogeneous isotropic continuum. By using this idealization, relatively mature damage modeling techniques developed for laminates of unidirectional plies are transferrable to fabrics. Cohesive interface elements and a continuum damage mechanics (CDM) model implemented in the software CompDam are used to account for the key damage modes including cracking at the tow/matrix interface, transverse matrix cracking in the tows, and fiber breakage in the tows. Matrix degradation is accounted for by plasticity. The modeling approach is demonstrated for a 3D orthogonal woven fabric. The main novelty of the proposed model construction framework is in its flexibility resulting from a formulation that is agnostic to the fabric architecture and implementation using mesh based operations. The algorithm does not make any assumptions about the tow sizes, shape, path, or proximity to other tows, thus it is applicable to a broad range of fabric architectures. The matrix region mesh surrounding the tows is constructed from domain boundary and tow surface meshes (i.e. through a series of mesh-based operations) such that the model domain can be arbitrarily shaped.

Andrew Cole Bergan↗