No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Stochastic Finite Element Analysis of Composite Body Armor
Abstract
The ballistic impact response of a composite target is an important investigation to assess its reliability for applications to light weight body and vehicle armors. The progressive damage model is developed and implemented in the finite element (FE) code ABAQUS as a user-defined subroutine (VUMAT). A numerical result is obtained using deterministic progressive damage model are validated against existing experimental study in literature. Stochastic finite element analysis (SFEA) is used to study the fiber failure in tension; fiber crushing and in-plane shear failure modes due to ballistic impact. The random variation in material properties and initial velocities are used to determining statistics of stress in the lamina. These are compared to the random strengths in the limit state function and P
f surface is obtained by using Gaussian process response surface method (GPRSM). The comparison of P
f obtained from Monte Carlo simulation (MCS) and GPRSM. MCS computationally 10 times more expensive in comparison to GPRSM. System P
f based on a fault tree analysis is determined to cross and angle ply arrangement in symmetric and anti-symmetric laminates. The P
f of symmetric cross ply laminate arrangement for simply supported composite beams are found to be minimum.
The low velocity impact (LVI) analysis of fiber-reinforced plastic (FRP) plates is a significant study to evaluate the reliability of lightweight structures. This study has wide applications in offshore and naval industries. Safety and reliability assessment as per the international standards is one of the basic objectives of the study. LVI on FRP plates are studied taking the material parameters and loading as random variables. FRP plates are subjected to failure under impact by in-plane loading. To evaluate the safe load carrying capacity and the reliability under impact, dynamic analysis of composite plate subjected to LVI is carried out. Reliability analysis is performed to calculate the stochastic behavior of FRP plates. During impact, the in-plane damage modes such as matrix cracking, fiber failure, and shear cracking are modeled using a failure criterion. The out of plane delamination is modeled using cohesive surfaces. The variability related with the system properties due to the inherent scatter in the geometric and material properties and input loads are modeled in a stochastic fashion. The stochastic finite element analysis (SFEA) is performed to determine the stochastic response of system using Gaussian process response surface method (GPRSM). The safety level qualification is achieved in terms of reliability level targeted.
Safety guarantee and failure calculation of polymer composites of an automobile industry due to impact is important for the connected probabilistic judgment. It is imperative to account scatters related toYoung’smodulus and strength properties and subjected to impact. Possibility of this vulnerability causing a succession of failure
events plays a vital role in reliability analysis. The Young’s modulus and strength properties of polymers typically reveal uncertainties due to their anisotropic characteristics and composite defects. In fact, the likelihood of incident of such a situation is due to huge scatters arising in the structures. Risk analysis of polymer composites
due to impact is determined incorporating variabilities of polymer composites and velocity of the impactor. A distinctive failure fissure initiates and propagates further into the boundary causing delamination between different plies. While individual defects in the lamina are complicated to track, the continuum damage model is used
in the FE code to overcome these problems. The Gaussian process response surface method is currently performed to estimate reliability. A comparative study is also performed for different arrangement of impactor masses and velocities. The sequence of failure events due to dissimilarmodes of failure is adopted to determine the consequences
of failure situation. Frequencies of incidence of precise shock hazards yield the estimated risk due to economic loss.
The problem of foreign object impact on composite structures has received considerable attraction in recent years. One aspect in the study of impact is the determination of force applied by the impactor and the dynamic response of the target. Mathematical models used for predicting the contact force history and the structural response to impact are classified into four categories: spring-mass models, energy balance models, impact on infinite plate models, and complete models. These models vary greatly in complexity and efficiency in obtaining a solution. The formulation of these different types of models is reviewed and a method for selecting an appropriate model. Several examples are presented to illustrate typical types of impact responses.
A 3-D explicit dynamic finite element analysis is performed to determine the contact force and displacement between the impactor and the target. The uncertainties associated with the properties of the composite material, loading condition, and assessment of critical stresses affect the failure limit state to a greater extent. The Gaussian response surface method is used to predict the probability of failure. It is found that the system probability of failure is influenced more by delamination than the failure due to matrix cracking. Shear strength (T12) and Young's modulus (E1 and E3) are the most sensitive parameters to influence the composite plate reliability.
A combined experimental and 3D dynamic nonlinear finite element (FE) approach was adopted to study damage in composite beams subject to ballistic impact using a high-speed gas gun. The time-histories of dynamic strains induced during impact were recorded using strain gages mounted on the front of the composite beam specimen. During ballistic impact tests, the impact velocity was also measured. The commercially available 3D dynamic nonlinear FE code, LS-DYNA, modified with a proposed user-defined nonlinear-orthotropic damage model, was then used to simulate the experimental results. In addition, LS-DYNA with the Chang–Chang linear-orthotropic damage model was also used for comparison. Good agreement between experimental and FE results was found from the comparisons of dynamic strain and damage patterns. Once the proposed nonlinear-orthotropic damage model was verified by experimental results, further FE simulations were conducted to predict the ballistic limit velocity (V50) using either the number of damaged layer approach or a numerically established relation between the projectile impact velocity versus residual velocity or energy similar to the classical Lambert–Jonas equation for metals.
7 pages, 4 figures.-- Issue title: "16th International Conference on Composite Materials (ICCM-16) -- ONR (Office of Naval Research) sessions on Dynamic Failure and Durability" (Kyoto, Japan, Jul 6–11, 2007). In this work, the effect of a biaxial preload in the behaviour of glass/polyester woven-laminate plates subjected to high-velocity transversal impact was studied. For this, an analytic model based on energy considerations that include the presence of an in-plane preload was used. The results of the analytic model for the biaxial preload state were compared with those found for a non-preload plate, the difference between them being minimal for the pre-stressed level reached in the tests (31% of the static UTS). Therefore, numerical simulations were made in order to study the effect of the preload in greater detail; furthermore, experimental tests were conducted, validating the analytic and numerical model. In general, the two methods revealed minimal differences between the values of the ballistic limit and those of the residual velocity. The authors are indebted to the Spanish Comisión Interministerial de Ciencia y Tecnología (Project MAT2001-0735) for the financial support of this work. Publicado
Determining the optimal (lightest, least expensive, etc.) design for an engineered component or system that meets or exceeds a specified level of reliability is a problem of obvious interest across a wide spectrum of engineering fields. Various formulations and methods for solving this reliability-based design optimization problem have been proposed, but they typically involve accepting a tradeoff between accuracy and efficiency in the reliability analysis. This paper investigates the use of the efficient global optimization and efficient global reliability analysis methods to construct surrogate models at both the design optimization and reliability analysis levels to create methods that are more efficient than existing methods without sacrificing accuracy. Several formulations are proposed and compared through a series of test problems.
Composites are used extensively in engineering applications. A constant concern is the effect of foreign object impacts on composite structures because significant damage can occur and yet be undetectable by visual inspection. Such impacts can range from the most ordinary at low velocity - a tool dropped on a product - to the hypervelocity impact of space debris on a spacecraft. This book explains how damage develops during impact, the effect of impact-induced damage on the mechanical behavior of structures, and methods of damage prediction and detection. Numerous examples are included to illustrate these topics. Written for graduate students, as well as researchers and practising engineers working with composite materials, this book presents state-of-the-art knowledge on impact dynamics while requiring only basic understanding of the mechanics of composite materials.
A ply-level material constitutive model for plain-weave composite laminates has been developed to enable computational analyses of progressive damage/failure in the laminates under high velocity ballistic impact conditions. In this model, failure-initiation criteria and damage evolution laws are introduced to account for the major fiber-failure modes (tensile, compressive, punch shear and crush loading). In addition, two matrices related failure modes (in-plane shear and through the thickness delamination) are also accounted for. These types of fiber and matrix failure modes are commonly observed during a ballistic event. The composite-material model has been implemented within LS-DYNA as a user-defined material subroutine and used successfully to predict the damage and ballistic behavior of composite laminates subjected to various ballistic impact conditions. It is hoped that the availability of this material model will help facilitate the development of composite structures with enhanced ballistic survivability.
The reliability analysis of large and complex structural requires approximate techniques in order to reduce computational efforts to an acceptable level. Since it is, from an engineering point of view, desirable to make approximative assumptions at the level of the mechanical rather than the probabilistic modeling, simplifications should be carried out in the space of physically meaningful system- or loading variables.Within the context of this paper, a new adaptive interpolation scheme is suggested which enables fast and accurate representation of the system behavior by a response surface (RS). This response surface approach utilizes elementary statistical information on the basic variables (mean values and standard deviations) to increase the efficiency and accuracy. Thus the RS obtained is independent of the type of distribution or correlations among the basic variables which enables sensitivity studies with respect to these parameters without much computational effort.Subsequently, the response surface is utilized in conjunction with advanced Monte Carlo simulation techniques (importance sampling) to obtain the desired reliability estimates.Numerical examples are carried out in order to show the applicability of the suggested approach to structural systems reliability problems. The proposed method is shown to be superior both in efficiency and accuracy to existing approximate methods, i.e., the first order reliability methods.
Ballistic impact behaviour of typical woven fabric E-glass/epoxy thick composites is presented in this paper. Specifically, energy absorbed by different mechanisms, ballistic limit velocity and contact duration are determined. The studies are carried out using the analytical method presented for the prediction of ballistic impact behaviour of thick composites in our earlier work [Naik NK, Doshi AV. Ballistic impact behaviour of thick composites: analytical formulation. AIAA J 2005;43(7):1525–36.]. The analytical method is based on wave theory and energy balance between the projectile and the target. The inputs required for the analytical method are: diameter, mass and velocity of the projectile; thickness and material properties of the target. Analytical predictions are compared with typical experimental results. A good match between analytical predictions and experimental results is observed. Further, effect of incident ballistic impact velocity on contact duration and residual velocity, effect of projectile diameter and mass on ballistic limit velocity and effect of target thickness on ballistic limit velocity and contact duration are studied. It is observed that shear plugging is the major energy absorbing mechanism.
The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.
Closed-form mechanical models to predict the behaviour of complex structural systems often are unavailable. Although reliability analysis of such systems can be carried out by Monte Carlo simulations, the large number of structural analyses required results in prohibitively high computational costs. By using polynomial approximations of actual limit states in the reliability analysis, the number of analyses required can be minimized. Such approximations are referred to as Response Surfaces. This paper briefly describes the response surface methodology and critically evaluates existing approaches for choosing the experimental points at which the structural analyses must be performed. Methods are investigated to incorporate information on probability distributions of random variables in selecting the experimental points and to ensure that the response surface fits the actual limit state in the region of maximum likelihood. A criterion for reduction in the number of experiments after the first iteration is suggested. Two numerical examples show the application of the approach.
Traditionally multivariate calibration models have been developed using regression based techniques including principal component regression and partial least squares and their non-linear counterparts. This paper proposes the application of Gaussian process regression as an alternative method for the development of a calibration model. By formulating the regression problem in a probabilistic framework, a Gaussian process is derived from the perspective of Bayesian non-parametric regression, prior to describing its implementation using Markov chain Monte Carlo methods. The flexibility of a Gaussian process, in terms of the parameterization of the covariance function, results in its good performance in terms of the development of a calibration model for both linear and non-linear data sets. To handle the high dimensionality of spectral data, principal component analysis is initially performed on the data, followed by the application of Gaussian process regression to the scores of the extracted principal components. In this sense, the proposed method is a non-linear variant of principal component regression. The effectiveness of the Gaussian process approach for the development of a calibration model is demonstrated through its application to two spectroscopic data sets. A statistical hypothesis test procedure, the paired t-test, is used to undertake an empirical comparison of the Gaussian process approach with conventional calibration techniques, and it is concluded that the Gaussian process exhibits enhanced behaviour.
A constitutive model for anisotropic damage is developed to describe the elastic-brittle behavior of fiber-reinforced composites. The main objective of the paper focuses on the relationship between damage of the material and the effective elastic properties for the purpose of stress analysis of structures. A homogenized continuum is adopted for the constitutive theory of anisotropic damage and elasticity. Internal variables are introduced to describe the evolution of the damage state under loading and as a subsequence the degradation of the material stiffness. The corresponding rate-equations are subjected to the laws of thermomechanics. Emphasis is placed on a suitable coupling among the equations for the rates of the damage variables with respect to different damage modes. Evolution equations for the progression of the passive damage variables complete the kinetic equations. Most material parameters are obtained from uniaxial and simple shear tests as demonstrated by the example.
In this work, an extended stochastic formulation of the triangular composite facet shell element TRIC is presented for the case of combined uncertain material (Young’s modulus, Poisson’s ratio) and geometric (thickness) properties. These properties are assumed to be described by uncorrelated two-dimensional homogeneous stochastic fields. The stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with Monte Carlo simulation (MCS) for the computation of the response variability. Useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined.
Up to now, the Young's modulus is mainly dealt within the analysis of response variability. However, since the Poisson's ratio is the other material constant which influences the behavior of structures, the independent evaluation of the effects of this parameter on the response variability is of importance. In this paper, a formulation to determine the response variability in plate structure due to the randomness of Poisson's ratio is given. To filter out the independent contributions of randomness in Poisson's ratio to the response variability, the constitutive matrix has to be decomposed into several sub-matrices. In order to include the Poisson's ratio in the constitutive relation as a non-linear parameter, a polynomial expansion of Poisson's ratio is introduced. To demonstrate the validity of the proposed formulation, an example is chosen and the results are compared with those obtained by means of Monte Carlo simulation. Through the formulation proposed in this paper, it becomes possible for the non-statistical weighted integral stochastic approach to deal with all the uncertain material parameters in its application.
Direct simulation method is used to perform the reliability analysis of mid-plane symmetric laminated plates. Applied uniform lateral pressure loads, material properties, geometric and ultimate strength values of the plates are treated as basic variables, and they are randomly generated in accordance with the corresponding probability distributions using statistical sampling techniques. Generated random values of the basic variables corresponding to the uniform lateral pressure loads, material properties and geometric values of the plates are used in a linear, elastic approach to assess the strength of the plates subjected to uniform pressure loads with both clamped and simply-supported edges. The limit state equations of the plates are developed by using anisotropic plate failure criteria such as maximum stress and Tsai-Hill. Calculated plate strengths and generated random values of the basic variables corresponding to the ultimate strength values of the plates are substituted into the limit state equations to define the failure or survival state of the plates under the given boundary and external loading conditions. Finally, statistical analysis of the results from the limit state equations is performed to estimate the probability of failure of the plates.
Probabilistic behavior of composite plate under ballistic impact
- S D Patel
- S Ahmad
- P Mahajan
Quantification of uncertainty in stochastic analysis of FRP composites
- S Sriramula
- Mk Chyssanthopoulos
Probabilistic failure analysis of composite beams under ballistic impact
- S D Patel
- S Ahmad
- P Mahajan