Despite gradual progress over the past decades, the simulation of progressive damage in composite laminates remains a challenging task, in part due to inherent uncertainties of material properties. This paper combines three computational methods - finite element analysis (FEA), machine learning and Markov Chain Monte Carlo - to estimate the probability density of FEA input parameters while accounting for the variation of mechanical properties. First, 15,000 FEA simulations of open-hole tension tests are carried out with randomly varying input parameters by applying continuum damage mechanics material models. This synthetically-generated data is then used to train and validate a neural network consisting of five hidden layers and 32 nodes per layer to develop a highly efficient surrogate model. With this surrogate model and the incorporation of statistical test data from experiments, the application of Markov Chain Monte Carlo algorithms enables Bayesian parameter estimation to learn the probability density of input parameters for the simulation of progressive damage evolution in fibre reinforced composites. This methodology is validated against various open-hole tension test geometries enabling the determination of virtual design allowables.

This study presents a mathematical framework for two-phase magnetostrictive composites composed of oriented and non-oriented magnetostrictive Terfenol-D particles embedded in passive polymer matrices. The phase constitutive behavior of the monolithic Terfenol-D with arbitrary crystal orientations is represented by a recently developed discrete energy averaged model. This unique Terfenol-D constitutive model results in close-form and linear algebraic equations accurately describing the nonlinear magnetostriction and magnetization in magnetostrictive composites subjected to a given loading or magnetic field increment. The effectiveness of this new mathematical framework in capturing magnetostrictive particle size orientation, phase volume fractions, mechanical loading conditions, and magnetic field excitations are validated using a series of experimental data available in literature. Compared to existing models that prevalently addressed particle orientation in composite constitutive level, the model framework in this study directly handles particle orientation in the phase constitutive level, and therefore achieves enhanced efficiency while maintaining comparable accuracy.

With a better balance among good mechanical performance, high freedom of design, and low material and manufacturing cost, chopped carbon fiber chip reinforced sheet molding compound (SMC) composites show great potential in different engineering applications. In this paper, bending fatigue behaviors of SMC composites considering the heterogeneous fiber orientation distributions have been thoroughly investigated utilizing both experimental and computational methods. First, four-point bending fatigue tests are performed with designed SMC composites, and the local modulus is adopted as a metric to represent the local fiber orientation of two opposing sides. Interestingly, SMC composites with and without large discrepancy in local modulus of opposing sides show different fatigue behaviors. Interrupted tests are conducted to explore the bending fatigue failure mechanism, and the damage processes of valid specimens are also closely examined. We find that the fatigue failure of SMC composites under four-point bending is governed by crack propagation instead of crack initiation. Because of this, the heterogeneous local fiber orientations of both sides of the specimen influence fatigue life. The microstructure of the lower side shows a direct influence while that of the upper side also exhibiting influence which becomes more prominent for high cycle fatigue cases. Furthermore, a hybrid micro-macro computational model is proposed to efficiently study the cyclic bending behavior of SMC composites. The region of interest is reconstructed with a modified random sequential absorption algorithm to conserve all the microstructural details including the heterogeneous fiber orientation, while the rest of the regions are modeled as homogenized macro-scale continua. Combined with a framework to capture the progressive fatigue damage under cyclic bending, the bending fatigue behaviors of SMC composites are accurately captured by the hybrid computational model comparing with our experimental analysis.

In this work, multi-scale finite element analyses based on three-dimensional (3D) hybrid macro/micro-scale computational models subjected to various loading conditions are carried out to examine the in-situ effect imposed by the neighboring plies on the failure initiation and propagation of cross-ply laminates. A detailed comparative study on crack suppression mechanisms due to the effect of embedded laminar thickness and adjacent ply orientation is presented. Furthermore, we compare the results of in-situ transverse failure strain and strength between the computational models and analytical predictions. Good agreements are generally observed, indicating the constructed computational models are highly accurate to quantify the in-situ effect. Subsequently, empirical formulas for calculating the in-situ strengths as a function of embedded ply thickness and different ply angle between embedded and adjacent plies are developed, during which several material parameters are obtained using a reverse fitting method. Finally, a new set of failure criteria for - , - , and - accounting for the in-situ strengths are proposed to predict laminated composites failure under multi-axial stress states. This study demonstrates an effective and efficient computational technique towards the accurate prediction of the failure behaviors and strengths of cross-ply laminates by including the in-situ effects.

The mechanical behaviors and damage evolutions of carbon/epoxy woven fabric composites with three different geometries, i.e., one plain weave and two twill weave patterns with different areal densities, are studied under tensile loading. The effects of weave patterns on mechanical properties are investigated by monotonic and cyclic tension tests. Remarkable variations in stress-strain curve, Poisson's ratio, residual strain and strain map exist in the three composites. Crimp ratio is found to be a critical factor to govern the mechanical properties. With smaller crimp ratio, a quasi-linear stress-strain curve with higher elastic modulus and strength is observed. The stress-strain curves of composites with higher crimp ratio contain transition stages with significant tangent modulus degradation. Elastic modulus, strength and damage initiation are all correlated with the crimp ratio linearly regardless of the fabric pattern. Dramatic nonlinear evolution in Poisson's ratio occurs in the composite with higher crimp ratio. Cyclic tension results indicate that the residual strain is a more appropriate damage indicator than the unloading elastic modulus. Microstructure examination shows that damage developments are essentially related to the fabric geometry, and result in various mechanical behaviors. This study provides important insights into the geometry-deformation mechanism-mechanical property relationship of the woven composites.

A method that employs a dual mesh, one for primary variables and another for dual variables, for the numerical analysis of functionally graded beams is presented. The formulation makes use of the traditional finite element interpolation of the primary variables (primal mesh) and the concept of the finite volume method to satisfy the integral form of the governing differential equations on a dual mesh. The method is used to analyze bending of straight, through-thickness functionally graded beams using the Euler-Bernoulli and the Timoshenko beam theories, in which the axial and bending deformations are coupled. Both the displacement and mixed models using the new method are developed accounting for the coupling. Numerical results are presented to illustrate the methodology and a comparison of the generalized displacements and forces/stresses computed with those of the corresponding finite element models. The influence of the coupling stiffness on the deflections is also brought out.

Functionally graded materials have found a wide usage in high temperature applications. The smooth transition from one material to another, in graded materials, may reduce thermal stresses, residual stresses and stress concentration factors as well as utilize properties of both materials. To perform accurate and efficient finite element analysis for heat transfer and transient thermal stress analyses in two-dimensional functionally graded materials, incompatible graded finite elements are developed and verified. User-defined subroutines in ABAQUS are developed to address the gradation of material properties within an element. An emphasis is made on an incompatible graded finite element (QM6) which is accurate and efficient compared to linear four-node (Q4) and quadratic eight-node (Q8) elements. With the help of posteriori error estimation, a critical comparison is made among three types of solid elements. Modified 6-node (QM6) incompatible graded elements provide better accuracy than Q4 elements and take less computational time than Q8 elements, thereby showing QM6 as an optimal element for engineering analysis.

Fiber-reinforced polymer matrix composite materials can fail by kink-band propagation mechanism when subjected to in-plane compressive loading. This mode of failure is especially prevalent in compressive loading of laminates with holes, cut-outs, or impact damage. Most of the successful models for predicting compressive strength of such laminates require "fracture" toughness associated with kink-band propagation under in-plane compression. However, this property is difficult to measure experimentally, limiting the use of such models in design practice. In this paper an inverse method is proposed to estimate the kink-band toughness of the laminate from its open-hole compression strength data, which is an easier property to measure experimentally. Furthermore, a scaling relationship is proposed to estimate kink-band toughness for other laminate configurations of the same material.

This paper presents a study of the impact resistance of honeycomb structure with the purpose to mitigate impact forces. The objective is to aid in the choice of optimal parameters to minimize the thickness of the honeycomb structure while providing adequate protection to prevent injury due to head impact. Studies are presented using explicit finite element analysis representing the case of an unprotected drop of a rigid impactor onto a simulated floor consisting of vinyl composition tile and concrete. Analysis of honeycomb material to reduce resulting accelerations is also presented where parameters such as honeycomb material modulus, wall thickness, cell geometry and structure depth are compared to the unprotected case. A simplified analysis technique using a genetic algorithm is presented to demonstrate the use of this method to select a minimum honeycomb depth to achieve a desired acceleration level at a given level of input energy. It is important to select a minimum material depth in that smaller dimensions lead toward more aesthetic design that increase the likelihood of that the device is used.