Computationally-efficient multiscale models for progressive failure and damage analysis of composites

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Development of BEM for ceramic composites

It is evident that for proper micromechanical analysis of ceramic composites, one needs to use a numerical method that is capable of idealizing the individual fibers or individual bundles of fibers embedded within a three-dimensional ceramic matrix. The analysis must be able to account for high stress or temperature gradients from diffusion of stress or temperature from the fiber to the ceramic matrix and allow for interaction between the fibers through the ceramic matrix. The analysis must be sophisticated enough to deal with the failure of fibers described by a series of increasingly sophisticated constitutive models. Finally, the analysis must deal with micromechanical modeling of the composite under nonlinear thermal and dynamic loading. This report details progress made towards the development of a boundary element code designed for the micromechanical studies of an advanced ceramic composite. Additional effort has been made in generalizing the implementation to allow the program to be applicable to real problems in the aerospace industry

Multifield-based modeling of material failure in high performance reinforced cementitious composites

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramatic improvement in their toughness and remedies their deficiencies. It is generally agreed that the fibers contribute primarily to the post-cracking response of the composite by bridging the cracks and providing resistance to crack opening. On the other hand, the multifield theory is a mathematical tool able to describe materials which contain a complex substructure. This substructure is endowed with its own properties and it interacts with the macrostructure and influences drastically its behavior. Under this mathematical framework, materials such as cement composites can be seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics theory, incorporating a new microstructure, is still applicable. A formulation, initially based on the theory of continua with microstructure Capriz, has been developed to model the mechanical behavior of the high perfor-mance fiber cement composites with arbitrarily oriented fibers. This formulation approaches a continuum with microstructure, in which the microstructure takes into account the fiber-matrix interface bond/slip processes, which have been recognized for several authors as the principal mechanism increasing the ductility of the quasi-brittle cement response. In fact, the interfaces between the fiber and the matrix become a limiting factor in improving mechanical properties such as the tensile strength. Particularly, in short fiber composites is desired to have a strong interface to transfer effectively load from the matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress concentration in front of the approaching crack. According to Naaman, in order to develop a better mechanical bond between the fiber and the matrix, the fiber should be modified along its length by roughening its surface or by inducing mechanical defor-mations. Thus, the premise of the model is to take into account this process considering a micro field that represents the slipping fiber-cement displacement. The conjugate generalized stress to the gradient of this micro-field verifies a balance equation and has a physical meaning. This contribution includes the computational modeling aspects of the high fiber rein-forced cement composites (HFRCC) model. To simulate the composite material, a finite element discretization is used to solve the set of equations given by the multifield approach for this particular case. A two field discretization: the standard macroscopic and the micro-scopic displacements, is proposed through a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling both fields is proposed, which provides a more convenient numerical treatment of the discrete equation system. The initiation of failure in HPFRCC at the constitutive level identified as the onset of strain localization depends on the mechanical properties of the all compounds and not only on the matrix ones. As localization criteria is considered the bifurcation analysis in combination with the localized strain injection technique presented by Oliver et al. It consists of injecting a specific localization mode during the localization stage, via mixed finite element formulations, to the path of elements that are going to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed. Model validation was performed using a selected set of experiments that proves the via-bility of this approach. The numerical examples of the proposed formulation illustrated two relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening be-havior after cracking in the HPFRCC and 2) the role that plays the finite element formulation in capturing the displacement localization in the localization stage

Computationally-efficient multiscale models for progressive failure and damage analysis of composites

A class of computationally-efficient tools to undertake progressive failure and damage analysis of composites across scales is presented. The framework is based on a class of refined one-dimensional (1D) theories referred to as the Carrera Unified Formulation (CUF), a generalized hierarchical formulation that generates a class of refined structural theories through variable kinematic description. 1D CUF models can provide accurate 3D-like stress fields at a reduced computational cost, e.g., approximately one to two orders of magnitude of degrees of freedom less as compared to standard 3D brick elements. The effectiveness of 1D CUF models to undertake physically nonlinear simulation is demonstrated through a class of problems with varying constitutive models. The virtual testing platform consists of a variety of computational tools such as failure index evaluations using component-wise modeling approaches (CUF-CW), CUF-CW micromechanics, concurrent multiscale framework, interface, and impact modeling. Failure index evaluation of a class of composite structures underlines the paramount importance of the accurate stress resolutions. Within the micromechanical framework, the Component-Wise approach (CW) is utilized to represent various components of the RVE. The crack band theory is implemented to capture the damage propagation within the constituents of composite materials and the pre-peak nonlinearity within the matrix constituents is modeled using the $J_2$ von-Mises theory. A novel concurrent multiscale framework is developed for nonlinear analysis of fiber-reinforced composites. The two-scale framework consists of a macro-scale model to describe the structural level components, e.g, open-hole specimens, coupons, using CUF-LW models and a sub-scale micro-structural model encompassed with a representative volume element (RVE). The two scales are interfaced through the exchange of strain, stress and stiffness tensors at every integration point in the macro-scale model. Explicit finite element computations at the lower scale are efficiently handled by the CUF-CW micromechanics tool. The macro tangent computation based on perturbation method which leads to meliorated performances. A novel numerical framework to simulate progressive delamination in laminated structures based on component-wise models is presented. A class of higher-order cohesive elements along with a mixed-mode cohesive constitutive law are integrated within the CUF-CW framework to simulate interfacial cohesive mechanics between various components of the structure. A global dissipation energy-based arc -length method to trace the complex equilibrium path exhibited by delamination problem. The capabilities of the framework are further extended through the introduction of contact kinematics to handle impact problems. A combination of the above tools is used to obtain an accurate material response of the structure in the non-linear regime, from the structural level i.e. macro-scale to the material constituent level i.e. the micro-scale, in a computationally efficient manner, providing a suitable virtual testing environment for the progressive damage analysis of composite structures. The accuracy and efficiency of the proposed computational platform are assessed via comparison against the traditional approaches as well as experimental results found in the literature

Multified-based modeling of material failure in high performance reinforced cementitious composites

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramatic improvement in their toughness and remedies their deficiencies. It is generally agreed that the fibers contribute primarily to the post-cracking response of the composite by bridging the cracks and providing resistance to crack opening (Suwaka & Fukuyama 2006). On the other hand, the multifield theory is a mathematical tool able to describe materials which contain a complex substructure (Mariano & Stazi 2005). This substructure is endowed with its own properties and it interacts with the macrostructure and influences drastically its behavior. Under this mathematical framework, materials such as cement composites can be seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics theory, incorporating a new microstructure, is still applicable. A formulation, initially based on the theory of continua with microstructure Capriz (Capriz 1989), has been developed to model the mechanical behavior of the high performance fiber cement composites with arbitrarily oriented fibers. This formulation approaches a continuum with microstructure, in which the microstructure takes into account the fibermatrix interface bond/slip processes, which have been recognized for several authors (Li 2003, Naaman 2007b) as the principal mechanism increasing the ductility of the quasi-brittle cement response. In fact, the interfaces between the fiber and the matrix become a limiting factor in improving mechanical properties such as the tensile strength. Particularly, in short fiber composites is desired to have a strong interface to transfer effectively load from the matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress concentration in front of the approaching crack. According to Naaman (Naaman 2003), in order to develop a better mechanical bond between the fiber and the matrix, the fiber should be modified along its length by roughening its surface or by inducing mechanical deformations. Thus, the premise of the model is to take into account this process considering a microfield that represents the slipping fiber-cement displacement. The conjugate generalized stress to the gradient of this micro-field verifies a balance equation and has a physical meaning. This contribution includes the computational modeling aspects of the high fiber reinforced cement composites (HFRCC) model. To simulate the composite material, a finite element discretization is used to solve the set of equations given by the multifield approach for this particular case. A two field discretization: the standard macroscopic and the microscopic displacements, is proposed through a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling both fields is proposed, which provides a more convenient numerical treatment of the discrete equation system. The initiation of failure in HPFRCC at the constitutive level identified as the onset of strain localization depends on the mechanical properties of the all compounds and not only on the matrix ones. As localization criteria is considered the bifurcation analysis in combination with the localized strain injection technique presented by Oliver et al. (Oliver et al. 2010a). It consists of injecting a specific localization mode during the localization stage, via mixed finite element formulations, to the path of elements that are going to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed. Model validation was performed using a selected set of experiments that proves the viability of this approach. The numerical examples of the proposed formulation illustrated two relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening behavior after cracking in the HPFRCC and 2) the role that plays the finite element formulation in capturing the displacement localization in the localization stage

Numerical modelling based on the multiscale homogenization theory. Application in composite materials and structures

A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents. The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs. Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala

Development of Finite Element Techniques to Simulate Concrete-Filled Fiber-Reinforced Polymer Tube Structures

This dissertation presents the development of finite-element (FE) techniques to simulate the behavior of concrete-filled fiber reinforced polymer (FRP) tubes (CFFTs) in support of more effective structural design and analysis methods for buried composite arch bridges (BCABs) that use CFFT arches as main structural members. The research includes three specific topics to make contributions in different aspects of the investigation of these complex structures. The first topic is the nonlinear three-dimensional FE modeling of steel-free CFFT splices. For model validation, comparisons were made between the model predictions and control beam and spliced beams with and without internal collars tested by others. The modeling was complex due to the need to capture the nonlinear constitutive response of the confined concrete, simulate concrete-FRP interaction, and explicitly incorporate the splice components. Therefore, the numerical analysis utilized the Abaqus/CAE software package with a modified damage concrete plasticity model to idealize the concretefill. The second topic of this research is the development of a computationally efficient structural FE analysis technique for the second-order inelastic behavior of these CFFT arches that includes initial arch curvature. A curved, planar, corotational, flexibility-based (FB), layered frame element is employed to handle geometric and material nonlinearities. An FRP-confined concrete stress-strain model that explicitly considers the effect of dilation of the concrete core and confinement provide by the FRP tube is implemented. Verification of the FB formulation was carried out for elastic-plastic analysis of a beam and elastic post-buckling analysis of a circular arch. The measured flexural responses of different isolated CFFT arches available in the literature were used to verify the proposed model. The model was shown to accurately predict the load-carrying capacity and ductility of the tested CFFT arches. The model captured arch collapse mechanisms arising from FRP rupture and concrete crushing at the apex of the arches. The third topic is an extension of the planar FB model to three-dimensions and incorporation of a soil-spring model to simulate soil-structure interaction using a recently developed horizontal earth pressure model. The model rigorously incorporates the interaction between axial load and bending effects in the arches and permits the examination of out-of-plane stability and arch deformations due to bridge skew. Parametric studies were conducted to assess the effect of abutment skew angle on the behavior of CFFT arch bridge components, an important practical design consideration

Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling

There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed. Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus

eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.Comment: 36 pages, 23 figures, 1 table, 2 algorithms; small changes after review, paper title change