Micromechanics-based Approach Research Articles

Stress Analysis and Life Prediction of a Ceramic Matrix Composite Vane Using a Micromechanics-Based Approach

The results of stress analysis of a ceramic matrix composite (CMC) vane using a physics-based model developed for two-dimensional woven CMCs are presented. The model considers the inherent defects and micromechanical damage in woven CMCs along with time-dependent deformation of the constituents. Predictions include damage state under general load conditions and the global deformation response of the vane. Strain-gage data from burst tests are compared to strain predictions obtained using the model. Results from time-dependent analysis and life prediction of the vane under constant loads and cyclic loads at elevated temperatures are presented. Effect of fatigue frequency on the deformation and long-term life of the vane are also discussed.

Agglomeration effect on biomechanical performance of CNT-reinforced dental implant using micromechanics-based approach

Dental implants have long played an important role in restoring lost teeth, but there are still concerns about their durability and long-term success. Commercial dental implants have traditionally been made of metallic and ceramic materials like titanium and zirconia; however, each kind of material has restrictions regarding osseointegration and mechanical characteristics that differ between native bone and the implant material, limiting the implant's longevity and reliability. To address these concerns, this research explores the use of carbon nanotubes (CNTs) in restorative dentistry, their excellent properties make them an ideal candidate for promoting bone growth around implanted device and ensuring long-lasting success. The objective of this study was to understand how CNT properties when incorporated into the titanium matrix may be able to better adapt to the oral environment taking into consideration the CNT agglomeration effects when designing reinforced nanocomposite materials for dental implant. A mathematical formulation of the micromechanics model was developed and improved to extend its application for the case of CNT-based composite materials for dental implants. A three dimensional (3D) model of bone structure around the osseointegrated dental implant was established considering different compositions of implant material. Finite Element Analysis (FEA) were conducted to assess the aggregation effect of implant incorporating CNTs into the titanium matrix, considering CNTs with both spherical inclusions (CNT clusters), and randomly dispersive ones (CNTs) in the titanium matrix, on osseointegration and bone remodeling around the dental implant and supporting bone system over a period of 48 months. Firstly, the effects of CNT-Ti implantation on time-dependent performance are evaluated in a computational remodeling framework. Then, Von Mises equivalent stresses are investigated to evaluate the stress distributions and micromotions in jaw bones of loaded implant with different composition of prosthetic material. Three agglomeration patterns are considered, particularly without agglomeration (ζ = ξ), partial and complete agglomeration (ζ < ξ, ξ = 1). Further, the influence of CNTs volume fraction variation is taken into account to predict the mechanical response of the bony system after CNT-reinforced dental implantation. It can be inferred that the agglomeration of CNTs reduces the elastic stiffness of the matrix. This is due to the fact that when CNTs are agglomerated, the inter-tube contacts are reduced and the effective stiffness of the matrix is decreased.

Unified analysis for tailorable multi-scale fiber reinforced cementitious composites in tension

Fibers applied to reinforce the cementitious matrix exhibit a wide range of scales, from distributed carbon nanomaterials, chopped short fibers to continuous fibrous reinforcements. When a cementitious matrix is jointly toughened by reinforcing fibers at multiple scales, Multi-Scale Fiber Reinforced Cementitious Composite (MSFRC) tailored built on the micromechanics-based approach and bond-slip mechanism is proposed in this study. The composite actions of MSFRC, namely, tension stiffening, ductility enhancing and synergetic effects, are explained within a universal perspective. In addition, a 1-D numerical model using spring elements is developed to simulate the tensile behavior of MSFRC based on the crack band theory, fiber-bridging model and Monte Carlo simulation. The scales, types and contents of reinforcing fibers, interface behavior and stochastic nature can be considered in the model. Finally, it is found that the predicted mechanical response and crack evolution process match well with the experimental results obtained from literatures.

Stochastic modelling of continuous glass-fibre reinforced plastics–considering material uncertainty in microscale simulations

This paper presents a probabilistic micromechanics-based approach to simulate the influence of scatter sources in composite materials as an alternative to deterministic approaches. Focus is given to the effect of microscopic and macroscopic voids, material inhomogeneity induced by manufacturing processes and stochastic fibre patterns on the mechanical properties of continuous glass-fibre reinforced polymer components. Various periodic unit cells of neat resin and embedded fibre clusters are generated with random distributions of the abovementioned scatter sources, while the voids are represented by degrading locally the pristine properties in an element-wise manner. Subsequently, the models are mechanically loaded under transverse tension as an exemplary case and the resulting responses are correlated with the stochastic inputs. In particular, the relative influence of pore size, porosity and fibre/resin interface strength on the transverse tension modulus and strength of unidirectional composites are numerically investigated. The present approach is suggested as a computational efficient but reliable alternative to geometrical representations of imperfection in composite materials.

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee C0-continuity of the solution at inter-element boundaries, and enforces the required C1 regularity with the aid of additional variational and interior penalty terms in the weak form. The phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

Steel Structures Research Update: Seismic Performance of Nonorthogonal Special Moment Frame Beam-to-Column Connections

Ongoing research on the seismic behavior of nonorthogonal special moment frame beam-to-column connections is highlighted. Featured is a comprehensive experimental and computational study under way at the University of Arkansas and led by Dr. Gary Prinz, Associate Professor in Structural Engineering. The research team includes PhD students Hossein Kashefizadeh and Damaso Dominguez. Dr. Prinz’s research interests include mechanics and simulation of ductile fracture, seismic design solutions for steel structures, and computer simulation of structures under dynamic loading. He received a National Science Foundation Faculty Early Career Development (CAREER) award to investigate a new micromechanics-based approach to ductile fracture simulation in additively manufactured steels for improved seismic structural fuse design. Dr. Prinz has also been awarded AISC’s Milek Fellowship. The four-year Milek Fellowship is supporting this research on the seismic performance of skewed special moment frame (SMF) connections. The research team is partway through the third year of the four-year study. Selected results from the computational parametric study are highlighted along with a preview of the experimental investigation.

Multiscale analysis of elastic waves in soft materials: From molecular chain networks to fiber composites

We provide a multiscale analysis of elastic waves in soft microstructured materials including the underlying molecular chain network mechanisms and micromechanics of hyperelastic fiber composites. First, we examine the interplay between the crosslinked and entangled polymer chains and elastic wave characteristics in finitely deformed materials. Next, we study the shear wave propagation in a class of heterogeneous hyperelastic composites. In particular, we consider the transversely isotropic fiber composites with phases characterized by the stiffening behavior stemming from the non-Gaussian statistics of polymer chains. By employing a micromechanics-based approach, we derive explicit expressions for phase velocities in terms of material properties and volume fraction of the phases. Our results indicate the significant influence of the variety of length-scales mechanisms on the elastic wave characteristics. We provide examples to illustrate the influence of the mechanisms under different loading conditions, wave propagation directionality, and material microstructure parameters.

Ductile fracture of high strength steels with morphological anisotropy, Part II: Nonlocal micromechanics-based modeling

The ductile fracture behavior of a high strength steel is addressed in this two-part study using a micromechanics-based approach. The objective of Part II is to propose, identify, and validate a numerical model of ductile fracture based on the Gurson–Tvergaard–Needleman model. This model is enhanced by the Nahshon–Hutchinson shear modification in combination with a generalization of the Thomason coalescence criterion within a fully nonlocal form and relying on a damage-to-crack transition technique. The material model involves parameters of different natures either related to the micro-mechanics of porous materials or to semi-empirical formalisms. The void nucleation model and elastoplastic behavior have been developed and identified in Part I. The other parameters are identified in this part using inverse modeling based on both the numerical results of void cell simulations and the experimental measurements. The model is shown to adequately predict the effect of stress triaxiality and Lode parameter on the fracture strain as well as the fracture anisotropy. While the cup-cone and slant fracture paths in the round bars and in the plane strain specimens, respectively, cannot be captured using the pure continuum approach, the damage-to-crack transition framework reproduces these experimental observations.

Ductile fracture of high strength steels with morphological anisotropy, Part I: Characterization, testing, and void nucleation law

The ductile fracture behavior of a high strength steel is investigated using a micromechanics-based approach with the objective to build a predictive framework for the fracture strain and crack propagation under different loading conditions. Part I of this study describes the experimental results and the determination of the elastoplastic behavior and damage nucleation under different stress triaxiality and Lode parameter values. The damage mechanism starts early void nucleation from elongated inclusions, either by particle cracking under loading oriented along the major axis, or by matrix decohesion when the main loading is transverse. Void nucleation is followed by plastic growth and coalescence. The long inclusion axis is preferentially aligned in one direction leading to significant failure anisotropy with the fracture strain in the transverse direction being almost 50% lower compared to the longitudinal one, even though the plastic behavior is isotropic. The experimental data are first used to calibrate the elastoplastic model. An enhanced anisotropic nucleation model is then developed and integrated into the Gurson–Tvergaard–Needleman scheme. The parameters identification of the anisotropic nucleation model is finally performed and validated towards the experimental results. All these elements are subsequently used in Part II to simulate the full failure behavior of all testing specimens in the entire spectrum of stress states, from nucleation to final failure.

Relationship between element-level and contact-level parameters of micromechanical and upscaled plasticity models for granular soils

The models for stress–strain behavior of granular soils can be generally categorized into two approaches: the conventional plasticity approach and the micromechanics-based approach. In this work, we upscale a micromechanical model to a commonly used isotropic hardening plasticity model by assuming the “same” constitutive laws at different scales. The mathematically derived relationships between element-level and contact-level parameters are presented based on the condition that the two models would predict the same mechanical response, and a parameter calibration procedure is proposed. A comparative study is then conducted to investigate the differences of the predicted element behaviors arisen from the two models.

Investigation on frequency-dependent hysteresis loops of ferroelectric materials

In this paper, a frequency-dependent theory is developed to study the polarization hysteresis loops of ferroelectric materials. From experimental observations, the polarization hysteresis loops strongly depend on the electric field loading frequency. When the frequency increases both remanent polarization and coercive electric field are increasing, while the dielectric constant remains unchanged at the given range of the frequency. An exponential function is introduced to express such frequency-dependent changes of the remanent polarization and the coercive field. Then a micromechanics-based approach can be applied to study hysteresis loops of ferroelectrics. To verify the developed theory, we first compare the results between the theoretical calculations and experimental data of PZT. Then we applied the model to study the frequency effects on hysteresis loops of a complex ceramic BaMn3Ti4O14.25 (BMT-134) under the electric field.

Investigation of Hydraulic Fracturing Behavior in Heterogeneous Laminated Rock Using a Micromechanics-Based Numerical Approach

Understanding hydraulic fracturing mechanisms in heterogeneous laminated rocks is important for designing and optimizing well production, as well as for predicting shale gas production. In this study, a micromechanics-based numerical approach was used to understand the physical processes and underlying mechanisms of fracking for different strata orientations, in-situ stresses, rock strengths, and injection parameters. The numerical experiments revealed a very strong influence of the pre-existing weakness planes on fracking. Geological models for rock without weakness planes and laminated rock behave very differently. Most simulated fractures in the rock without weakness planes were caused by tensile failure of the rock matrix. In an intact rock model, although a radial damage zone was generated around the injection hole, most of the small cracks were isolated, resulting in poor connectivity of the fracture network. For rock models with pre-existing weakness planes, tension and shear failure of these structural planes formed an oval-shaped network. The network was symmetrically developed around the injection well because the strength of the pre-existing weakness planes is generally lower than the rock matrix. The research shows that the angular relations between the orientation of the structural planes and the maximum horizontal stress, as well as the in-situ stress ratios, have significant effects on the morphology and extent of the networks. The strength of the pre-existing weakness planes, their spacing, and the injection rate can dramatically influence the effectiveness of hydraulic fracturing treatments.

Micromechanics-based approach for the effective estimation of the elastic properties of fiber-reinforced polymer matrix composite

In this paper, we proposed a revised Mori–Tanaka model for the effective estimation of the elastic properties at lower fiber volume fraction. A review of some notable micromechanics-based models with the theories proposed by Voigt and Reuss, Hashin–Shtrikman model, Mori–Tanaka method and dilute dispersion scheme is carried out, and a critique is presented focusing on the limitations of these models. Finite Element (FE) simulations are performed using Representative Volume Element (RVE) technique to rationalize the analytical results. Our results revealed that revised Mori–Tanaka estimates and FE predictions are in agreement. Elastic properties of the test material are dependent on size of RVE suggesting the effective elastic modulus evaluated using RVE forms the lower bounds of true effective values. However, we still believe that there is room for the debate for evaluating the elastic properties of these composites at larger volume fractions with the inclusion of Eshelby’s tensor in Mori–Tanaka scheme. Thus the efficacy of micromechanics-based models for the effective estimation of elastic properties of polymer matrix composites is highlighted. Our findings may provide new significant insights of the effective estimation of elastic properties of PMC using micromechanics-based approach.

Effects of crack inclination on shear failure of brittle geomaterials under compression

A micromechanics-based approach is proposed to predict the shear failure of brittle rocks under compression. Formulation of this approach is based on an improved wing microcrack model, the Mohr-Coulomb failure criterion, and a micro-macro damage model. The improved wing microcrack model considers the effects of crack inclination angle on mechanical behaviors of rocks. The micro-macro damage model describes the relation between crack growth and axial strain. Furthermore, comparing experimental and theoretical relations between crack initiation stress and confining pressure, model parameters (i.e., μ, a, β, and φ) hardly measured by test are solved. Effects of crack inclination angle, crack size, and friction coefficient on stress-strain relation, compressive strength, internal friction angle, cohesion, shear failure plane angle, and shear strength are discussed in details. A most disadvantaged crack angle is found, which is corresponding to the smallest compressive strength, cohesion, internal friction angle, and shear strength of rocks. Rationality of the theoretical results is verified by the published experimental results. This approach provides a theoretical prediction for effects of microcrack geometry on macroscopic shear properties in brittle rocks under compression.

Probabilistic first ply failure prediction of composite laminates using a multi-scale M-SaF and Bayesian inference approach

This paper presents a probabilistic first ply failure analysis of composite laminates using a high-fidelity multi-scale approach called M-SaF (Micromechanics-based approach for Static Failure). To this end, square and hexagonal representative unit cells of composites are developed to calculate constituent stresses with the help of a bridging matrix between macro and micro stresses referred to as the stress amplification factor matrix. Separate failure criteria are applied to each of the constituents (fiber, matrix, and interface) in order to calculate the damage state. The successful implementation of M-SaF requires strength properties of the constituents which are the most difficult and expensive to characterize experimentally, limiting the use of M-SaF in the early design stages of a structure. This obstacle is overcome by integrating a Bayesian inference approach with M-SaF. An academic sample problem of a cantilever beam is used to first demonstrate the calibration procedure. Bayesian inference calibrates the M-SaF first ply failure model parameters as posterior distributions from the prior probability density functions drawn from lamina test data. The posterior statistics were then used to calculate probabilistic first ply failure for a range of different laminates.

Multilevel assessment method for reliable design of composite structures

ABSTRACTThis work aims at demonstrating the interest of a new methodology for the design and optimization of composite materials and structures. Coupling reliability methods and homogenization techniques allow the consideration of probabilistic design variables at different scales. The main advantage of such an original micromechanics-based approach is to extend the scope of solutions for engineering composite materials to reach or to respect a given reliability level. This approach is illustrated on a civil engineering case including reinforced fiber composites. Modifications of microstructural components properties, manufacturing process, and geometry are investigated to provide new alternatives for design and guidelines for quality control.

Micromechanical characterizing elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites

In this work, elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites are investigated using a 3-dimensional micromechanics-based approach. The main advantage of the proposed micromechanical model is its ability to give closed-form formulation for predicting the effective properties of nanocomposites. In the micromechanical modeling, the interphase formed due to non-boned van der Waals interaction between the continuous CNT and polymer matrix is considered through employing an individual representative volume element. The validity of the model is examined by comparing its results with other theoretical approaches and experimental data available in the literature. The effects of various types of CNTs arrangement in the matrix, i.e. uniform distribution and different functionally graded distributions on the elastic, thermoelastic and viscoelastic properties of polymer nanocomposites are investigated in detail. Furthermore, random arrangement of CNTs in the matrix is modelled. The influences of CNT/polymer matrix interphase and CNT volume fraction on the effective properties of nanocomposites are also studied. Finally, the viscoelastic response of nanocomposites under multiaxial loading is extracted and interpreted.

Nonlinear finite element analysis of fibre-reinforced polymer/concrete joints

The objective of this research work is to simulate the interfacial shear response of fibre-reinforced polymer/concrete joints using a micromechanics-based concrete approach. The M4 version of the microplane concrete theory is coded in FORTRAN and implemented as a parallel user-defined subroutine into the commercial finite element software package ADINA. This article first focuses on three-dimensional nonlinear micromechanics-based finite element analyses. Then, validations are carried out using experimental results of 40 fibre-reinforced polymer/concrete joints. The objective is to assess the accuracy of the microplane approach to represent the interfacial shear behaviour of the fibre-reinforced polymer/concrete joints as an alternative to implementing interface elements. At the end of this article, numerical comparisons are presented between the predictions using a phenomenological concrete constitutive law adopted in the software package (with a smeared crack model) and the micromechanics-based analysis (microplane theory) to simulate the concrete behaviour.

Micromechanics-based progressive failure analysis of carbon fiber/epoxy composite vessel under combined internal pressure and thermomechanical loading

A progressive failure analysis algorithm based on micromechanics of failure (MMF) theory and material property degradation method (MPDM) is developed, wherein the MMF is used to predict the failure initiation at constituent level and the MPDM is employed to account for the post failure behavior of the damaged materials. The progress of damage is controlled by a linear damage evolution law, which is based on the fracture energy dissipating during the process. This micromechanics-based approach is implemented by a user-material subroutine (UMAT) in ABAQUS, which is sufficiently general to predict the ultimate strength and complex failure behaviors of the composite vessel subject to both high pressure and thermal loading. In addition, the predictions of the model are also compared with those by experiment and traditional finite element analysis.

Anisotropic unilateral damage with initial orthotropy: A micromechanics-based approach

A micromechanics-based damage model able to describe the brittle response of initially anisotropic materials is presented. A special emphasis is put on the account of damage-induced anisotropy and unilateral behaviour related to microcracks closure effects. These both features clearly influence the inelastic deformation of microcracked materials and lead to even more complex consequences in the context of initial anisotropy. The aim of this work is then to derive a new strain-based formulation which allows representing the related interactions between all these phenomena. This is achieved through a recent two-dimensional energy-based micromechanical analysis that accounts for the fully anisotropic multilinear response of orthotropic materials weakened by arbitrarily oriented microcracks. On the other hand, the thermodynamics framework gives a standard procedure for the development of the damage evolution law. Throughout the paper, attention is put on the mathematical and thermodynamical consistency of the model to avoid difficulties usually associated to the simultaneous description of damage-induced anisotropy and unilateral effects. In addition to elastic constants, the model requires the identification of only two parameters related to damage evolution. The model has been implemented within the commercial finite-element code ABAQUS, and various numerical simulations are presented to illustrate its capabilities. Especially, evolution of the material symmetry and influence of opening-closure states of microcracks on the damage process are illustrated in the case of brittle matrix composites subjected to different loading cases (axis and off-axis loads, tension and compression, tension followed by compression).