Micromechanical Framework Research Articles

A viscoelastic constitutive model for shape memory polymer composites: Micromechanical modeling, numerical implementation and application in 4D printing

In this work, a novel micromechanics-based thermo-viscoelastic constitutive model for shape memory polymer composites (SMPCs) is proposed and applied to four-dimensional (4D) printed SMPCs. The multi-branch constitutive model is used to simulate the time- and temperature-dependent mechanical behavior of the shape memory polymer matrix. According to the elastic–viscoelastic correspondence principle, the equivalent viscoelastic stiffness tensor of the composite is obtained in the micromechanics framework of energy-based effective strain theory and the Mori-Tanaka homogenization scheme, in which a two-parameter interfacial damage model is adopted to consider the displacement discontinuity and traction continuity conditions at the interface between the inclusion and the matrix. The numerical integration scheme for the three-dimensional (3D) viscoelastic constitutive model of SMPCs is presented, and the finite element application is implemented by the user material subroutine UMAT of ABAQUS. After identifying the model parameters with experimental data, the tensile stress-strain curves and stress relaxation phenomena of 4D printed unidirectional SMPCs are successfully described by theoretical simulations. Besides, theoretical simulations also adequately predict the shape memory behavior of 4D printed composites and complex members.

A continuum damage model for fatigue life prediction of 2.5D woven composites

Abstract A new model based on continuum damage mechanics is proposed to predict the fatigue life of 2.5D woven composites. First, a full-cell model reflecting the real microstructure of 2.5D woven composites is established in ANSYS. Subsequently, three independent damage variables are defined in the framework of the composite micromechanics to establish the component constitutive relations associated with damage. The strain energy density release rate and damage evolution equations for the matrix, fiber in yarns, and matrix in yarns are derived. Finally, the proposed model is implemented for fatigue life prediction and damage evolution analysis of 2.5D woven composites at 20 and 180°C. The results show that the numerical results are in good agreement with the relevant experimental results.

Microstructural integrity characterization of cement-based construction materials

In this paper, a new micromechanical framework to characterize the microstructural integrity and predict the effective properties of multi-phase particulate composites is presented. Within the framework, a new scalar micromechanical parameter is identified and used to derive new expressions for the effective elastic properties of particulate composites using the mean-field homogenization technique. The derived equations are then generalized for composites with multiple phase constituents. The generality of the proposed framework is demonstrated by combining the derived equations with the existing homogenization techniques such as the Mori–Tanaka method and the Generalized Maxwell’s Approach (GMA). The results show that the theory delivers consistent estimates of the effective properties of two-phase elastic composite materials. The new scalar micromechanical parameter is also used to characterize the microstructural integrity of both asphalt mixtures and Portland cement concrete. The results show that the new scalar micromechanical parameter correlates well with multiple key fundamental properties of asphalt concrete mixture, including the creep rate, the fracture energy density, the endurance limit, and the damage rate parameters. The results also show that the new micromechanical framework can be used to accurately predict the effective modulus properties of Portland cement concrete mixtures.

Hydraulic transport properties of unsaturated cementitious composites with spheroidal aggregates

Understanding of the coupled effects of aggregates and interfacial transition zones (ITZs) on hydraulic transport properties of unsaturated cementitious composites (CC) is of great importance for the design of CC durability. In this work, a comprehensive micromechanical theoretical framework is devised for the accurate predictions of the effective hydraulic conductivity, diffusivity and sorptivity of saturated and unsaturated CC, in which CC are regarded as a three-phase structure consisting of spheroidal aggregates with a certain gradation, their surrounding permeable ITZs with a specific thickness, and homogeneous cement paste at a mesoscopic level. Comparisons against experimental, numerical and analytical data suggest that the proposed framework is a reliable means to predict these effective hydraulic transport properties. The micromechanical framework can be regarded as a generic model that suits for predicting other hydraulic-like transport properties of multiphase composites not limited to cementitious composites involving spheroidal inhomogeneities and their surrounding interphase. This framework sheds light on the coupled effects of properties of aggregates (shape, gradation, mean size, and volume fraction) and ITZ (volume fraction, thickness, and hydraulic properties) on the effective hydraulic transport properties of CC. The results elucidate the complex relationship of components-structures-transport properties, which in turn can provide insights for understanding degradation of concrete in practical applications.

An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

Concurrent material and structure optimization of multiphase hierarchical systems within a continuum micromechanics framework

We present a concurrent material and structure optimization framework for multiphase hierarchical systems that relies on homogenization estimates based on continuum micromechanics to account for material behavior across many different length scales. We show that the analytical nature of these estimates enables material optimization via a series of inexpensive “discretization-free” constraint optimization problems whose computational cost is independent of the number of hierarchical scales involved. To illustrate the strength of this unique property, we define new benchmark tests with several material scales that for the first time become computationally feasible via our framework. We also outline its potential in engineering applications by reproducing self-optimizing mechanisms in the natural hierarchical system of bamboo culm tissue.

How stress triaxiality affects cavitation damage in high-density polyethylene: Experiments and constitutive modeling

The aim of this article is to investigate how the stress triaxiality affects the plastic deformation behavior of high-density polyethylene using an approach combining experiments and micromechanics-based modeling. The stress-strain behavior along with the cavitation damage accumulation are experimentally quantified under well-controlled transversal response of hourglass-shaped tensile specimens with different curvature radii in order to set different triaxial stress states in the median cross-section. A constitutive elastic-plastic-damage representation is then presented within a continuum-based micromechanical framework. The model, constrained by the same boundary conditions as the experimental tests, is used to examine the stress triaxiality effects on the separate and synergistic effects of plasticity and cavitation damage micromechanisms that govern the macro-response.

Statistical micromechanical damage model for SH-SFRC under tensile load considering the interfacial slip-softening and matrix spalling effects

Strain hardening behavior can be observed in steel fiber reinforced concretes under tensile loads. In this paper, a statistical micromechanical damage framework is presented for the strain hardening steel fiber reinforced concrete (SH-SFRC) considering the interfacial slip-softening and matrix spalling effects. With a linear slip-softening interface law, an analytical model is developed for the single steel fiber pullout behavior. The crack bridging effects are reached by averaging the contribution of the fibers with different inclined angles. Afterwards, the traditional snubbing factor is modified by considering the fiber snubbing and the matrix spalling effects. By adopting the Weibull distribution, a statistical micromechanical damage model is established with the fracture mechanics based cracking criteria and the stress transfer distance. The comparison with the experimental results demonstrates that the proposed framework is capable of reproducing the SH-SFRC’s uniaxial tensile behavior well. Moreover, the impact of the interfacial slip-softening and matrix spalling effects are further discussed with the presented framework.

A new hybrid homogenization theory for periodic composites with random fiber distributions

A new homogenization theory is constructed for unidirectional composites with periodic domains containing random fiber distributions. Periodic domains are partitioned into subdomains comprised of single fibers embedded in matrix phase. The subdomain displacement field solutions combine finite-volume and locally-exact elasticity approaches. Inclusions are regarded as meshfree components whose displacement fields are represented by discrete Fourier transforms that satisfy exactly Navier’s equations. In contrast, the matrix is discretized into subvolumes and handled within the finite-volume micromechanics framework. Novel use of traction and displacement continuity conditions at the inclusion/matrix interface seamlessly connect inclusion and matrix phases. Subdomains’ assembly enforces traction, displacement continuity and periodicity conditions in a surface-average sense. Quadratic convergence of stress fields with decreasing matrix discretization relative to exact elasticity solution is obtained, yielding accurate homogenized moduli with relatively coarse matrix meshes. Fourfold and greater reductions in execution times relative to the finite-volume micromechanics justify the new theory’s construction. The proposed theory facilitates accurate and efficient studies of the rarely reported effect of random fiber distributions on homogenized moduli and local stress fields as a function of inclusion content and number of microstructural realizations. We illustrate this by computing probability distributions of homogenized moduli for up to 60,000 microstructural realizations of multi-inclusion periodic domains that may be used in machine-learning algorithms.

A Micromechanics Analysis for Creep of Powder Metallurgy Aluminum Alloys with Continuous Precipitation

In this study, a micromechanics framework considering both interface diffusion and matrix creep is proposed to analyze the creep behavior of PM alloys. Based on the mean-field micromechanics theory, the creep strain rate induced by interface diffusion in the particulate composite under uniaxial loading is derived. The creep strain is introduced as an eigenstrain into the inclusion, whose rate is expressed in the tensor-form with three non-zero components and naturally satisfies incompressibility. An incremental analysis procedure is employed to model the creep behavior of particulate composites. The aluminum alloy is treated as a composite material, with precipitated particles as the reinforcements. We then adopt the proposed micromechanics approach to study the creep behavior of the powder metallurgy aluminum alloy with continuous precipitation, accounting for both the creep of matrix and the creep induced by interfacial diffusion along the precipitate/matrix interface. The predicted creep curves agree well with experimental results and the explanation for the creep phenomenon has never been proposed before. We have also derived the minimum or steady-state creep rate of the alloy by the micromechanics approach, which turns out to be similar to the expression of improved power-law creep with a threshold stress.

Investigation of Instabilities in Granular Media and Their Numerical Simulation

The inception of instabilities in sand across different “length-scales,” viz., continuum, discrete, and laboratory element tests, has been highlighted in this study. With instability onset, the material behavior no longer remains “single element” in the sense of continuum mechanics, and due care is required while calibrating different constitutive relationships for use in various numerical simulations. A laboratory “element” test can instead be viewed as a boundary value problem at the instability onset. The post-instability response of a soil specimen represents the “system-response” with the evolution of inhomogeneities being primarily influenced by the boundary conditions among various other factors. Instability onset in drained and undrained biaxial tests has been explored by adopting the bifurcation framework with the aid of a generalized nonassociative elastoplastic material model. For the locally drained globally undrained scenario within a continuum numerical framework, instability onset is found to be influenced by the refinement of mesh discretization. Signatures of rate-dependent localized behavior of sand specimens are also commented on from numerical simulations of drained biaxial tests. To address the “pathological mesh dependence” of classical continuum modeling, we resort to a micromechanical discrete granular framework that considers the actual particle morphology. The numerical predictions match reasonably well with the flexible boundary plane strain experiments. The inherent grain fabric arrangement is found to be the triggering mechanism behind the localized strain accumulation at multiple zones. The influence of loading boundary conditions and various signatures of local nonuniformities is also explored with the aid of image analysis in plane strain and triaxial tests.

A micromechanical model of elastic-damage properties of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

Innovative pothole patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD, C10H12), have been experimentally proven to be effective in repairing cracked asphalt pavements and can significantly enhance their durability and service life. In this paper, a three-dimensional micromechanical framework is proposed based on the micromechanics and continuum damage mechanics to predict the effective elastic-damage behaviors of this innovative pothole patching material under the splitting tension test (ASTM D6931). In this micromechanical model, irregular coarse aggregates are approximated and simulated by randomly allocated multi-layer-coated spherical particles in certain representative sizes. Fine aggregates, asphalt binder (PG64-10), cured DCPD (p-DCPD), and air voids are formulated into an isotropic elastic asphalt mastic matrix based on the multilevel homogenization approach. The theoretical micromechanical elastic-damage predictions are then systemically compared with properly designed laboratory experiments as well as three-dimensional finite elements numerical simulations for the innovative pothole patching materials.

A tangent finite-volume direct averaging micromechanics framework for elastoplastic porous materials: Theory and validation

In this communication, we present a reformulated finite-volume direct averaging micromechanics (FVDAM) framework for periodic multiphase materials with elastic-plastic phases. The original elastoplastic version is formulated using the secant stiffness matrix approach, which requires a computationally intensive solution procedure of the governing differential equations. For the first time, the reformulation makes use of the tangent plasticity matrix approach that incorporates linearities to the unit cell boundary value problem. The tangential FVDAM theory is implemented using a quasi-Newton-Raphson strategy that quantifies errors in the evaluation of surface-averaged stresses due to the linearization, hence allowing large load increments. The tangential formulation is vigorously and fully assessed vis-à-vis the secant approach for porous unit cells on several aspects, including the convergence of the algorithmic implementation with mesh and step sizes, solution accuracy, and computation times. The reformulation simplifies the solution to the governing differential equations relative to its predecessor, albeit at the cost of more computational efforts for the reforming and reinverting of the global tangent stiffness matrix (or the so-called tangent operator). Additionally, advantages of the FVDAM theory relative to the classical finite-element homogenization are highlighted. The tangent FVDAM is employed to demonstrate the plasticity-triggered architectural effects in the response of periodic porous materials under different loading modes. The common mechanisms responsible for differences in the elastic-plastic response are attributed to the effective and hydrostatic stress alteration in the matrix phase. The current work paves the ground for the incorporation of FVDAM into readily-available commercial computational tools through the user material subroutines that are based on tangent stiffness approaches, which will produce a paradigm shift for FVDAM to solve the challenging multiscale structural problem.

Physical and mechanical degradation behaviour of semi-crystalline PLLA for bioresorbable stent applications

This study presents a systematic evaluation of the physical, thermal and mechanical performance of medical-grade semi-crystalline PLLA undergoing thermally-accelerated degradation. Samples were immersed in phosphate-buffered saline solution at 50 °C for 112 days and mass loss, molecular weight, thermal properties, degree of crystallinity, FTIR and Raman spectra, tensile elastic modulus, yield stress and failure stress/strain were evaluated at consecutive time points. Samples showed a consistent reduction in molecular weight and melting temperature, a consistent increase in percent crystallinity and limited changes in glass transition temperature and mass loss. At day 49, a drastic reduction in tensile failure strain was observed, despite the fact that elastic modulus, yield and tensile strength of samples were maintained. Brittleness increase was followed by rapid increase in degradation rate. Beyond day 70, samples became too brittle to test indicating substantial deterioration of their load-bearing capacity. This study also presents a computational micromechanics framework that demonstrates that the elastic modulus of a semi-crystalline polymer undergoing degradation can be maintained, despite a reducing molecular weight through compensatory increases in percent crystallinity. This study presents novel insight into the relationship between physical properties and mechanical performance of medical-grade PLLA during degradation and could have important implications for design and development of bioresorbable stents for vascular applications.

Long-Term Strength of Porous Geomaterials by a Micromechanical Model considering Alternate Wetting and Drying Condition

This study is devoted to determining the long-term strength of porous geomaterials under alternate wetting and drying condition by statical shakedown analysis. In the framework of micromechanics of porous materials, Gurson’s hollow sphere model with Drucker-Prager solid matrix is adopted as the representative volume element. The effects of alternate wetting and drying are considered as variable water pressure imposed on the inner boundary surface of the unit cell. The cyclic responses are separated as a pure hydrostatic part under compressive/tensive loads and an additional deviatoric part to capture shear effects. The reduction of the long-term strength due to inner water pressure is observed by the illustration of obtained macroscopic criteria with respect to various load parameters. In addition, the accuracy of the analytical solution is also verified by comparing to the results of FEM-based step-by-step computations.

A micromechanical framework of arterial tissue growth in the context of medial calcification

Growth and remodelling (G&R) of biological tissues are mechanisms which respectively involve a change in mass and material properties. In particular, arterial media calcification (AMC) is a patholo...

Multiscale damage plasticity modeling and inverse characterization for particulate composites

In this paper, we propose a multiscale damage plasticity model for particulate composites within an incremental Mori-Tanaka (MT) micromechanics framework and present numerical and experimental verification. J2 plasticity and Lemaitre-Chaboche ductile damage models account for damage in the matrix and a linear spring model accounts for interface damage between the matrix and inclusions. Local and global strain concentration tensors are iteratively updated by minimizing errors caused by the constantly changing algorithmic tangent operator of the ductile damage matrix. Finite element (FE)-based direct numerical simulation (DNS) models are used as baseline models for verification. Properties of the ductile damage matrix and interface damage variables are inversely identified from experimental data. FE-MT multiscale damage plasticity model with the identified properties are experimentally verified with uniaxial tensile test results of glass bead/epoxy composites. Ductile damage evolution and patterns from the proposed model are verified with digital image correlation (DIC) test results. Increasing porosity within the matrix and interface damage from micro-computed tomography (CT) and microscope, respectively, prove the importance of damage modeling in the prediction of structural response by the model.

Evaluation of the influence of voids on 3D representative volume elements of fiber-reinforced polymer composites using CUF micromechanics

This paper presents numerical results on the micromechanical linear analysis of representative volume elements (RVE) containing voids. The modeling approach is the micromechanical framework within the Carrera Unified Formulation in which fibers and matrix are 1D finite elements (FE) with enriched kinematics and component-wise capabilities. RVE models are 3D and consider all six stress components. Such a modeling strategy leads to a twofold reduction of the degrees of freedom as compared to 3D FE. The numerical assessments address the influence of the volume fraction and distribution of voids, including comparisons with data from the literature and statistical studies regarding homogenized properties and stress fields. The proposed modeling approach can capture the local effects due to the presence of voids, and, given its computational efficiency, the present framework is promising for nonlinear analysis, such as progressive failure.

Micromechanical modelling of the longitudinal compressive and tensile failure of unidirectional composites: The effect of fibre misalignment introduced via a stochastic process

Initial fibre misalignment is recognised to be one of the precursors leading to longitudinal compressive failure in fibre-reinforced composites. Thus, to properly model their mechanical behaviour, an accurate spatial representation of the fibrous reinforcements must be assured. This work presents a three-dimensional micromechanical framework that is capable of analysing in detail the longitudinal tensile and compressive failure mechanisms which are inherent in unidirectional composites. This is achieved through the incorporation of initial fibre waviness via a combination of a stochastic process and an optimisation procedure. A robust micro-scale framework is developed by assigning, to both constituents and their interface, proper thermodynamically consistent damage models. Several microstructures having different degrees of misalignment are modelled and a clear trend is observed for the longitudinal compressive load case, i.e. by increasing initial fibre misalignment, the overall performance of the material decreases. In contrast, the models subjected to longitudinal tension exhibit a similar overall response, despite the misalignment. However, local mechanisms seem to change with the degree of friction and fibre misalignment, but these smaller-scale mechanisms do not play a decisive role on the overall longitudinal tensile performance of the material.

Micromechanical investigation for the probabilistic behaviorof unsaturated concrete

There is an inherent randomness for concrete microstructure even with the same manufacturing process. Meanwhile, the concrete material under the aqueous environment is usually not fully saturated by water. This study aimed to develop a stochastic micromechanical framework to investigate the probabilistic behavior of the unsaturated concrete from microscale level. The material is represented as a multiphase composite composed of the water, the pores and the intrinsic concrete (made up by the mortar, the coarse aggregates and their interfaces). The differential scheme based two-level micromechanical homogenization scheme is presented to quantitatively predict the concrete\'s effective properties. By modeling the volume fractions and properties of the constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the material\'s inherent randomness. Monte Carlo simulations are adopted to reach the different order moments of the effective properties. A distribution-free method is employed to get the unbiased probability density function based on the maximum entropy principle. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, commonly used probability density functions and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the material\'s effective properties. Finally, the effects of the saturation degrees and the pore shapes on the concrete macroscopic probabilistic behaviors are investigated based on our proposed stochastic micromechanical framework.