In the family of smart materials termed as “self-healing materials”, there is a prominent number of them sharing many similarities in the way that healing is affecting their post-damaged mechanical response. In this work, a generic and multi-material phenomenological-based healing formulation is proposed to investigate and characterize the self-healing effect in the mechanical response of materials exhibiting strong nonlinearities like rate-dependent plasticity, visco-damage initiation and evolution. The proposed healing formulation uses objective experimental measures such as resting time, loading rate and damage level. This formulation is integrated in a combined computational–experimental procedure, the so-called Generic Healing-Oriented Multi-Material Modeling Framework (GHOM ³) that facilitates (i) the understanding of a strongly nonlinear response, (ii) a robust material characterization and (iii) the predictive simulation via the finite element analysis. As study case, the intrinsic self-healable mechanical response of a highly nonlinear asphalt-based composite matrix is characterized at room temperature using the proposed framework. As additional novelty in the framework, an ultra-fast optimization-based material parameter identification process is developed using a master–slave parallelization paradigm that leads to save up to 90% of data processing time. The framework is put into practice to virtually predict the mechanical response influenced by the healing process of the validated material in a dog-bone specimen under Load–Unload–Resting–Reload at multiple loading rates and damage levels. The implemented approach gives direct access to the entire damage and healing histories, which are experimentally inaccessible, as well as providing an alternative definition of the healing indices commonly used in experimentation.

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Nonlinear matrices employed in asphalt-based composites exhibit a prominent nonlinear elastic-viscoplasticviscodamageable mechanical response. The constitutive model for this type of matrices requires a significant experimental effort to identify the material constants. To alleviate the characterization effort without losing reliability in the mechanical prediction, this paper presents a fast procedure decoupling the elasto-viscoplastic response from the viscodamageable one and facilitating the identification of the material constants via efficient optimization. This procedure relies on a combined experimental-numerical also applicable to other rheologically complex materials like polyurea, thermoplastics or elasto-viscoplastic polycrystals. The experimental part is deliberately designed to only conduct cost-and time-effective monotonic loads at different strain rates in tension and compression. These pure monotonic results are used in the constitutive model to predict more complex loading conditions such as multiple load-unload-reload (LUR) cycles. To do this, an elasto-viscoplastic constitutive model suitable to describe creep-like phenomena and large irreversible deformations is proposed. This model incorporates pressure and strain rate sensitivity, which is essential to capture the compression- tension asymmetry in asphalt-based composites. A rate-dependent damage model is proposed to describe the degradation rate of the elasto-viscoplastic part. The stress and the consistent tangent modulus are derived. The model implementation for user-defined finite element subroutines are given for explicit or implicit solvers. The proposed decoupling facilitates an efficient identification of the constant parameters via an in-house Nelder-Mead-based optimization method. To accelerate the identification, all the stress-strain curves, either in tension or compression, are simultaneously used with applying physically-based constrains. The framework is validated with asphalt matrix at room temperature (24 C) and verified under LUR conditions at different rates. The identified model predicts correctly the experimental observations, proving its applicability to investigate particle-based composites with highly nonlinear matrices.@en

The fracture process in self-healing concrete with embedded brittle capsules entails challenges in terms of understanding how and when these capsules break to release the agent. This paper presents a combined experimental–numerical investigation in which a versatile three-dimensional simulation model is developed to investigate the fracture of this type of beams under three-point bending load. The model allows for correlating the overall strength with different damage events occurring in every constituent: the concrete, the capsules and the capsule-concrete interface. The constitutive concrete damage model uses a pressure-dependent failure initiation criterion followed by a bilinear softening law, whose parameters are validated by using a modified Nelder-Mead optimization algorithm enriched with user-defined constraints aimed at increasing the convergence ratio. The validated virtual model demonstrates that the ratio of capsule slenderness to concrete-capsule interface strength is the key parameter for an effective self-healing process as it gives full control to break the capsule at the right moment. The shorter the capsule is, the longer the breakage process can be. Additionally, it has been found that by increasing the length of the capsules can help to enhance the overall fracture energy of the beam even after fully broken.@en

The constitutive modelling of semi-crystalline polymers (SCP) has to consider several aspects as rate- and temperature-dependence, self-heating, and in particular, the double yield (DY) phenomenon. A full characterization of all these complex features involves prominent efforts in terms of material testing and parameter identification (PI). The contribution of the crystalline phase plays an important role in the evolution of the plastic yield in the SCPs. In this work, a constitutive model, named Unified SCP (USCP), is proposed by modifying the physically-based Boyce-Parks-Argon (BPA) glassy model. The contribution of the crystalline phase is introduced in the strain softening/hardening evolution law of the strength, providing an alternative interpretation of the underlying morphological changes caused by the crystalline phase embedded in the amorphous phase. The proposed formulation extends the BPA model with a new contribution to capture the crystalline phase. A full thermo-mechanical coupled numerical framework is developed for the USCP model validation. The DY phenomenon at different strain rates with self-heating and thermal softening effects is investigated and predicted. The proposed model extension needs three material constants with clear physical meaning. To identify them, a fast in-house optimization process based on Nelder-Mead is used, in which only a single element test is required. The model accurately predicts the experimental results for both thermosets and thermoplastics such as epoxy, nylon 101, PA6 and LDPE under monotonic loadings reported by different authors.

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The double yield (DY) phenomenon observed in a wide variety of semi-crystalline polymers (SCP) adds difficulties in the material characterization. In this paper, a constitutive model, termed as explicit semi-crystalline polymer (ESCP) model, is proposed to study DY phenomenon as well as the rate- and temperature-dependent thermomechanical response below the glass transition temperature. The underlying yield kinetics due to the morphological changes of the spherulite micro-structure is represented by a rheological analogue described by a physically-based amorphous intermolecular resistance and a rate-independent crystalline interlamellar resistance. Independently-identified viscoelastic response and network resistance are also implemented to complete the model description. The activation and disclosure of the crystalline component depend on the saturated state of amorphous phase. The proposed model is validated against ex- perimental data obtained from different authors for three commonly used SCPs: nylon 101, LDPE and PA6. A straightforward parameter identification procedure, requiring a minimum number of calibration tests, is presented to illustrate the model usage. The thermomechanical-coupled analyses provide satisfactory predictions using simulated models of a cylinder compression and dogbone tensile tests at different rates, where the self-heating and thermal softening effects are naturally captured by the model.@en

This research presents an experimental and numerical approach to study the mechanics of asphalt matrix, a crucial component in asphalt concrete. Understanding its response is essential to guide the new designs in advanced asphalt concrete. The dynamic mechanical analysis (DMA) is used to execute a variety of quasi-static and dynamic tests under tension and compression. Uniaxial tests reveal a remarkable rate-dependent compression-tension (C-T) asymmetry of the asphalt matrix in terms of stiffness and strength. The creep rupture envelop is derived by performing creep tests at different stress levels. Amplitude and frequency sweep tests and fatigue-recovery test are performed to explore the fatigue response. A user-material visco-elasto-plastic-damageable (VEPD) model is developed to simulate the asphalt via finite element method (FEM).@en

The bonding properties of the asphalt mortar-aggregate interface at low-temperatures are investigated in this study. A novel method based on mortar-aggregate-mortar sandwich beam and four-point bending test is established. The effects of temperature, loading speed, material type, asphalt aging level and aggregate surface roughness on the bonding properties of the mortar-aggregate interface are methodically examined. Three cracking indexes, including peak bending stress, fracture energy and interface stiffness, are considered for the evaluation. It is concluded that the proposed testing method can effectively distinguish the low-temperature bonding performance of the asphalt mortar-aggregate system under different conditions. The obtained results reveal that the fracture energy can be increased by 700 % with the failure mode changing from brittle failure (−6 °C) to ductile failure (0 °C), and the positive correlation between loading speed and asphalt-mortar system fracture resistance at low temperature is verified. Additionally, the bonding properties are apparently affected by the type of asphalt and aggregate, aging level of the specimen, and aggregate surface roughness. Specimens composed of the styrene butadiene styrene (SBS) modified asphalt and basalt have the best bonding properties. The moderate aging of the specimen or increasing surface roughness of the aggregates has a positive incorporation into the bonding properties of the asphalt mortar-aggregate system, but severe aging or over-dense grooving act adversely.

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This research presents an experimental approach to study the mechanics of asphalt matrix, a crucial component in asphalt concrete, consisting of asphalt binder, fine aggregates and filler. Understanding its response is essential to guide and improve the new designs in advanced asphalt concrete. The proposed approach makes use of the dynamic mechanical analysis (DMA) to execute a variety of quasi-static and dynamic tests under tension and compression. Uniaxial tests reveal a remarkable compression-tension asymmetry of the asphalt matrix in terms of stiffness and strength. The peak stress and stiffness can be 5 and 3 times, respectively, larger under compression than in tension. Both properties strongly depend on the strain rate, albeit stiffness and peak stress in compression are more sensitive than in tension. A straightforward equation for the creep rupture envelop is derived by performing creep tests at different stress levels. Amplitude and frequency sweep tests and fatigue-recovery test are performed to explore the inherent self-healing capabilities of asphalt matrix at room temperature. Doubling the regularity of resting periods significantly helps to regain the stiffness and it leads to a 4-times extension of the fatigue life.@en

Smart asphaltic, cementitious and composite materials are drawing great attention in civil engineering and material science. The aim of smart material is to extend the lifespan and improve the mechanical performance of structures. These materials have in common complex behaviors like visco-elasticity, visco-plasticity, progressive damage and fracture. A good understanding of these phenomena is required to improve and extend the capabilities of smart materials. To do that, constitutive laws are needed to describe the non-linear mechanisms where the crucial parameters must be identified. The development of a mathematical and simulation framework is the key to predict and investigate new developments in smart materials. In this paper, a three-dimensional visco-elasto-plastic-damageable constitutive model is proposed, consisting of three basic modules: visco-elasticity, plasticity and damage, which can provide rate-dependency on stiffness and strength, and describe progressive degradation and failure. An efficient gradient-less optimization algorithm with user-defined constraints is developed to identify the material parameters. This methodology can solve a highly non-linear function with multiple variables, where the physical meaning and the effect of each variable are understood. The model and the optimization approach are implemented using the finite element code ABAQUS via user-defined material subroutines (V)UMAT. The proposed constitutive model is thoroughly validated and verified with experimental results. This numerical framework will allow for adding additional features like the effect of temperature on the mechanical properties and the self-healing capability in further research.@en

Visual intervention has a significant influence on drivers’ behaviour, which may cause the redistribution of wheel tracks, relieving the stress from the concentration of axial loads so that the rutting can be mitigated, which has been introduced and validated in a companion paper (Part I). Reasonable determination of the visual intervention timing with a three-stage intervention method can reduce rutting. In this paper, an initial development rate method is proposed, and the rutting prediction method based on finite element model is established. The data of rutting depth is segmentally fitted to obtain the rate curve of rutting deformation, based on which the intervention timings of three kinds of typical pavement structure are determined. It is found that SUPERPAVE pavement is the latest to set intervention while AC pavement is the earliest one. The analysis also shows the higher the capability of resisting rutting deformation is, the later the rutting deformation enters the second stage (steady state), which means the intervention is delayed. For the same pavement structure, the intervention of longitudinal slope section is earlier than that of flat slope section. Moreover, the service life of asphalt pavement can be prolonged by 16–31% in an intervention cycle.@en

Identifying the properties of the region where the cement paste meets the aggregate surface (interfacial transition zone, ITZ) is critical to understanding the strength and fracture behavior of carbon nanofiber (CNF) reinforced cement concrete. In this study, the finite element method is employed to investigate the effect of the ITZ on the Young's modulus of cement concrete made with CNF. The numerical models for cement concrete with and without CNF are constructed based on the digital image processing technique. To consider the interface effect, the concept of “effective aggregate” is put forward, namely, the Young's modulus and Poisson's ratio for each aggregate particle are replaced by an effective Young's modulus and effective Poisson's ratio, in which the effect of thickness and the Young's modulus of ITZ is taken into account in an averaged manner. Then, the quantitative nanomechanical mapping (based on atomic force microscopy) technique is adopted to measure the Young's modulus and thickness of ITZ with and without CNFs, which are further used as the input parameters in the numerical model. The numerical simulation results are verified by experimental testing, which indicates that the ITZ effect should be considered when implementing the numerical simulation. In addition, this analysis shows that compared with the plain cement concrete, CNFs can greatly enhance the mechanical properties of ITZ, which will in turn improve the Young's modulus of cement concrete significantly. Finally, the effect of thickness and Young's modulus of ITZ on the Young's modulus of CNF reinforced cement concrete is also discussed.@en

Thermal expansion of concrete is a main factor of concrete failures especially in underground waterproof engineering, overlong structural engineering and mass concrete construction. Thus, the coefficient of thermal expansion (CTE) of concrete is an important parameter to be determined. A micromechanical model, namely the 3D Two-Layer Built-in Model is developed to obtain the overall CTE of cement concrete. The existence of interfacial transition zone (ITZ) between aggregate and cement paste is considered in the model, and the ITZ model is simplified as a spring layer with a certain stiffness k. According to the existing testing data of three types of cement concrete whose aggregates are siliceous river gravel (RG), dolomitic limestone (DL) and granite (GR) respectively, the CTEs of prediction model are obtained and validated by the measured values. Moreover, the effects of interface, water cement ratio, volume fraction ratio of fine aggregate to coarse aggregate, air voids, CTE of coarse aggregate and elastic modulus of cement paste on the CTE are analyzed.@en