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This is an Open Review of the paper: S. André, J. Boisse, C. Noûs, An FFT solver used for virtual Dynamic Mechanical Analysis experiments: Application to a glassy/amorphous system and to a particulate composite, Journal of Theoretical, Computational and Applied Mechanics (2021). 10.46298/jtcam.6450

Polymeric glasses exhibit complex behaviour when subjected to deformation below the glass transition temperature. Uniaxial stress-strain curves typically include post-yield strain softening, strain hardening, and non-linear unloading. In addition, the deformation and failure responses are sensitive to the rate of deformation, pressure, and temperature. Sophisticated (visco-)elastic-(visco-)plastic continuum constitutive models have been developed to simulate the large strain deformation of (glassy) polymers; they generally give excellent fits to uniaxial stress-strain curves. However, they require the calibration of a large number of mostly phenomenological parameters, give limited insights into failure, and struggle to accurately predict the response for more complicated loading states and histories. At the opposite scale, molecular dynamics (MD) simulations have been used to elucidate the discrete molecular deformation mechanisms leading to the heterogeneous inelastic behaviour of polymeric glasses. The results of MD calculations suggest that plastic deformation of polymeric glasses is caused by thermally activated molecular rearrangements and conformational changes of a collection of polymer chains parts. The use of a mesoscale numerical model based on the activation of shear transformation zones (STZs) offers a convenient approach to bridge continuum and molecular dynamics simulations, which are typically limited to small length and time scales. We have used the implementation by Homer and Schuh [1] of Argon’s STZ theory [2] to develop a mesoscale finite element model for polymeric glasses. It is assumed that the elementary deformation mechanism giving rise to macroscopic plastic deformation in a polymeric glass is a pure shear deformation of an STZ; this corresponds to a change in molecular conformational state. Plastic deformation is governed by these changes and their interaction with the surrounding (visco-)elastic matrix. The mesoscale STZ framework requires the calibration of only five parameters and successfully predicts the complex large deformation response of glassy polymers, including creep and non-linear unloading [3]. In this contribution, we will summarise the key building blocks of the mesoscale framework and discuss a possible route for model calibration. In addition, we discuss the role of the visco-elastic matrix on the model predictions. These insights can be used to simulate the time- and temperature-dependent visco-plastic deformation and failure response of a fibre-reinforced polymer composite matrix at the fibre-diameter length scale.

Advanced constitutive models for polymers have been essentially developed for thermoplastics with relatively limited applications/extensions to thermosets. Recent extensions of these constitutive models provide accurate predictions over a wide range of loading configurations, strain rates and temperature, encompassing below and above transition temperature regimes, although at the prize of a very large number of parameters, often larger than 30. Still, these models, mixing phenomenological and micromechanics ingredients, are often not rich enough to capture complex behaviors such as for instance severe non-linearity upon unloading or possible size effects, while missing also micromechanical connection to the failure process. This directly impacts the development of predictive multiscale models for polymer based composites. Based on extensive experimental test program on the highly cross-linked RTM6 epoxy, the viscoplastic response is found very similar to thermoplastics, with hardening-softening-rehardening, large back stress upon unloading and existence of shear band patterns at very small scale [1]. Furthermore, size effects are revealed when looking at nanoindentation data as well as indirectly when looking at the response of unidirectional composites. A molecular physics-based model of the deformation process occurring through the activation of nanometer scale shear transformation zones (STZ) has been worked out [2]. The viscoplastic deformation is the result of the cooperative activation of STZ’s, sensitive to rate, temperature, stress state and stress level. This model involves only 7 parameters to identify, all with physical meaning. The model quantitatively captures the experimental trends, even some complicated responses during creep tests performed after plastic deformation at intermediate stress levels showing backward followed by forward creep. It also captures the size dependent strength resulting from large strain gradients putting a constraint on the development of the micro-shear banding process. In addition, a new micromechanics-based fracture model based on the attainment of a local maximum principal stress at the tip of microdefects is proposed and validated for a wide range of stress states [3]. The implication of these results and micromechanical models on composite modelling is not straightforward. This is addressed through the analysis of in situ SEM compression tests on thick UD carbon fiber reinforced RTM6 matrix composite, involving the determination of digital image correlation strain fields [4]. Difficulties remain to quantitatively capture the experimental response with the models identified on bulk resin data.

Advanced constitutive models for polymers have been essentially developed for thermoplastics with relatively limited applications/extensions to thermosets. Recent extensions of these constitutive models provide accurate predictions over a wide range of loading configurations, strain rates and temperature, encompassing below and above transition temperature regimes, although at the prize of a very large number of parameters, often larger than 30. Still, these models, mixing phenomenological and micromechanics ingredients, are often not rich enough to capture complex behaviors such as for instance severe non-linearity upon unloading or possible size effects, while missing also micromechanical connection to the failure process. This directly impacts the development of predictive multiscale models for polymer based composites. Based on extensive experimental test program on the highly cross-linked RTM6 epoxy, the viscoplastic response is found very similar to thermoplastics, with hardening-softening-re-hardening, large back stress upon unloading and existence of shear band patterns at very small scale [1]. Furthermore, size effects are revealed when looking at nanoindentation data as well as indirectly when looking at the response of unidirectional composites. A molecular physics-based model of the deformation process occurring through the activation of nanometer scale shear transformation zones (STZ) has been worked out [2]. The viscoplastic deformation is the result of the cooperative activation of STZ’s, sensitive to rate, temperature, stress state and stress level. This model involves only 7 parameters to identify, all with physical meaning. The model quantitatively captures the experimental trends, even some complicated responses during creep tests performed after plastic deformation at intermediate stress levels showing backward followed by forward creep. It also captures the size dependent strength resulting from large strain gradients putting a constraint on the development of the micro-shear banding process. In addition, a new micromechanics-based fracture model based on the attainment of a local maximum principal stress at the tip of microdefects is proposed and validated for a wide range of stress states [3]. The implication of these results and micromechanical models on composite modelling is not straightforward. This is addressed through the analysis of in situ SEM compression tests on thick UD carbon fiber reinforced RTM6 matrix composite, involving the determination of digital image correlation strain fields [4]. Difficulties remain to quantitatively capture the experimental response with the models identified on bulk resin data.

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Advanced constitutive models for polymers have been essentially developed for thermoplastics with relatively limited applications/extensions to thermosets. Thermosets differ from thermoplastics by the cross-linking. Recent extensions of these constitutive models provide accurate predictions over a wide range of loading configurations, strain rates and temperature, encompassing below and above transition temperature regimes, although at the prize of a very large number of parameters, often larger than 30. Still, these models, mixing phenomenological and micromechanics ingredients, are often not rich enough to capture complex behaviors such as for instance severe non-linearity upon unloading, while missing also micromechanical connection to the failure process. Based on an extensive experimental test program on the highly cross-linked RTM6 epoxy, the viscoplastic response is found very similar to thermoplastics, with hardening-softening-re-hardening, large back stress upon unloading and existence of shear band patterns at very small scale. A molecular physics-based model of the deformation process occurring through the activation of nanometer scale shear transformation zones (STZ) has been developed, borrowed from the metallic glass field. The viscoplastic deformation is the result of the cooperative activation of STZ’s, sensitive to rate, temperature, stress state and stress level. This model involves only 5 parameters to identify, all with physical meaning. The model quantitatively captures all the experimental trends, even some complicated responses during creep tests performed after plastic deformation at intermediate stress levels showing backward followed by forward creep. Such as model will never replace closed form constitutive models for the treatment of large scale components but can be used to understand small scale mechanics as well as for identifying macroscopic models. In this research, a new micromechanics-based fracture model based on the attainment of a local maximum principal stress within a given volume is also proposed and validated for a wide range of stress states.

Dual-phase steels have long been used in the automotive industry for their excellent mechanical properties in terms of strength and ductility balance combined to a low processing cost. The good compromise between strength and ductility results from the very different properties of the constituent phases, namely ductile ferrite and hard martensite. Dual-phase steels can be produced with either equiaxed or platelet-like second phases. Even though the behaviour of dual-phase steels is well understood as for the effects of martensite volume fraction, composition and grain size in the case of equiaxed microstructures, the impact of morphology of martensite particle and of its orientation with respect to the loading direction has not been much investigated. Effects of structural heterogeneities and of martensite interconnectivity on plasticity are also incompletely established. A better understanding of the latter variables is needed to guide the generation of steels with improved mechanical properties. This work investigates therefore the effects at single grain level and at the multigrain level, using a two-scale strategy based on FE calculations performed on unit cells, bypassing the large computational cost of full-field models on RVEs, following earlier works in [1] and [2]. An important outcome is that, although structural heterogeneities - among others morphology - have a limited impact on the effective plastic behaviour until necking, they considerably influence the mechanical fields at the micro-scale and thus largely impact the damage behaviour. An island of interconnected martensite constitutes a particular morphology that does however significantly impact the effective plastic behaviour. Furthermore, taking into account martensite interconnectivity leads to an improved prediction of experimental curves.