Necessary conditions of the Legendre–Hadamard type for energy minimizers are derived in the setting of a special Cosserat elasticity theory for fiber-reinforced solids. These extend and generalize earlier results pertaining to fiber flexure-twist strain vectors formed from the Cosserat wryness tensors. New necessary conditions involving the associated Cosserat deformation tensors are also derived.

As AM lattices become more popular in medical devices, it is important to consider how lattice design parameters affect the mechanical integrity and performance of a device. This research investigated the effect of lattice orientation on the compressive mechanical response of five common lattice geometries: Hexagonal Honeycomb (Hex), Diamond, Voronoi Tessellation Method (VTM), sheet-based Gyroid, and Face-Centered-Cubic (FCC). Samples were tested at two relative densities and eight orientations, printed in Nylon 12 (PA2200) on an EOS P396. The mechanical response was compared to simulated finite element analysis (FEA) response for Hex and FCC lattices. Hex lattices displayed significant orientation dependance. Diamond lattices demonstrated some orientation dependance when at a lower relative density. Gyroid, FCC, and VTM all displayed minimal orientation dependance. Increasing lattice relative density appeared to reduce anisotropy among tested orientations of all lattice geometries except Hex. FEA simulations were able to produce a trend response that matched the mechanical response trends based on the investigated orientations. These results support the need for multi axial lattice mechanical test considerations. It also bolsters the need for lattice FEA models to have a sufficient comparator when identifying “worst-case” lattice test scenarios.

The selection of alloying elements with the effect of “Solid solution strengthening and ductilizing” (SSDD) is an important way to develop high-performance magnesium (Mg) alloys recently, and the critical shear stress (CRSS) is an intrinsic parameter that characterizes the effect of SSDD. In this study, the CRSS of four slip systems in Mg-X (X = Al, Zn, Ca, Li, Mn, Sn, Bi, Ag Ga, In, Zr), all of which have a solid solubility (>0.5 at%) in Mg, are calculated using a combination of first-principles and the Peierls-Nabarro (P–N) model, and the SSDD effect of the alloying elements is studied systematically and experimentally verified. Calculations indicate that solid solutions of Mn, Ag, and Li can increase the CRSS of basal system and reduce the difference between the three non-basal and basal systems. Solid solutions of Zn, Ca and Zr can narrow the CRSS gap between at least one non-basal slip system and the basal slip system, but other elements have no positive effect. A smaller equilibrium volume and larger charge density around Mn or Ag element than that of Li, which makes CRSS larger. At the same time, the simulation results are validated by experiment. Mg–Ag alloy exhibits improved strength and plasticity, as well as a large number of dislocations under TEM, which is consistent with the calculation finding that Ag promotes dislocation slip. This study can provide guidance for the selection of solid solution elements for Mg alloys.

Delayed long-term strains of concrete caused by creep are a known problem leading to, e.g., the loss of pre-stress and additional microcracking in concrete structures. In order to improve predictions of the creep strains and damage state of cementitious materials, a coupled experimental and numerical study of the creep/microcracking interactions was designed. Compressive creep tests on cement paste and mortar were carried out to analyze the influence of the material heterogeneity and stress level on the creep rate. The obtained data were used for the calibration of a creep constitutive model and as benchmark for predictions of the creep/damage interactions. The creep model was supplemented with separate damage models for the bulk matrix and matrix-aggregate interfaces. The resulting viscodamage models were applied on artificial microstructures of mortar to simulate, using the finite element method, damage effects on the effective mortar creep behavior. This numerical model was able to reproduce the compressive creep behavior of mortar at low stresses and predicted a tertiary creep stage in tension. Nonlinear creep at higher stresses could only be partially reproduced by taking into account these damage mechanisms, pointing toward nonlinear creep phenomena at the microscale.

Soft materials exhibit large deformation material nonlinearity when stretched and possess enhanced elongation-at-break strain prior to rupture. As a result, these materials can cater to several state-of-the-art biomedical and microfluidic applications that require cross-domain energy transduction. Furthermore, they are often impregnated with external multi-functional filler materials (e.g., hard-magnetic particles) to result in hard-magnetic soft materials (hMSM). This gives rise to an inherent complexity owing to the multi-physics coupling due to magnetics and solid dynamics (along with geometric and material nonlinearities), which demands a rigorous magneto-mechanical model for a thorough understanding of their large deformation mechanical behavior under magneto-mechanical loads. It is also mandatory to understand their rate-dependent, hyperelastic, and flow behavior that is omnipresent during their deformation process. This paper focuses on the development of a novel thermodynamically-consistent micromechanics-based constitutive model that incorporates all these attributes using the finite deformation theory. A statistical mechanics-based approach has been undertaken to model the mechanics of the elastomer matrix. The plastic behavior due to the elastomer and the dispersed magnetic phases has been further accounted using a double-yield function with a micromechanical approach. The developed model shows a good agreement for a wide range of hMSM subjected to a variety of complex loading conditions. Finally, a parametric study has been carried out to provide physical insights into the different model parameters.

The thermal effects on tension compression asymmetry and anisotropy of several metallic materials with a hexagonal close-packed (HCP) crystal structure have been discussed in this study. The Yoon2014 asymmetric yield criterion is combined with a simple Arrhenius type temperature function and a modified Johnson-Cook strain rate model to formulate a thermal dependent plasticity model with analytical solutions for parameter calibration. The temperature and strain rate effects on the strength differential (SD) effects of both isotropic and anisotropic materials have been discussed. Both anisotropy and SD affect the shape of yield locus. In order to quantitatively distinguish the thermal effects on the strength differential and anisotropic effects of metallic materials, the evolution of yield locus and distribution of yield stress under two extreme scenarios has been discussed based on virtual experimental results. For the general application of the thermal dependent asymmetric plasticity model at different temperatures and strain rates, the calibration and validation of the model using uniaxial tensile/compressive results along different directions and biaxial tensile/compressive results have been elaborated for various metallic alloys.

This paper introduces a publicly available PyTorch-ABAQUS deep-learning framework of a family of plasticity models where the yield surface is implicitly represented by a scalar-valued function. In particular, our focus is to introduce a practical framework that can be deployed for engineering analysis that employs a user-defined material subroutine (UMAT/VUMAT) for ABAQUS, which is written in FORTRAN. To accomplish this task while leveraging the back-propagation learning algorithm to speed up the neural-network training, we introduce an interface code where the weights and biases of the trained neural networks obtained via the PyTorch library can be automatically converted into a generic FORTRAN code that can be a part of the UMAT/VUMAT algorithm. To enable third-party validation, we purposely make all the data sets, source code used to train the neural-network-based constitutive models, and the trained models available in a public repository. Furthermore, the practicality of the workflow is then further tested on a dataset for anisotropic yield function to showcase the extensibility of the proposed framework. A number of representative numerical experiments are used to examine the accuracy, robustness and reproducibility of the results generated by the neural network models.

It is well known that the widely used forming limit curve (FLC) based upon in-plane stretching fails to account for the delay in plastic instability in the presence of appreciable bending and tool contact pressure. The recently proposed General Incremental Stability Criterion (GISC) – a generalization of the Modified Maximum Force Criterion (MMFC) to triaxial loading – revealed the dependence of the boundary conditions on the formation of tensile instabilities. Nevertheless, it remains unclear how the combined effect of radial bending stresses and tool contact pressure affects the formation of an acute neck. It is shown in this study that a compressive normal stress causes a shift of the strain state from initial plane strain tension to positive minor strains for material layers within the cross-section. The convex (outer) layer remains in a state of plane strain-plane stress. Accounting for the shift in the strain state is key to capture the dependence of the contact pressure on necking. A simplified modelling approach, which enforces plane strain tension of the cross-section, was able to capture the formability gain due to bending but failed to account for the delay in plastic instability due to the contact pressure. An incremental multi-layer model was required to account for non-monotonic loading due to bending over the punch and the biaxial shift in the strain path caused by the contact pressure. The models were then applied to the experimental forming limits of a 3rd Gen 1180 advanced high strength steel to demonstrate the formability gains under triaxial loading due to the contact pressure.

In this work, an austenitic 316 L steel was processed by surface mechanical attrition treatment (SMAT), and the induced gradient microstructure was highlighted by experimental measurements. A combined dislocation density-based and grain size-dependent constitutive model is developed to describe the mechanical behaviour of the gradient-microstructured material. In addition, this model also incorporates the grain size-dependent initial twin distribution and evolution of deformation twinning. Residual stress, initial dislocation density and twins are considered to reconstruct the depth-dependent residual fields induced by SMAT. Furthermore, the evolution of dislocation density and twin volume fraction is described during uniaxial tensile loading. Particular attention is devoted to investigate the effect of residual stress and deformation twinning on mechanical behaviour. Results of finite element simulation showed that the gradient microstructure enhances the yield strength, which is in agreement with previous experimental observations. It was revealed that residual stress significantly weakens the yield strength at the initial deformation stage, whereas it has little influence on the plastic behaviour at large deformation. The assumed grain size-dependent deformation twinning model allows describing the evolution of deformation twinning on gradient microstructure. The deformation twinning increases in relation to increased strain hardening during tensile loading. However, the evolution of twin volume fraction shows almost no twin and no variation of twinning within the nanocrystalline grain region.

Three-dimensional (3D) truss-based metamaterials (or architected materials) have been the subject of an increasing amount of studies, owing to their impressive and tunable mechanical properties. Unfortunately, experimentally studying their mechanical multiscale behavior under dynamic loading presents a challenge due to the complex time-dependent correlation between the overall truss response and the deformation of individual beams and beam junctions. Tracking the time-dependent deformation of 3D-printed low-density trusses is challenging for traditional techniques such as Digital Image Correlation (DIC), owing to the discrepancy between typical feature (strut) sizes and the field of few of the overall truss, further difficulty in applying speckle patterns, as well as the lack of a stable bright background during testing—especially when high rates and large 3D deformation are involved. As a remedy, we present an efficient DIC-based technique, which admits tracking the nodal displacements of points of interest (such as, e.g., the strut junctions) in periodic and non-periodic truss networks across a range of loading rates. We use this technique to identify the time-dependent nodal displacements of different truss architectures, whose large deformation is of interest for energy absorption capabilities of truss metamaterials. The quality of results is assessed by performing multiple trackings on each truss topology, which reveals that errors are negligible for the reported range of conditions.

Overcoming the time scale limitations of atomistics can be achieved by switching from the state-space representation of Molecular Dynamics (MD) to a statistical-mechanics-based representation in phase space, where approximations such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic ensemble in a time-coarsened fashion. In practice, this requires the computation of expensive high-dimensional integrals over all of phase space of an atomistic ensemble. This, in turn, is commonly accomplished efficiently by low-order numerical quadrature. We show that numerical quadrature in this context, unfortunately, comes with a set of inherent problems, which corrupt the accuracy of simulations—especially when dealing with crystal lattices with imperfections. As a remedy, we demonstrate that Graph Neural Networks, trained on Monte-Carlo data, can serve as a replacement for commonly used numerical quadrature rules, overcoming their deficiencies and significantly improving the accuracy. This is showcased by three benchmarks: the thermal expansion of copper, the martensitic phase transition of iron, and the energy of grain boundaries. We illustrate the benefits of the proposed technique over classically used third- and fifth-order Gaussian quadrature, highlight the impact on time-coarsened atomistic predictions, and discuss the computational efficiency. The latter is of general importance when performing frequent evaluation of phase space or other high-dimensional integrals, which is why the proposed framework promises applications beyond the scope of atomistics.

Advancements in machine learning have sparked significant interest in designing mechanical metamaterials, i.e., materials that derive their properties from their inherent microstructure rather than just their constituent material. We propose a data-driven exploration of the design space of growth-based cellular metamaterials based on star-shaped distances. These two-dimensional metamaterials are based on periodically-repeating unit cells consisting of material and void patterns with non-trivial geometries. Machine learning models exploiting large datasets are then employed to inverse design growth-based metamaterials for tailored anisotropic stiffness. Firstly, a forward model is created to bypass the growth and homogenization process and accurately predict the mechanical properties given a finite set of design parameters. Secondly, an inverse model is used to invert the structure–property maps and enable the accurate prediction of designs for a given anisotropic stiffness query. We successfully demonstrate the frameworks’ generalization capabilities by inverse designing for stiffness properties chosen from outside the domain of the design space.

The complex magneto-mechanical coupling that governs the material response of magnetorheological elastomers (MREs) requires computational tools to assist the design process. Computational models are usually based on finite element frameworks that often simplify and idealise the magnetic source and the associated magnetic boundary conditions (BCs). However, these simplifications may lead to important disagreement between the actual material behaviour and the modelled one, even at the qualitative level. In this work, we provide a comprehensive study on the influence of magnetic BCs and demonstrate the importance of considering them in the overall material-structure modelling strategy. To this end, we implement a magneto-mechanical framework to model the response of soft- and hard-magnetic MREs under magnetic fields generated by an idealised far-field uniform magnetic source, a permanent magnet, a coil system, and an electromagnet with two iron poles. The results unveil remarkable heterogeneities in computed local magnetostriction and magnetic fields depending on the magnetic setup used. A detailed discussion based on material and structural contributions provides a robust, rigorous, and necessary modelling route for future works.

Several Semi-Crystalline Polymers (SCPs) exhibit a Double-Yield (DY) phenomenon in the stress vs. strain response when subjected to uniaxial tensile load. There are only few constitutive models that can predict the DY phenomena at different temperatures and strain rates. These models were developed considering no deformation of crystalline phase, when the amorphous phase gets deformed, whereas in reality all the phases deform concurrently. In this investigation, a Three-Network (TN) viscoplastic model was employed to capture the DY phenomenon in the Low-Density Polyethylene (LDPE) films by considering simultaneous deformations in the amorphous and crystalline (lamellar) phases. The TN model comprised of three parallel networks, A, B, and C, with A and B consisting of non-linear springs and dashpots in series with each other and C containing a non-linear spring solely. While network A of the TN model influences the inter-lamellar shear resistance and the first yield point in the engineering stress vs. strain curve, networks B and C operate together to predict the second yield point. Furthermore, network B regulates the resistance to intra-lamellar shear fragmentation and orientation of lamellar phases. Network C accounts for both the rubbery effect of the amorphous phase and the resistance to fibril deformation along the loading direction at higher strains. To retrieve the TN model parameters, uniaxial tensile tests were conducted on the LDPE films at two different strain rates and temperatures ranging from ambient temperature (25 °C) to 110 °C. The engineering stress vs. strain graphs exhibited the DY phenomenon for all temperatures considered. Stress vs. strain curves were calibrated using the TN model in MCalibration software at certain temperatures (25 °C, 50 °C, 70 °C, and 90 °C) and loading rates (∼10−3/s and 10−2/s). The calibration results corroborated the experimental findings, particularly in terms of capturing the DY phenomenon. Also, simulations using calibrated TN model parameters satisfactorily predicted experimental stress-strain plots at remaining temperatures (40 °C, 60 °C, 80 °C, and 110 °C), demonstrating its versatility in predicting stress and strain characteristics. For the wide range of temperature (25 °C–110 °C) and strain rates considered, an overall difference of ∼5% is observed between the experimental and predicted stress vs. strain data.

Pentahexoctite (PH) is a pure sp2 hybridized planar carbon allotrope whose structure consists of a symmetric combination of pentagons, hexagons, and octagons. The proposed PH structure was shown to be an intrinsically metallic material exhibiting good mechanical and thermal stability. PH nanotubes (PHNTs) have also been proposed, and their properties were obtained from first principles calculations. Here, we carried out fully-atomistic simulations, combining reactive (ReaxFF) molecular dynamics (MD) and density functional theory (DFT) methods, to study the PHNTs elastic properties and fracture patterns. We have investigated the mechanical properties behavior as a function of the tube diameter and temperature regimes. Our results showed that the PHNTs, when subjected to large tensile strains, undergo abrupt structural transitions exhibiting brittle fracture patterns without a plastic regime.

Recently a new phenomenon of bonding polymeric films in solid-state, via symmetric rolling, at ambient temperatures (≈20 °C) well below the glass transition temperature (Tg ≈78°C) of the polymer has been reported. In this new type of bonding, polymer films are subject to plane strain active bulk plastic compression between the rollers during deformation. Here, we analyze these plane strain cold rolling processes, at large strains but slow strain rates, by finite element modeling. We find that at low temperatures, slow strain rates, and moderate thickness reductions during rolling (at which the Bauschinger effect can be neglected for the particular class of polymeric films studied here), the task of material modeling is greatly simplified and enables us to deploy a computationally efficient, yet accurate, finite deformation rate-independent elastic–plastic material behavior (with the inclusion of isotropic-hardening). The finite deformation elastic–plastic material behavior based on (i) the additive decomposition of stretching tensor ( D = De+Dp, i.e., a hypoelastic formulation) with incrementally objective time integration and, (ii) multiplicative decomposition of deformation gradient (F=FeFp) into elastic and plastic parts, are programmed and carried out for cold rolling within Abaqus Explicit. Frictional interactions are modeled using a consistent rate-independent Coulombic law. Predictions from both formulations, i.e., hypoelastic and multiplicative decomposition, closely match the experimentally observed rolling loads. No specialized hyperelastic/visco-plastic material model is required to describe the behavior of the particular blend of polymeric films under the conditions described here, thereby significantly speeding up the computation for steady-state rolling simulations. It is revealed that under the deformation conditions when principal axes show negligible rotation, hypoelastic formulation can be valid at large elastic stretches. Moreover, the use of classical rigid-plastic modeling (often applicable to metals) is found to greatly underestimate the rolling loads for polymers due to large elastic stretches in the polymer films at large strains. Deformation aspects of solid-state polymeric sheets presented here are expected to facilitate the development of new processes involving (or related to) cold roll-bonding of polymers.

The true contact area between two surfaces is only a small fraction of the apparent macroscopic contact area; it governs many interfacial properties such as friction and contact resistance and depends sensitively on roughness. However, for real-world multi-scale surface topography, it is not clear which size scales of roughness govern the true contact area. This study investigates true contact area for a real-world surface that has been characterized across all scales from Angstroms to centimeters. Elastic and elastic-plastic contact is investigated using both a multiscale framework and a statistical roughness model. The multiscale method is a rough-surface contact-modeling technique based on Archard's stacked scales from a spectrum of the surfaces, which has shown promise when compared to previous experimental and numerical results. In contrast, statistical models assume that the asperities follow a defined height distribution and are in contact when taller than the mean surface separation. The results show that even the smallest scales can have a significant influence on the contact area, especially when the contact is elastic. However, when the contact is elastic-plastic, the influence of smaller scales can be limited depending on the character of the roughness. For self-similar, fractal-like roughness across some scales, the pressure tends to saturate at those scales. This work also explores the inclusion of scale-dependent yield strength. Both the multiscale and statistical models predict that the inclusion of scale-dependent strength causes the predicted contact area of the elastic-plastic models to come into closer agreement with that of the elastic model, especially when a wider range of size scales are included. In addition, both types of models predict that below a certain scale, smaller asperities flatten under contact pressure and will no longer influence the predicted contact area. Taken together, this work helps to guide the accurate modeling of rough-surface contact, and provides insights into which scales can be modified to improve performance in manufactured components.

Under mechanical loading, the strain hardening behavior of crystalline face-centered cubic (FCC) metals is of critical importance in determining fracture behavior and overall mechanical performance. While strain hardening is typically accompanied by a decrease in ductility, it can also simultaneously enhance the material's resistance to plastic deformation and improve its load bearing capacity. Hence, we conducted a detailed study using copper (Cu) single-crystal micropillars as a model system to investigate and delineate the relationship between strain hardening and defect behavior. We employed in situ compression in a scanning electron microscope (SEM) and dislocation density-based crystal plasticity (DCP) modeling. The strain hardening rate varied with the compression crystallographic orientation, ranging from negligible values (of approximately 80 MPa) to relatively high hardening rates (of approximately 1150 MPa) for nominal strains of up to 15%. Various analysis methods were applied, including slip trace characterization, electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and transmission Kikuchi diffraction (TKD). These techniques allowed us to identify the distributions of active slip systems, dislocation structures after compression, and correlated internal lattice rotations. Furthermore, the DCP model was developed to specifically understand how serration events are related to dislocation-density evolution or strain bursts, and this was validated with the micropillar experiments. This integrated experimental and modeling investigation offers valuable insights and predictions regarding the evolution of both total and partial dislocations, including Hirth and Lomer junctions, as well as lattice rotations.

This work proposes a novel artificial neural network (ANN)-based framework to explore the mechanical behaviour of shape memory alloy (SMA) Schwartz primitive triply periodic minimal surfaces (TPMSs) architectures where a loop with multiple conditions (LMCs) is introduced into the framework to improve its accuracy. Remarkably, it is found that the introduced ANN-based framework comprehends extremely well the example data and then provides a highly accurate prediction for the topology-driven mechanical behaviour of the SMA TPMS lattice architectures, which do not belong to the example. Indeed, the mechanical responses obtained from ANN-based approach excellently agree with that from numerical homogenization, with the maximum percent difference below 2.7% attained when the TPMS is subjected to tension or shear during the loading and unloading processes. More interestingly, the ANN-based approach can perform well with the increment of relative density or temperature 1000 times smaller than that in the homogenization, only requiring a little simulation time or thousands of times faster than that in the homogenization at the same computer setup. Hence, the mechanical behaviour of SMA TPMSs can be accurately characterized by the proposed framework at almost any value of the relative density or the temperature after the training. Subsequently, the ANN-based framework is used to map two-dimensionally the impact of varying relative density, temperature, and deformation on the effective hardness and superelasticity of the SMA TPMS architectures. The results show that the superelasticity of SMA TPMS scaffolds increases with decreased temperature and relative density and with increased deformation, in a nonlinear pattern. This work lays the foundation for further research on using ANN to explore the mechanical response and advanced applications of the complex SMA-based structures, such as smart composite systems, helical springs, and metamaterials at considerably reduced computational and financial costs.

In this study, a multi-stage model is proposed to predict the creep behavior of semi-crystalline polymer nanocomposites considering the impact of nanoparticle aggregation/agglomeration, polymer/particle interphase region and self/induced crystallization phenomenon. A specific equivalent box model (EBM) was designed, based on excluded volume concept, to evaluate the different roles of dispersed or aggregated/agglomerated nanoparticle domains in the system. The tensile modulus of these domains was defined using mechanical and cohesive energy-based parameters in the melt-mixing stage. In the next stage, the physical/mechanical characteristics of the polymer/particle interphase were indicated using an analytical model and mechanical properties of the system. Another EBM was developed using standard linear viscoelastic (SLV) model components to study the time-dependent creep behavior of the matrix and polymer/particle interphase region. The impact of polymer/particle compatibility on the creep behavior of the samples was also experimentally evaluated by applying different amounts of compatibilized and un-compatible silica nanoparticles to the high-density polyethylene (HDPE) matrix. Different experimental tests were used to provide the required data or verify the obtained theoretical results. Both model predictions and experimental results showed that increasing the nanoparticle content and polymer/particle compatibility increases the resistance of the semi-crystalline nanocomposite system against the time-dependent creep.