Nonlinear Constitutive Behavior Research Articles

Simulation and parameterization of nonlinear elastic behavior of cables

AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Nonlinear Soil–Pile–Structure Interaction Behaviour of Marine Jetty Structures

Nonlinear soil–pile–structure interaction (SPSI) phenomena are known to play a vital role in the response of bottom-fixed marine structures. For such structures, these phenomena are commonly considered by the imposition of p-y, τ-z, and q-z springs, representing the lateral and axial shaft and axial base soil resistances, respectively. The importance of each resistance mechanism depends on the type of foundation system, with only very limited studies investigating their roles in the response of piled marine structures, such as jetties. Within this context, this study presents numerical three-dimensional pushover analysis results for two marine jetties, a smaller model with four piles and a larger model supported by twenty-four piles. SPSI effects are considered through p-y, τ-z, and q-z springs, the behaviours of which are determined by following commonly employed procedures. The structures’ responses are investigated under the influence of various assumptions regarding the behaviours of springs, as well as steel plasticity. The current investigation underscores the substantial influence of the axial soil–pile interaction on the response of the jetty, particularly in terms of its failure mode. Moreover, it demonstrates the importance of incorporating p-y springs, even though the choice between their linear or nonlinear constitutive behaviour is found to be less critical. Finally, the study concludes that the behaviours of the springs significantly affect the system’s ductility and the degree of steel yielding in the piles, while also highlighting the unconservative influence of neglecting SPSI phenomena.

Nonlinear Soil–Pile–Structure Interaction Behaviour of Marine Jetty Structures

Nonlinear soil–pile–structure interaction (SPSI) phenomena are known to play a vital role in the response of bottom-fixed marine structures. For such structures, these phenomena are commonly considered by the imposition of p-y, τ-z, and q-z springs, representing the lateral and axial shaft and axial base soil resistances, respectively. The importance of each resistance mechanism depends on the type of foundation system, with only very limited studies investigating their roles in the response of piled marine structures, such as jetties. Within this context, this study presents numerical three-dimensional pushover analysis results for two marine jetties, a smaller model with four piles and a larger model supported by twenty-four piles. SPSI effects are considered through p-y, τ-z, and q-z springs, the behaviours of which are determined by following commonly employed procedures. The structures’ responses are investigated under the influence of various assumptions regarding the behaviours of springs, as well as steel plasticity. The current investigation underscores the substantial influence of the axial soil–pile interaction on the response of the jetty, particularly in terms of its failure mode. Moreover, it demonstrates the importance of incorporating p-y springs, even though the choice between their linear or nonlinear constitutive behaviour is found to be less critical. Finally, the study concludes that the behaviours of the springs significantly affect the system’s ductility and the degree of steel yielding in the piles, while also highlighting the unconservative influence of neglecting SPSI phenomena.

Study on mechanical properties and meso-damage mechanism of carbon-polyvinyl alcohol hybrid fiber reinforced recycled coarse aggregate concrete under the coupling action of sodium sulfate and dry-wet cycles

In order to investigate the influence of the coupling effect of sodium sulfate dry-wet (DW) cycles on the mechanical properties of carbon-polyvinyl alcohol hybrid fiber reinforced recycled coarse aggregate concrete (HFRAC), HFRAC specimens were subjected to uniaxial compression tests. The total volume fraction of fibers was kept constant at 0.4%, and various volume fractions of carbon fibers (CF) were added to the recycled coarse aggregate concrete (RAC), namely 0%, 0.1%, 0.2%, 0.3%, and 0.4%, with polyvinyl alcohol (PVA) fibers replacing a portion of CF in equivalent volume. Uniaxial compressive stress–strain curves were obtained for HFRAC specimens subjected to different numbers of DW cycles (0, 30, 60, and 120 cycles). Microscopic testing methods including acoustic emission (AE), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), and nuclear magnetic resonance (NMR) were employed to analyze the microstructure, erosion product composition, and pore structure changes of the specimens. The results revealed that, for RAC specimens, the peak stress (σp) and elastic modulus (E) initially increased and then decreased, whereas the peak strain (εp) initially decreased and then increased with an increase in the number of DW cycles. After adding hybrid fibers, the σp values of CF, Hybrid 3:1, Hybrid 1:1, Hybrid 1:3, and PVA specimens increased (or decreased) by 12.0%, 11.43%, 0.9%, −9.5%, and −8.5%, respectively, compared to RAC. The Hybrid 1:3 specimen exhibited a negative hybrid effect. With an increase in the erosion age, the Hybrid 3:1 specimen demonstrated enhanced resistance to sulfate attack and achieved the highest σp value after 120 cycles. The influence of sulfate DW cycles coupling on the microscopic damage mechanism of HFRAC was analyzed using a statistical damage constitutive model. The microscopic damage evolution process was characterized by five characteristic parameters: E0, εa, εh, εb, and H. The analysis results indicated a clear correlation between the variation of these characteristic parameters and the number of DW cycles. An effective connection was established between the microscopic damage mechanism and the macroscopic nonlinear constitutive behavior. The phenomenon of relative lagging of acoustic emission signals during the uniaxial compression process was explained from the perspective of effective stress. This study provides a theoretical basis for the promotion and application of RAC under sulfate DW cycle environments

A New Macro-Element for Predicting the Behavior of Masonry Structures under In-Plane Cyclic Loading

A new macro model for the finite element modeling of unreinforced masonry (URM) exhibiting in-plane nonlinear cyclic behavior is proposed. The ultimate objective is to predict the seismic response of multi-story URM buildings. The macro model enables the modeling of URM shear walls with a limited number of degrees of freedom (DOF) at low computation times. The macro model consists of a deformable elastic frame supported by diagonal struts with nonlinear behavior aiming to capture all dissipative phenomena occurring during seismic events. The nonlinear constitutive behavior of diagonal struts is inspired by models documented in the literature, ensuring a robust foundation for the proposed approach. This paper first provides a comprehensive review of the principal models currently available for URM analysis. It then articulates the rationale behind the development of this new numerical model, aiming to address the limitations encountered in existing methodologies and to offer a simple and fast tool for predicting the seismic behavior of URM buildings. Afterward, the new model is presented and tested with the simulations of two experimental campaigns performed on different URM walls. The comparison between experimental and numerical results shows that with a limited number of DOF and parameters, it is possible to obtain a prediction of the experimental results with satisfying accuracy.

Mechanical performance analysis of prestressed socket assembled concrete frame structure relying on computer simulation analysis

In order to improve the mechanical performance analysis of assembled concrete frame structure, this paper combines with computer simulation technology to analyze the mechanical performance of concrete frame structure, and uses the concrete damage plastic constitutive model provided by ABAQUS to define the nonlinear constitutive behavior of concrete. Based on the elastic-plastic model, the damage variables are added to the model, which can better reflect the performance of concrete under cyclic loading, such as stiffness degradation. In addition, this paper uses ABAQUS finite element analysis software to further analyze the structural parameters of this form of joints, and design related prestressed socket assembled concrete frame to study the seismic performance of prestressed socket assembled frame structure. Finally, the effectiveness of this model is verified by computer simulation.

Non-linear analysis of rectangular cross-sections with different reinforcements: dimensionless closed form solution

This paper presents an algorithm to solve a non-linear rectangular cross-section analysis by means of closed form equations. The equations are provided in a dimensionless form in order to provide generalizable results. The algorithm is based on the direct integration of the non-linear constitutive behaviour of the materials into the stress-block constitutive behaviour. The algorithm is based on masonry rectangular cross-sections characterized by an external axial load similar to Reinforced-Concrete cross-sections. The failure of the strengthening system and the masonry are analysed in the proposed algorithm, in an unconventional manner, analysing the behaviour even after the attainment of the ultimate strains, accounting for progressive damage. The algorithm allows to prevent the cross-section fiber analysis and the consequential iterative procedure to retrieve the neutral axis depth. Furthermore, the direct integration allows to evaluate the exact solution of the problem without numerical approximations. The results are discussed by means of several parametric analyses in terms of P–M domains and bending moment–curvature diagrams in dimensionless form. The proposed approach aims to simplify the cross-section analysis process in complex algorithms as in the risk analysis based on a large scale approach, where a large number of structures and structural members are analysed in the vulnerability process.

Physics-based neural network as constitutive law for finite element analysis of sintering

In the sintering of advanced ceramics, a digital twin consisted of a finite element model can predict the final shape and microstructure of a sintered ceramic. However, to minimise uncertainties, it is essential to continually update the mechanical properties in the digital twin using data collected from the manufacturing process. One promising approach for achieving this is through artificial neural networks (ANN). This study introduces a machine learning strategy to update the constitutive behaviour of advanced ceramics in finite element analysis of sintering deformation. A major challenge in implementing machine learning in material processing is the huge amount of data required by the training and validation of an ANN, which are often unavailable or incomplete in a real manufacturing process. This study demonstrates that the data requirement can be reduced by employing a two-step training technique. Firstly, the ANN is trained using a nonlinear constitutive law, which describes a general relationship between the strain rates and stresses. Subsequently, the weights and biases of the ANN are transferred for the retraining using limited experimental data for an actual ceramic. It is shown that such approach can successfully capture the nonlinear constitutive behaviour of fine-grained alumina without demanding for large amount of experimental data. A case study is provided, highlighting the feasibility of implementing the ANN in a commercial finite element package, to replace the constitutive law and predict the shrinkage and distortion of a sintering part. In particular, the sintered dumb-bell shape part, simulated using the retrained ANN, showed grain size and relative density that markedly different from those using the nonlinear constitutive law. It is important to note that the proposed methodology is generic and can be used to create ANNs to replace constitutive laws in finite element analysis in digital twins for a wide range of other engineering processes.

Mechanical Characterization of MWCNT-Reinforced Cement Paste: Experimental and Multiscale Computational Investigation.

Computational approaches could provide a viable and cost-effective alternative to expensive experiments for accurately evaluating the nonlinear constitutive behavior of cementitious nanocomposite materials. In the present study, the mechanical properties of cement paste reinforced with multi-wall carbon nanotubes (MWCNTs) are examined experimentally and numerically. A multiscale computational approach is adopted in order to verify the experimental results. For this scope, a random sequential adsorption algorithm was developed to generate non-overlapping matrix-inclusion three-dimensional (3D) representative volume elements (RVEs), considering the inclusions as straight elements. Nonlinear finite element analyses (FEA) were performed, and the homogenized elastic and inelastic mechanical properties were computed. The use of a multiscale computational approach to accurately evaluate the nonlinear constitutive behavior of cementitious materials has rarely been explored before. For this purpose, the RVEs were analyzed both in pure tension and compression. Young's modulus as well compressive and tensile strength results were compared and eventually matched the experimental values. Moreover, the effect of MWCNTs on the nonlinear stress-strain behavior of reinforced cement paste was noted. Subsequently, three-point bending tests were conducted, and the stress-strain behavior was verified with FEA in the macro scale. The numerical modeling reveals a positive correlation between the concentration of MWCNTs and improved mechanical properties, assuming ideal dispersion. However, it also highlights the impact of practical limitations, such as imperfect dispersion and potential defects, which can deteriorate the mechanical properties that are observed in the experimental results. Among the different cases studied, that with a 0.1 wt% MWCNTs/CP composite demonstrated the closest agreement between the numerical model and the experimental measurements. The numerical model achieved the best accuracy in estimating the Young's modulus (underestimation of 13%), compressive strength (overestimation of 1%), and tensile strength (underestimation of 6%) compared to other cases. Overall, these numerical findings contribute significantly to understanding the mechanical behavior of the nanocomposite material and offer valuable guidance for optimizing cement-based composites for engineering applications.

Mechanical Characterization of Soft Membranes with One-Shot Projection Moiré and Metaheuristic Optimization

Mechanical characterization of soft materials is a complicated inverse problem that includes nonlinear constitutive behavior and large deformations. A further complication is introduced by the structural inhomogeneity of tested specimens (for example, caused by thickness variations). Optical methods are very useful in mechanical characterization of soft matter, as they provide accurate full-field information on displacements, strains and stresses regardless of the magnitude and/or gradients of those quantities. In view of this, the present study describes a novel hybrid framework for mechanical characterization of soft membranes, combining (i) inflation tests and preliminary in-plane equi-biaxial tests, (ii) a one-shot projection moiré optical setup with two symmetric projectors that project cross-gratings onto the inflated membrane, (iii) a mathematical model to extract 3D displacement information from moiré measurements, and (iv) metaheuristic optimization hybridizing harmony search and JAYA algorithms. The use of cross-gratings allows us to determine the surface curvature and precisely reconstruct the shape of the deformed object. Enriching metaheuristic optimization with gradient information and elitist strategies significantly reduces the computational cost of the identification process. The feasibility of the proposed approach wassuccessfully tested on a 100 mm diameter natural rubber membrane that had some degree of anisotropy in mechanical response because of its inhomogeneous thickness distribution. Remarkably, up to 324 hyperelastic constants and thickness parameters can be precisely identified by the proposed framework, reducing computational effort from 15% to 70% with respect to other inverse methods.

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

We introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

A numerical two-scale approach for nonlinear hyperelastic beams and beam networks

We introduce a numerical framework for modeling hyperelastic slender trusses, oftentimes used as elementary building blocks in architected materials, which accounts for both the geometric nonlinearity inherent in thin structures and the nonlinear constitutive behavior of the base material. Akin to the FE2 method in homogenization, our approach is based on a formal, two-scale expansion. We decompose the three-dimensional (3D) description of a slender structure into a macroscale problem solving for the deformation of the beam center-line (based on an effective strain energy density, which depends on the stretching, bending, and torsional strains of the beam’s center-line) and a series of two-dimensional (2D) microscale boundary value problems (defined over the beam cross-section). We solve a series of 2D problems (covering a range of macroscopic strain combinations) for a given cross-sectional geometry and material distribution in an offline, pre-processing step. Using this pre-computed energy landscape, we solve the macroscopic boundary value problem within a geometrically exact, nonlinear discrete beam framework. We demonstrate the accuracy of this approach through a set of benchmark problems highlighting the nonlinear effects of the cross-sectional geometry and constitutive material, including material heterogeneity and pre-strains. We further illustrate how this technique is applied to truss-based architected materials consisting of networks of slender struts, which are typically made of polymeric base materials and thus allow for large nonlinear elastic deformation.

Sensitivity modelling with objective damage assessment of unreinforced masonry façades undergoing different subsidence settlement patterns

This study aims to investigate the damage response of unreinforced masonry (URM) façades resting on strip foundations and subjected to ground settlements via numerical models. The models depict the non-linear constitutive behaviour of both the masonry, via smeared cracking, and of the soil-foundation interaction, via nonlinear interface elements. The influence of building features, such as the masonry material, the length over height (L/H) ratio of the geometry, the wall thickness, the number and size of openings and different types of strip foundations (i.e. reinforced concrete and unreinforced) is examined. A sensitivity study additionally investigates the influence of the interface stiffness and its constitutive model. A Gaussian curve is used to replicate the shape of the ground settlements; These simulate the loss of support underneath the foundation due to urban subsidence. Eight settlement shapes are applied in the FE models, including both symmetric and asymmetric profiles, while the angular distortion is used to measure their intensity. A new aspect is that the extent of the induced damage to the façade is assessed objectively using a damage parameter that represents the number, length and width of cracks in a single scalar value. The method distinguishes between the applied settlement profile at the bottom of the interface and the retrieved settlement profile measured on the façade. The analyses indicate that for a value of the angular distortion equal to 2 ‰ (or 1/500), computed from the resulting deformations of the façades, 60% of the models exhibit serviceability damage associated with cracks of about 5 mm width. Accordingly, the limit values available in the literature are observed to be too optimistic and not conservative in relation to the analyses presented in this study. A key outcome is that facades with an L/H smaller or equal to 1 do not exhibit cracks wider than 1 mm. Façades on reinforced concrete foundations were observed to be less susceptible to settlement damage, compared to unreinforced ones.

Data-driven computational framework for snap-through problems

The distance-minimizing data-driven computing is an emerging field of computational mechanics, which reformulates the classical boundary-value problem as a discrete-continuous optimization problem, seeking a minimum distance between the discrete material data space and the physical constraint space. However, the optimization problem becomes non-convex due to the limit equilibrium instability in snap-through phenomenon, which makes it challenging to obtain a desired convergent solution, especially near critical points. Towards this end, we propose a data-driven computational framework by virtue of the structural stability theory for analyzing snap-through problems. First, an auxiliary linearized perturbed system is established at each equilibrium state (i.e., convergent data-driven solution), which can be solved with the stiffness-based method and data-based method. Then, a stability indicator is employed to detect the critical point and the corresponding buckling mode, which is utilized to construct a proper start point to trace the equilibrium path in the neighborhood of critical points. Several numerical examples are performed to evaluate the reliability of the proposed framework. It is proved that even for the complex problem with nonlinear constitutive behavior, the proposed framework can correctly trace the entire equilibrium path of snap-through behavior.

One-Step Patterned Contact-Resistance-Free Stretchable Strain Sensors With High Linearity and Repeatability for Body-Motion Detection

AbstractMost of the resistive-type stretchable strain sensors exhibit large sensing ranges and high sensitivity but suboptimal repeatability and linearity because of the contact-resistance mechanism. To achieve high repeatability and linearity, several sensors with contact-resistance-free structures are proposed. However, due to the different geometric layouts of the conductive materials and the insulating substrates, the patterning of these sensors requires multiple processes including photolithography and etching, which may cause high costs and are not suitable for consumer wearable applications. Here, we report a design for stretchable strain sensors based on a one-step patterned contact-resistance-free structure, i.e., the independent-sensing-and-stretchable-function structure (ISSFS). The stretchability mainly comes from the overall large deformation of the wide curved segments (the stretchable parts), while the resistance variation is mainly attributed to the tensile strain of the narrow straight segments (the sensing parts). High linearity (R2 = 0.999) and repeatability (repeatability error = 1.44%) are achieved because neither unstable contact resistance nor nonlinear constitutive and geometric behaviors occur during the sensing process. The conductive materials and the insulating substrates do not need to have different geometric layouts; thus, they can be patterned by only one-step laser cutting. The proposed sensors show great potential in body-motion detection for wearable devices.

Multi-criteria decision-making analysis and numerical simulation of the low-velocity impact response of inter-ply S2-glass/aramid woven fabric hybrid laminates

Hybrid composites have gained a lot of attention due to their superior mechanical performance and energy absorption capacity compared to single-fibre counterparts, but studies on the hybridization of aramid and S2-glass fabrics are still scarce. This paper presents a multi-criteria decision-making analysis and numerical simulation applied to the study of the performance of asymmetric inter-ply hybrids of plain-weave aramid and satin-weave S2-glass fabrics/epoxy laminates subjected to low-velocity impact. Different aramid/glass fibre ratios, impact sides and impact energies (19 J, 37 J and 72 J) were investigated. A multi-criteria decision-making analysis was performed to identify the best laminate design based on the technique for order of preference by similarity to the ideal solution which considered areal density, deformation and absorbed energy as design criteria. A novel numerical FE model based on continuum damage mechanics was developed considering non-linear material constitutive behaviour and different interlaminar and intralaminar failure modes. The material model was implemented in Abaqus/Explicit solver using a user-defined material model, and the non-linear material behaviour in the normal direction is considered by defining instantaneous stiffnesses using third-degree polynomials. The results identified single fibre laminates as the worst designs and hybrid laminates with aramid on the impact side as the best design. Besides, for similar fibre ratios, the total delamination area was larger for the impact on aramid layers.

A mean-field shear transformation zone theory for amorphous polymers

The complex nonlinear constitutive behavior of amorphous polymers has been extensively investigated in numerous experiments, displaying a strong dependence on the thermal history and loading path. Theoretical models have been proposed to conjoin the underlying mechanisms to certain aspects of mechanical features, such as yielding, strain hardening, physical aging, and the Bauschinger effect. However, an urgent need for theoretical understanding capable of fulfilling the comprehensive predictions of the featured constitutive behaviors of amorphous polymers is to be addressed. In this paper, we develop a micromechanical mean-field shear transformation zone (STZ) model to systematically describe the stress responses of amorphous polymers. The dynamics of STZ is affected by the nonequilibrium structural state described by effective temperature and also related to the anisotropic internal structure induced by the microscopical deformation. Our model exhibits the ability to fully capture the behaviors of amorphous polymers in constant rate/switch rate loading, creep, relaxation, and loading-unloading-reloading cycles. The model is further verified by reproducing the Bauschinger effect in experiments, which remains a challenge to other widely used models. Our results show that the deformation-induced material polarization, in the form of an anisotropic distribution of STZs, is the governing mechanism of the Bauschinger effect. This work establishes a comprehensive relationship between the microscopic mechanisms and the constitutive behaviors of deforming amorphous polymers, which advances the fundamental understanding of complex mechanical behaviors in amorphous glassy polymers.

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

• Recurrent neural network-based surrogate model for nonlinear, non-monotonic CMC constitutive response presented. • Physics-informed constraints employed through regularization to enforce requisite physics. • Surrogate model accurately represents non-monotonic, included reversed loading, behavior of multiple textile CMC material systems. • Efficiency over multiscale numerical approach improved several orders of magnitude. A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. The trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

Effective nonlinear responses of three-phase magnetoelectric composites

A computational method, dubbed simplified unit-cell micromechanics model, is generalized and applied to establish the effective nonlinear responses of three-phase magnetoelectric composites that are composed of two distinct magnetostrictive and piezoelectric phases embedded in elastic polymer matrices. The nature of nonlinear constitutive behavior of each constituent is expected to significantly influence the overall responses of the composites. To obtain the effective nonlinear responses, a mathematical linearization is first introduced to perform the constitutive linearization for the nonlinear materials, and the resulting constitutive equations are then unified and nested into the micromechanics model followed by iterations in order to minimize errors from the linearization process. For the purpose of comparison, we also reformulate the well-established Mori–Tanaka micromechanics model insofar as its mathematical structure is aligned with that of the simplified unit-cell model. Numerical results are first validated against limited experimental measurements available in literature. Parametric studies are then conducted in order to reveal the effect of phase constitutive laws, volume fractions, and geometries on the overall nonlinear responses of there-phase magnetoelectric composites. The contributions of this work complement those of earlier studies that prevalently devoted to two-phase magnetoelectric composites and linear magneto-electro-elastic coupled responses only.

A New Computational Method for Predicting Ductile Failure of 304L Stainless Steel

Austenitic stainless steel is useful for storing and transporting liquefied natural gas (LNG) at temperatures below −163 °C due to its superior low-temperature applications. This study develops a computational method for the failure prediction of 304L stainless steel sheet to utilize its usability as a design code for industrial purposes. To consider material degradation in a phenomenological way during the numerical calculation, the combined Swift–Voce equation was adopted to describe the nonlinear constitutive behavior beyond ultimate tensile strength. Due to the stress state-dependent fracture characteristics of ductile metal, a modified Mohr–Coulomb fracture criterion was adopted using stress triaxiality and Lode angle parameter. The numerical formulation of the elastoplastic-damage coupled constitutive model with fracture locus was implemented in the ABAQUS user-defined subroutine UMAT. To identify the material and damage parameters of constitutive models, a series of material tests were conducted considering various stress states. It has been verified that the numerical simulation results obtained by the proposed failure prediction methodology show good agreement with the experimental results for plastic behavior and fractured configuration.