Inelastic Material Behavior Research Articles

Modelling and analysing failure modes of buried pipelines perpendicularly crossing landslide boundaries

The pipeline response to shallow translational landslides is investigated using semianalytical and numerical methods. The orthogonality of a pipeline and the landslide boundary is considered in this study. In the finite element (FE) analyses, ground movements are simplified as spatially distributed horizontal transverse deformation. The pipe-soil interaction is modelled accounting for large ground deformation, inelastic material behavior, and special contact conditions at the soil–pipe interface. Pipeline failure patterns are summarized based on a series of FE models with varying diameter thickness ratios of the pipe and soil conditions. According to the FE analysis results and the published literature, the existing failure criteria are evaluated and extended to cover new failure modes. The dynamic evolution in the predominant failure modes due to the pipe elongation effects is investigated. A semianalytical solution for the sliding distance to the onset of pipe wall wrinkling is given. In addition, a pipeline failure criterion is proposed based on the relative stiffness. This dimensionless parameter is correlated with failure features, including failure modes, sliding distances to failure initiation, and failure positions. The reliability of the proposed FE model and failure prediction methodology is validated using published results from centrifuge tests and FE analyses. Simple charts for failure prediction in terms of relative stiffness parameters are provided. The proposed approach allows efficient and reliable safety evaluation on X65 steel pipelines subjected to horizontal transverse ground deformation without conducting numerical modelling.

Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)

The mechanical behavior of inelastic materials with microstructure is very complex and hard to grasp with heuristic, empirical constitutive models. For this purpose, multiscale, homogenization approaches are often used for performing reliable, accurate predictions of the macroscopic mechanical behavior of solids and structures. Nevertheless, the calculation cost of such approaches is extremely high and prohibitive for real-scale applications involving inelastic materials.Recently, data-driven approaches based on machine learning and, in particular, deep learning have risen as a promising alternative to replace ad-hoc constitutive laws and speed-up multiscale numerical methods. However, such approaches require huge amounts of high quality data, fail to give reliable predictions outside the training range and they lack a rigorous frame based on the laws of physics and thermodynamics. As a result, their application to model materials with complex microstructure in inelasticity is not yet established.Here, we propose the so-called Thermodynamics-based Artificial Neural Networks (TANN) for the constitutive modeling of materials with inelastic and complex microstructure. Our approach integrates thermodynamics-aware dimensionality reduction techniques and thermodynamics-based deep neural networks to identify, in an autonomous way, the constitutive laws and discover the internal state variables of complex inelastic materials. The ability of TANN in delivering high-fidelity, physically consistent predictions is demonstrated through several examples both at the microscopic and macroscopic scale.The efficiency and accuracy of TANN in predicting the average and local stress–strain response, the free-energy and the dissipation rate is demonstrated for both regular and perturbed two- and three-dimensional lattice microstructures in inelasticity. TANN manage to identify the internal state variables that characterize the inelastic deformation of the complex microstructural fields. These internal state variables are then used to reconstruct the microdeformation fields of the microstructure at a given state. Finally, a double-scale homogenization scheme (FEM×TANN) is used to solve a large scale boundary value problem. The high performance of the homogenized model using TANN is illustrated through detailed comparisons with microstructural calculations at large scale. An excellent agreement is shown for a variety of monotonous and cyclic stress–strain paths.

Experimental study on one-way arching masonry specimens under monotonic and cyclic loads

Characterizing the behavior and the mechanical properties of masonry assemblies subjected to out-of-plane static loading is a fundamental step towards the understanding of their response to more complex loading scenarios. The more challenging case is that of arching walls where the load resistance mechanism couples bending and axial components. This study presents a combined experimental and theoretical effort aiming at gaining insight into the behavior of such arching walls. The experimental phase is conducted on small-size one-way specimens that are comprised of two or four masonry units loaded in a four-point-bending scheme. The experimental methodology aims at collecting new quantitative data on the response under monotonic and cyclic loadings. The 2-block configuration mimics the basic form of arching walls and focuses on the interaction between the masonry units and the mortar layer, features that are essential for any quantitative, analytical or numerical assessment of such walls. The 4-block configuration mimics the more complex response when additional mortar joints are part of the structural system. Along with the global load–displacement curve, the experiments also monitor the arching force, as well as local aspects such as the axial deformations at the tensed and compressed extreme fibers of the mortar joints. The latter aims at studying the constitutive behavior of the mortar joints. The complete set of test results is then used as a benchmark for comparison with an analytical model. The comparison examines the model capabilities, reveals further aspects of the physical behavior, and explores the cracking process, the deformation profile, and the effect of inelastic behavior of the mortar material. The combined experimental and theoretical findings reveal the spectrum of phenomena governing the behavior of masonry walls and highlight the role of the arching mechanism through macro and micro perspectives.

Expanding application of the voussoir beam analog to horizontally bedded and passively bolted flat-roof excavations using the discrete element method

The voussoir beam analog is a well-established analytical method that has been successfully applied to the design of flat-roof excavations in discontinuous rockmasses. However, application of voussoir beam theory is limited to very specific conditions. Previous authors have attempted to account for more realistic loading and geometric conditions, but have not presented systematic or verified methods to account for variations in inelastic material behavior or supported roof geometry. This study presents multiple original numerical models that methodically assess the effects of increasing material and geometric complexity on voussoir beam mechanical behavior and develops adjustments to the Diederichs & Kaiser (1999) analytical solution to account for variations in post-peak material behavior and the interactions between multiple passively bolted layers. A step-by-step guide is presented for implementing these adjustments.

Microbuckling of viscoplastic composites by the high-fidelity generalized method of cells micromechanics

The high-fidelity generalized method of cells (HFGMC) micromechanical analysis is employed for the prediction of microbuckling stresses of composite materials which are composed of elastic–viscoplastic constituents. The inelastic material behavior is represented by a unified viscoplasticity theory which can model non-proportional loading paths, namely it is capable of providing the effect of axial loading on the reduction of shear modulus which dominates the microbuckling. By applying an incremental procedure and in conjunction with the instantaneous stiffnesses of the viscoplastic material, an eigenvalue problem at each time step is established by the HFGMC micromechanical method, which is modified to include the buckling terms arising from the linearization of the nonlinear equations of equilibrium. These buckling terms are provided by HFGMC analysis which predicts the local stress field and the effective current tangent properties of the composite. The present approach is verified by comparison of its predictions with an exact solution that can be established in the special case of composites that consist of periodic viscoplastic layers. Applications are given for the prediction of the microbuckling stresses of bi-layered, continuously reinforced and aligned short-fiber viscoplastic composites. In addition, the microbuckling stresses of viscoplastic lattices and layered plates are presented.

Experimental and numerical analysis of cord\u2013elastomer composites

In this paper, experimental and numerical investigations on cord–elastomer composites are presented. A finite-element model is introduced, which was developed within the framework of an industrial project. The model is able to simulate an elastomer matrix with inserted cords as load bearing elements and to predict the strains and stresses in cord and elastomer sections. The inelastic material behavior of the elastomer matrix and the yarns is described by corresponding material models suitable for large deformation processes. With the help of a specially developed demonstrator bellows, which is similar to an air spring, the simulation results are compared with experiments. For this purpose, the digital image correlation method is used to determine the deformations on the outer surface of the demonstrator bellows and to calculate the strains on and between the cords. The comparison of the results shows that the employed simulation method is very well suited to predict the strains in these cord–elastomer composites.

Comparative investigation on the mechanical behavior of injection molded and 3D-printed thermoplastic polyurethane

3D printing opens up new possibilities for the production of polymeric structures that would not be possible with injection molding. However, it is known that the manufacturing method might have an impact on the mechanical properties of manufactured components. To this end, the mechanical behavior of test specimens made of thermoplastic polyurethane is compared for two different manufacturing methods. In particular, the SEAM technology (screw extrusion additive manufacturing) is compared to a conventional injection molding process. Uniaxial tension test specimens from both manufacturing methods are analyzed in two testing sequences (multi-hysteresis tests to analyze inelastic properties and uniaxial tension until rupture). To get as less perturbation as possible, the 3D-printed samples are printed with only one strand per layer. Moreover, a correction approach based on optical measurements is applied to determine the true cross-sectional area of the test specimens. The mechanical tests reveal that the inelastic material behavior is the same for both manufacturing methods. Instead, 3D-printed specimens show lower maximal stretch values at rupture and an increased variance in the results, which is related to the surface structure of 3D-printed specimens.

Plastic analysis of steel arches and framed structures with various cross sections

This paper presents a displacement-based numerical methodology following the Euler-Bernoulli theory to simulate the 2 nonlinear behavior of steel structures. It is worth emphasizing the adoption of co-rotational finite element formulations considering large displacements and rotations and an inelastic material behavior. The numerical procedures proposed considers plasticity concentrated at the finite elements nodes, and the simulation of the steel nonlinear behavior is approached via the Strain Compatibility Method (SCM), where the material constitutive relation is used explicitly. The SCM is also applied in determining the sections bearing capacity. Moreover, the present numerical approach is not limited to a specific structural member cross-sectional typology, with the residual stress models introduced explicitly in subareas of steel cross-sections generated by a 2D discretization. Finally, results consistent with the literature and with low processing time are presented.

Three-dimensional nonlinear response of utility tunnels under single and multiple earthquakes

The behavior of utility lined tunnels under single and multiple earthquakes is studied under the assumptions of inelastic material behavior of the liner and the rock medium and full three-dimensionality. Inelasticity in both media is modeled by the theory of damage mechanics. The seismic response of the rock-structure-fluid system is parametrically studied in order to assess the degree of influence of the various parameters on that response. These parameters are material parameters, such as Poisson's ratio of concrete liner and rock, geometrical parameters, like depth of the tunnel from the ground surface or the liner thickness, seismic load parameters, like seismic intensity, multiplicity of earthquakes and seismic incident angle, and interaction parameters, like rock-structure interaction and fluid-structure interaction. Thus, the seismic response of utility tunnels, as influenced by the above parameters, is assessed and useful conclusions are drawn.

Investigation of deformation behavior of PETG-FDM-printed metamaterials with pantographic substructures based on different slicing strategies

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a so-called pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In this substructure, two planes, which consist of two arrays of beams being orthogonally aligned to each other, are interconnected by cylinders/pivots. Different inner geometries were taken into account and additively manufactured by means of fused deposition modeling technique using polyethylene terephthalate glycol (PETG) as filament material. To further understand the effect of different manufacturing parameters on the mechanical deformation behavior, three types of specimens have been investigated by means of displacement-controlled extension tests. Different slicing approaches were implemented to eliminate process-related problems. Small and large deformations are investigated separately. Furthermore, 2D digital image correlation was used to calculate strains on the outer surface of the metamaterial. Two finite-element simulations based on linear elastic isotropic model and linear elastic transverse isotropic model have been carried out for small deformations. Standardized extension tests have been performed on 3D-printed PETG according to ISO 527-2. Results obtained from finite-element method have been validated by experimental results of small deformations. These results are in good agreement with linear elastic transverse isotropic model (up to about [Formula: see text] of axial elongation), though the response of large deformations indicates a nonlinear inelastic material behavior. Nevertheless, all samples are able to withstand outer loading conditions after the first rupture, resulting in resilience against ultimate failure.

Inelastic behavior and destruction of materials under isothermal and non-isothermal, simple and complex loads

The paper deals with mathematical modeling of inelastic behavior and destruction of structural materials (steels and alloys) under simple, complex, isothermal and non-isothermal loads in repeated and long-term exposures to thermomechanical loads. The modeling is carried out on the basis of the applied theory of inelasticity, which belongs to the class of flow theories in combined hardening. The main provisions are formulated and a summary of the main equations of the applied theory of inelasticity is given. The material functions closing the applied theory of inelasticity are determined, and the connection of the defining functions with the material ones is given. Further, the results of some original experimental studies are considered, which are compared with the results of calculations based on the applied theory of inelasticity. In all studies, inelastic deformation is performed under conditions repeated and long-term exposures to thermomechanical loads. Inelastic deformation of AL-25 aluminum alloy samples under uniaxial tension-compression under both isothermal and non-isothermal cyclic loading is considered. Inelastic deformation under complex loading along the two-link polyline deformation paths with different deformation rates under high temperature conditions is studied on tubular 30HGSA alloy samples. Inelastic deformation of tubular stainless steel 304 samples under complex loading at elevated temperatures is considered. Soft cyclic loading is performed along two-link stress trajectories with different fracture angles. At the end of the links of the stress trajectory, exposure is carried out for 8 hours. The results of the calculations based on various theories used in the calculations are analyzed. Inelastic deformation and destruction of samples made of 12X18N9 stainless steel under rigid cyclic deformation under both isothermal and non-isothermal loads is considered. The duration of the loading cycle is 4 minutes, which allowed the effects of healing and embrittlement to appear at a high temperature. There is a significant difference (much higher) in the number of cycles to failure in common-phase and anti-phase modes of changes in force strain and temperature.

Sustainability Characteristics of Damaged Carbon Fiber Composites

Usage of composites has increased in many fields of application ranging from space to repair and rehabilitation. Damage of composites in the form of cracking or de-lamination is quite common during its life. Performance of the composites after damage with or without repair is an indicator to one of its sustainability aspects. Here in this study, the damage parameter from the point of cracking is studied beyond normal yield considerations using inelastic material model to assess its remaining life. It is observed that, based on the load quantity of damage occurrence, sustainability is measured as life cycle analysis in terms of remaining life that can change significantly if one accounts for inelastic material behaviour.

Macro-Scale Numerical Modeling of Unreinforced Brick Masonry Squat Pier Under In-Plane Shear

Numerical modeling of brick masonry behaviour under different performance conditions has always remained a challenging task. Several modeling strategies have been developed for masonry, in general, through the course of time that have been simplified to speed up modeling and analysis duration. This ranges from a simplified strut model to a highly discontinuous micro-scale nonlinear model. With the current advent of high-speed computing and modeling tools, more realistic numerical modeling of masonry is now possible. In this paper, the strategy adopted is based on macro-scale modeling, where isotropic material properties are considered for the homogenous continuum. ABAQUS is used as a state-of-the-art finite element-based analysis and modeling tool. The Concrete Damage Plasticity (CDP) model is used for simulating inelastic material behaviour of brick and mortar, which is available in the ABAQUS library. This material model can be used in both implicit and explicit schemes of integration but the explicit procedure is highly preferred as it overcomes the convergence issues. Various parameters required for CDP modeling of brick and mortar are adapted from literature. The model is assembled in two parts, first part is modeled for masonry with both elastic and plastic properties, while the other part simulates a rigid beam at the top of the masonry part to create a uniform in-plane shear loading effect. The masonry part has been fixed at the bottom with free vertical ends, while horizontal in-plane displacement was applied to the top rigid beam. The load-displacement curves were generated from these models for monotonic push, to compare them with the envelopes of experimental results, loaded similarly. Since brick masonry is a highly disjointed material, it is a complicated procedure to develop an exact model and predict its exact behaviour. However, the overall representative load-displacement curve developed numerically was in good agreement with the ones produced experimentally.

A Lagrangian meshfree mesoscale simulation of powder bed fusion additive manufacturing of metals

AbstractWe present a powder‐scale computational framework to predict the microstructure evolution of metals in powder bed fusion additive manufacturing (PBF AM) processes based on the hot optimal transportation meshfree (HOTM) method. The powder bed is modeled as discrete and deformable three‐dimensional bodies by integrating statistic information from experiments, including particle size and shape, and powder packing density. Tractions in Lagrangian framework are developed to model the recoil pressure and surface tension. The laser beam is applied to surfaces of particles and substrate dynamically as a heat flux with user‐specified beam size, power, scanning speed, and path. The linear momentum and energy conservation equations are formulated in the Lagrangian configuration and solved simultaneously in a monolithic way by the HOTM method to predict the deformation, temperature, contact mechanisms, and fluid‐structure interactions in the powder bed. The numerical results are validated against single track experiments. Various powder bed configurations, laser powers, and speed are investigated to understand the influence of dynamic contact and inelastic material behavior on the deformation, heat transfer, and phase transition of the powder bed. The formation of defects in the microstructure of 3D printed metals, including pores, partially, and unmelted particles, is predicted by the proposed computational scheme.

A single Gauss point continuum finite element formulation for gradient-extended damage at large deformations

Some years ago, a family of large deformation continuum finite elements based on reduced integration was investigated by Reese (2005), Schwarze and Reese (2011) and Frischkorn and Reese (2015). Many structural components with different kinds of elastic and inelastic material behavior were considered and these elements showed accurate results while being more efficient than similar three-dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to non-local damage and fracture. To this end, the incorporation of the gradient-extended damage plasticity model for large deformations of Brepols et al. (2020) into the framework of reduced integration-based continuum elements is presented. For the sake of brevity, the present work is restricted to solids with only one integration (Gauss) point in the center of the element. The weak form of the formulation, which is based on a two-field variational functional closely related to the enhanced-assumed strain (EAS) method is extended by the weak form of the micromorphic balance equation. The steps required in order to transform the extended formulation into a stable, robust and efficient single Gauss point concept are described in detail. Due to the analogy to fully-coupled thermomechanical problems, the derivation of a novel micromorphic hourglass stabilization is based on earlier contributions of the research group. Therein, the Taylor series expansion of all constitutively dependent quantities plays a crucial role. Representative numerical examples of quasi-brittle and ductile fracture reveal the accuracy and efficiency of the proposed approach. Besides the ability to deliver mesh-independent results, the framework is especially suitable for constrained situations in which conventional low-order finite elements suffer from well-known locking phenomena.

Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization

Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for linear elastic beams undergoing finite rotations). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D – through the addition of torsional deformation modes and the handling of 3D rotations – results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body's boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach.

Deep convolutional neural networks in structural dynamics under consideration of viscoplastic material behaviour

The aim of the present study is to develop a deep convolutional neural network (DCNN) to predict geometrically and physically nonlinear structural deformations. Training data is obtained by short-time measurements in shock tubes, wherein metal plates are subjected to impulsive loadings, leading to viscoplastic vibrations and inelastic deflections. Due to the fact that, in literature, feed forward neural networks (FFNN) are more distributed for applications in structural mechanics, comparative calculations are presented between structural deformations based on DCNNs and FFNNs. Special attention is focused on the ability of DCNNs to capture also path-dependent deformations inside the network, which is an essential feature for inelastic material behaviour.

Geometric and material nonlinear analysis of thin-walled members with arbitrary open cross-section

Abstract This paper describes the formulation of a thin-walled beam finite element for arbitrary open cross-sections, including doubly-, singly- and non-symmetric cross-sections. The formulation is developed within the co-rotational framework of OpenSees – an open source program available for the simulation of structural and geotechnical systems. The formulation accounts for eccentricity between the shear centre and the centroid of the cross-section, as well as warping. Both elastic and inelastic material behaviour is considered. The stiffness relation for the displacement-based beam element is established based on the Green-Lagrange strain. A local cross-section transformation matrix is derived to relate the end actions with the axial force acting at the centroid to the end actions with the axial force acting at the member axis system. The elastic and inelastic performance of the beam finite element is demonstrated through a series of instability problems comprising doubly-, singly- and non-symmetric sections subjected to compression, bending, and torsion. The buckling and post-buckling behavior predicted by the beam element is shown to be in close agreement with the results of shell finite element models, thereby demonstrating its reliability.

On the micromechanics of deep material networks

We investigate deep material networks (DMNs), recently introduced by Liu et al. [Comput. Method Appl. M., vol. 345, pp. 1138–1168, 2019], from the viewpoint of classical micromechanics at small strains. We aim to establish the basic micromechanical principles of deep material networks, shed light on the characteristics of the building blocks and introduce a simple, robust and fast solution technique for inelastic deep material networks.In their original formulation, DMNs are solely trained by linear elastic data, but applied to nonlinear and inelastic problems with astonishing accuracy. We clarify this phenomenon theoretically by showing that, to first order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization. Our argumentation applies to arbitrary microstructures comprising nonlinear generalized standard materials at small strains. The main technical tool is a Volterra series approximation of the stress of a generalized standard material, which we adapt from nonlinear dynamical systems theory.Next, we establish that deep material networks inherit thermodynamic consistency and stress-strain monotonicity from their phases. These properties root in the definition of the DMN as a tree of hierarchical laminates and contrast with other applications of neural networks to the approximation of material laws, where consistency and monotonicity typically cannot be guaranteed far away from the training set.Last but not least, we introduce rotation-free DMNs with arbitrary directions of lamination and exploit a novel formulation, uniting the implementation of DMNs of arbitrary tree topology and multi-phase laminates, and apply our insights to microstructures of industrial complexity.

Effect of Manufacturing Process on Lined Pipe Bending Response1

Abstract The effects of manufacturing process on mechanically lined pipe structural performance are investigated. Alternative manufacturing processes are considered, associated with either purely hydraulic or thermo-hydraulic expansion. The problem is solved numerically, accounting for geometric nonlinearities, local buckling phenomena, inelastic material behavior and contact between the two pipes. A three-dimensional model is developed, which simulates the manufacturing process in the first stage of the analysis and, subsequently, proceeds in the bending analysis of the lined pipe. This integrated two-stage approach constitutes the major contribution of the present research. Thermo-hydraulically expanded lined pipes are examined, with special emphasis on the case of partially heated liners, and reverse plastic loading in the liner pipe wall has been detected during depressurization. Furthermore, the numerical results show that the thermo-mechanical process results in higher mechanical bonding between the two pipes compared with the purely mechanical process and that this bonding is significantly influenced by the level of temperature in the liner pipe. It is also concluded that the value of initial gap between the two pipes before fabrication has a rather small effect on the value of liner buckling curvature. Finally, numerical results on imperfection sensitivity are reported for different manufacturing processes, and the beneficial effect of internal pressure on liner bending response is verified.