Isotropic Material Behavior Research Articles

Research of Acoustic Emission Characteristics and Applicability of Artificial Intelligence for Source Localization

Within this research, the deployment of artificial intelligence for the localization of acoustic emissions (AE) is being investigated. In detail, series of experiments were conducted on a plate of granite with homogeneous and isotropic material behavior. Acoustic emissions could be generated by the breaking of pencil leads, as well as the impact of rice grains and steel balls on 81 specific positions with a distance of 50 mm in both horizontal axes to each other. The response of the system was recorded using 16 acoustic emission sensors, of which 8 sensors were positioned on each surface side of the plate. In further steps the data could be processed, so that the resulting characteristic signal features could be translated into spec-trograms and furthermore being used as input for the artificial intelligence. Additionally, the corresponding source locations appeared as labels. Both, the signal features as well as the labels, could be implemented in the process of supervised learning using a convolutional neural network (CNN). The results of this network indicated a validation accuracy of over 99% as well as a low loss value by classifying the inserted features to the right labels. Thus demonstrates the excellent applicability of artificial intelligence for the source localization of acoustic emission (AE).

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.

Stress-strain curve estimation from micropillar compression with transverse contraction effect

The Focused Ion Beam (FIB) technique and the associated compression testing capabilities provide versatile access to understanding the microstructural behaviour of materials. Among many objectives, determining the stress-strain relationship from experimental or numerical force-displacement data remains a fundamental challenge. However, for micropillers under compression, the inside deformation constraint is complex like in components and the transformation of a measured force-displacement curve into an accurate uniaxial stress-strain curve is not straightforward. In this context, in a previous numerical based analysis for perfect volume constancy or incompressibility the determination of reliable and accurate stress-strain curves from nonlinear load-deformation curves of micropillers was already verified. In the case of transverse contractions, however, numerical simulations of micropillers provide unexpected force-displacement behaviour, i.e. their force-displacement curves are almost superimposing and are very close to the force-displacements for incompressibility. This effect implies, that transverse contraction would have no contributions in micropillar compression. In contrast, independent simulations using a single finite element accurately explore the true uniaxial stress-strain behaviour for the whole range of transverse contractions. These are considered as the reference behaviour and are also treated by an analytical expression. With the presented new stress-strain estimation approach, including transverse contraction, any force-displacement curve from a micropillar under compression can be stepwise corrected. The first step of the new stress-strain curve estimation method, including transverse contraction, is carried out in the same way as in the preceding analysis for incompressibility, followed by further steps to obtain the final true stress-strain curve. Although the presented numerical analysis is exemplarily performed for the behaviour of fused silica, but the stress-strain approach is in the same manner generally applicable for a material behaviour with other stress-strain curves. The assumption behind is isotropic and nonlinear material behaviour.

Improved concept of representative directions: cluster approach

The concept of representative directions is a method for constitutive modelling that generalises uniaxial constitutive equations to the general multiaxial case. The simplicity of the concept allows both novice and experienced users to develop advanced material models, covering a wide range of nonlinear phenomena. This paper introduces the cluster approach, a new version of the concept that operates with clusters of fibres. Similar to the original concept, the cluster approach ensures objectivity and inherits the thermodynamic consistency of uniaxial models. The paper details the computational algorithms and presents numerical tests, highlighting the advantages of the new approach. Due to the smearing of fibres in orientation space, the cluster approach efficiently represents initially isotropic material behaviour with fewer clusters, making it computationally more efficient than the classical concept of representative directions. As a demonstration, the paper shows the adequacy of the cluster approach in capturing the actual inelastic behaviour of certain polymers and metals.

The rock mechanical relevance of anisotropy in tunnel design

AbstractThe assumption of an isotropic material behaviour is still common practice for tunnel design. Strictly speaking, this assumption is only valid if the influence of directional dependencies on the resulting deformations and stresses is marginal. In lithologies that have a high degree of anisotropy, such as shales and phyllites, the orientation characteristics of material properties such as strength and stiffness should be taken into account in order to avoid serious misinterpretations of the bearing capacity and deformation characteristic of the surrounding rock and the tunnel lining. The main focus is to accurately distinguish between the different types and terminology of anisotropy.

A framework for neural network based constitutive modelling of inelastic materials

Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes the behaviour of the new materials. The formulation of accurate constitutive equations is generally complex and time consuming. Hence, suitable machine learning strategies may be used to render this process obsolete and bridge the gap between experimental data and finite element analysis. In this work, a generic stress update procedure is presented that is suitable for the modelling of rate-independent, elastic or inelastic, isotropic or anisotropic material behaviour. The proposed strategy is based on a recurrent neural network architecture and must be trained on stress and strain data sequences that represent physical or numerical experiments. A training strategy based on gradient-free optimisation is presented. It is shown that piecewise linear behaviour, such as uniaxial elasto-plasticity, can be represented exactly. Further numerical examples include uniaxial damage mechanics and elasto-plasticity under plane strain conditions. An efficient criterion for the verification of thermodynamic consistency is proposed and applied to the trained stress update models. The strategy is compared to GRU or LSTM based architectures and shown to offer advantages.

Composite material: A review over current development and automotive application

The quantity and quality of studies undertaken to find new applications for the material indicate its importance in the modern world. It used to be accepted wisdom that a design engineer would only employ tried-and-true components, but times have changed. The field of current material engineering would be severely lacking without using composites. Designers of all stripes now have better options for utilizing cheaper, less labour-intensive materials thanks to advancements in composite technology. Composites have several potential applications and are currently employed in some of them. This research describes the process for creating composite propeller shafts and examines their vibrational qualities. This research will look into the results of switching out steel drive shafts for composite ones. Two of the most crucial parts of a composite drive shaft's construction are the shaft itself and the couplings. Critical speed, static torque, and nonlinear isotropic material behaviour are assumed for adhesive joints, but these assumptions are disregarded for metal and a composite shaft. For the design and accompanying analysis, finite element software is used (ANSYS). As a result, the research provides crucial information for developing a composite drive shaft.

Remarks on bifurcation of an inflated and extended swellable isotropic tube

We consider a tubular membrane whose mechanical behavior is defined by a strain energy density function that combines the neo-Hookean model with the Demiray model. Both, the neo-Hookean and the Demiray models are isotropic material models, which found their application in the modeling of the mechanical behavior of biological soft tissue. This tubular membrane is subjected to an inner pressure, an axial stretch, and a change in the material volume due to swelling or deswelling. The interplay between the cylinder geometry and the loading conditions and different instability modes, namely, bulging bifurcation, bending bifurcation, and prismatic bifurcation, are studied. It is shown that a change in the material volume has a strong effect on the occurrence of these bifurcation modes because a change in the material volume may stabilize the cylinder against a particular bifurcation mode and may trigger another bifurcation mode at the same time. Despite the restriction to isotropic material behavior, this article shows that the material response to pressure, axial stretch, and material volume change is quite complex.

Data‐driven finite element computation of microstructured materials

AbstractThis paper presents a model‐free data‐driven strategy for linear and non‐linear finite element computations of open‐cell foam. Employing sets of material data, the data‐driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem.The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open‐cell microstructure and the properties of the polyurethane material. Their computation provides the required stress‐strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to derive suitable material data sets for the different cases of (non‐)linear and (an‐)isotropic material behavior efficiently. The numerical example of a rubber sealing illustrates possible areas of application, and the proposed strategy's versatility.

A constitutive model for modeling the mechanical behavior of the peltate leaf of Stephania japonica (Menispermaceae)

AbstractIn this contribution, we present a continuum mechanical transversely isotropic viscoelastic material model at finite deformations to model the mechanical behavior of the plant tissues of peltate leaves of Stephania japonica. Not many research efforts have been devoted to investigate the mechanical properties of this type of leaf shape. The model is obtained by postulating a particular Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on the structural tensors to account for the transversely isotropic material behavior. The evolution equations are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The numerical example reveals that the proposed model is capable of predicting the mechanical response of the real plant tissues at different loading rates.

Texture-based residual stress analysis of laser powder bed fused Inconel 718 parts.

Although layer-based additive manufacturing methods such as laser powder bed fusion (PBF-LB) offer an immense geometrical freedom in design, they are typically subject to a build-up of internal stress (i.e. thermal stress) during manufacturing. As a consequence, significant residual stress (RS) is retained in the final part as a footprint of these internal stresses. Furthermore, localized melting and solidification inherently induce columnar-type grain growth accompanied by crystallographic texture. Although diffraction-based methods are commonly used to determine the RS distribution in PBF-LB parts, such features pose metrological challenges in their application. In theory, preferred grain orientation invalidates the hypothesis of isotropic material behavior underlying the common methods to determine RS. In this work, more refined methods are employed to determine RS in PBF-LB/M/IN718 prisms, based on crystallographic texture data. In fact, the employment of direction-dependent elastic constants (i.e. stress factors) for the calculation of RS results in insignificant differences from conventional approaches based on the hypothesis of isotropic mechanical properties. It can be concluded that this result is directly linked to the fact that the {311} lattice planes typically used for RS analysis in nickel-based alloys have high multiplicity and less strong texture intensities compared with other lattice planes. It is also found that the length of the laser scan vectors determines the surface RS distribution in prisms prior to their removal from the baseplate. On removal from the baseplate the surface RS considerably relaxes and/or redistributes; a combination of the geometry and the scanning strategy dictates the sub-surface RS distribution.

Neural networks meet hyperelasticity: A guide to enforcing physics

In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using different sets of invariants as inputs, a hyperelastic potential is formulated as a convex neural network, thus fulfilling symmetry of the stress tensor, objectivity, material symmetry, polyconvexity, and thermodynamic consistency. In addition, a physically sensible stress behavior of the model is ensured by using analytical growth terms, as well as normalization terms which ensure the undeformed state to be stress free and with zero energy. In particular, polyconvex, invariant-based stress normalization terms are formulated for both isotropic and transversely isotropic material behavior. By fulfilling all of these conditions in an exact way, the proposed physics-augmented model combines a sound mechanical basis with the extraordinary flexibility that neural networks offer. Thus, it harmonizes the theory of hyperelasticity developed in the last decades with the up-to-date techniques of machine learning. Furthermore, the non-negativity of the hyperelastic neural network-based potentials is numerically examined by sampling the space of admissible deformations states, which, to the best of the authors’ knowledge, is the only possibility for the considered nonlinear compressible models. For the isotropic neural network model, the sampling space required for that is reduced by analytical considerations. In addition, a proof for the non-negativity of the compressible Neo-Hooke potential is presented. The applicability of the model is demonstrated by calibrating it on data generated with analytical potentials, which is followed by an application of the model to finite element simulations. In addition, an adaption of the model to noisy data is shown and its extrapolation capability is compared to models with reduced physical background. Within all numerical examples, excellent and physically meaningful predictions have been achieved with the proposed physics-augmented neural network.

Thermomechanically coupled theory in the context of the multiphase-field method

The modeling and simulation of microstructure evolution is usually subject to the multiphase-field method. In this context, thermomechanical coupling is often neglected, even when non-isothermal phase transformations are considered. Using a simplified example, the present work shows that this assumption is not justified for small strains and small strain rates with respect to a non-vanishing coefficient of thermal expansion. To this end, both a thermomechanically coupled and a thermomechanically weakly coupled theory are briefly revisited. The difference between the coupled and the weakly coupled theory regarding the growth of an inclusion is discussed. The considered elastoplastic inclusion, subjected to eigenstrains, is embedded in an elastoplastic matrix under load. It is shown, that the weakly coupled theory overestimates the growth of the inclusion, and, thus, the volume concentration, compared to the coupled theory. Moreover, only the application of the coupled theory reflects a load-induced anisotropic growth of the inclusion, which exhibits an isotropic material behavior, due to non-vanishing uniaxial Neumann boundary conditions. In addition, it is shown that the smaller the heat conduction coefficient, the more pronounced the anisotropic growth of the inclusion.

Implementation of subloading surface model for hyperelastoplasticity with nonlinear kinematic/isotropic hardening based on reference and intermediate configurations

In this paper, the elastoplastic behavior of isotropic materials under finite strains is modelled and simulated under consideration of the subloading surface concept. Using the subloading surface model has many advantages, such as the ability of modeling more smoothly transition from elastic to plastic state and also more realistic modeling of the Bauschinger effect. For this purpose, three time integration algorithms are utilized in the reference and intermediate configurations in the present study. The first algorithm is based on a time integration scheme, available in the literature, and the second time integration is proposed by tensor exponential-based time integration and the third one is represented by a standard backward Euler time integration scheme. In the second proposed time integration, which is defined in the intermediate configuration, there is no need to use co-rotational objective time rates. However, in the third one, although it is based on the intermediate configuration, the Zaremba–Jaumann co-rotational rate is employed. Besides, in the second two time integrations, the constitutive equations are derived based on the unknown tensors defined in the intermediate configuration and as a consequence there is no restriction of using different hyperelastic models. For case studies, diverse deformation gradient tensors with and without volume changes are considered. These studied cases are accomplished for SUS 304 stainless steel and a glassy polymer (oriented PET). The obtained results of some cases are compared with available results in the literature. The agreement among the predicted results in this paper and the results from literature is good.

Reduced order modeling of modular parameter dependent structures based on proper orthogonal decomposition and mesh tying

AbstractA model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.

Mechanical investigations of the peltate leaf of Stephania japonica (Menispermaceae): Experiments and a continuum mechanical material model.

Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work.

An advanced constitutive model for transversely isotropic rock - Evaluation of two different regularization approaches

The mathematical description of the material behavior of rock is a demanding task in engineering practice. Rock is classified as a frictional cohesive material characterized by highly nonlinear mechanical behavior with irreversible deformation, strain hardening, strain softening and degradation of stiffness. In addition, depending on the origin of a particular rock type, the orientation of minerals and grains as well as the formation of stratification planes lead to inherent anisotropic behavior. Especially in stratified rock types like shales or phyllites, often the special case of transversely isotropic material behavior is encountered. In a previous work, a novel continuum-based material model for describing both, the highly nonlinear and transversely isotropic material behavior of rock, denoted as TI-RDP model, was presented. By means of the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, an established isotropic damage plasticity model for rock was extended. In this contribution two different regularization approaches, which are well established for isotropic models, i.e., the mesh-adjusted softening modulus and the implicit gradient-enhancement, are adopted for the TI-RDP model. Based on uniaxial tension and triaxial compression tests considering different orientations of the principal material directions with respect to the direction of axial loading, their capabilities are assessed in terms of predicting the direction-dependent mechanical behavior in a mesh-insensitive manner.

3D deformation modeling of CrAlN coated tool steel compound during nanoindentation

The finite element method (FEM) nanoindentation simulations of nitride hard coatings are either focused on the coating only or contain an axisymmetric model of the coated compound with isotropic material behavior. Moreover, the material model parameters are optimized at only one particular indentation load. The current work aims to develop a 3D FEM model for studying deformation behavior of a CrAlN PVD coated HS6-5-2C tool steel compound during nanoindentation at varying indentation loads. A machine learning (ML)-based algorithm was used to characterize the coating microstructure. This information allowed to set up a 3D FEM model containing a digital clone of the compound microstructure along with the local orientations of the grains embedded into a larger elastically modelled frame. The material model parameters such as Young's modulus E, yield stress Y, strain hardening coefficient B and strain hardening exponent n for coating, interlayer and substrate were determined by fitting the simulated force-displacement curves to the experimental ones through an iterative optimization approach at four different indentation loads. An overall good agreement between the simulated and experimental force-displacement curves along with physically reasonable material model parameters was achieved. The obtained yield stress of CrAlN coating was comparable to ceramics. Moreover, elastic-plastic deformation in interlayer and elastic deformation in substrate at indentation depth below 10 % of the coating thickness was observed. This necessitates the interlayer and substrate consideration for FEM nanoindentation simulations of PVD coated compounds as in the present study. Therefore, the used modeling approach, based on orthotropic elastic material law for the coating combined with 3D digital clone of the compound microstructure, was successfully implemented and validated for low as well as high indentation loads.

An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split

AbstractThis work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws—ordinary differential equations—that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton–Raphson scheme of the nonlinear finite element framework. The implementation of membrane and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is also shown that the proposed formulation can be straightforwardly applied to model boundary viscoelasticity of 3D bodies.

Data-driven finite element computation of open-cell foam structures

This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem.The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open-cell microstructure and the properties of the polyurethane material. Their computation provides the required stress–strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to derive suitable material data sets for the different cases of (non-)linear and (an-)isotropic material behavior efficiently.Exemplarily, we compare data-driven finite element computations with linearized and finite deformations and show that in a data-driven computation the linear kinematic is sufficiently accurate to capture the material’s non-linearity up to 50% of straining. The numerical example of a rubber sealing illustrates possible areas of application, the expenditure, and the proposed strategy’s versatility.