Large-scale Finite Element Simulations Research Articles

A theoretical framework for predicting the heterogeneous stiffness map of brain white matter tissue

Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress-strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments.

Quantitative guided wave imaging with shear horizontal waves and deep convolutional descent full waveform inversion

Effectively determining the size and thickness distributions of corrosion damages is a vital problem in nondestructive testing (NDT). In this article, a new approach is introduced that employs magnetostrictive transducers (MST) to excite the first dispersive shear horizontal mode (SH1), and utilizes the DCD-FWI (deep convolutional descent full waveform inversion) to provide comprehensive thickness mapping in just 1 s. Compared with traditional imaging techniques, DCD-FWI network is an intrinsically full waveform inversion (FWI) based method, which yields reliable imaging results in large scale finite element simulations. Moreover, the shorter wavelength and resistance to water loading of SH guided waves bring about reliable imaging results. Combined with these advantages, the high energy transfer efficiency of the MST enhances the proposed method's robustness, as demonstrated by guided wave tomography experiments on aluminum plates.

Geomechanical reservoir modelling with Thermodynamics-based Artificial Neural Networks (TANNs)

Geological subsurface storage is a promising strategy for large-scale, cost-efficient energy storage systems. Stress sensitivity has notably influence on the long-term stability and serviceability of subsurface reservoirs set for energy storage use. The evolution of the field stress of stress-sensitive reservoirs and the associated structural deformation, often a consequence of fluid production and injection, can cause significant changes to the reservoir stress-dependent properties [1]. These properties include pore and void compressibility, and porosity. For fractured and faulted reservoirs, field stress variation may also impact fracture conductivity, alter pre-existing fractures, and reactivate faults [4].
 Current geomechanical reservoir simulators incorporate the evolution of the reservoir mechanical state by means of material constitutive modelling, typically within a Finite Element Modelling (FEM) framework. In efforts to honour the heterogeneity and multi-scale nature of subsurface reservoirs, multi-scale solution methods are commonly adopted. For a reservoir multi-scale simulation, the micro-scale problem must be iteratively solved for different input parameters, render-ing the solution method computationally exhaustive, particularly for two-way coupled problems.
 The combination of machine learning-based solution methods and FEM frameworks can address the computational inefficiency of conventional multi-scale reservoir modelling schemes. In principle, a machine learning algorithm trained to learn the constitutive behaviour of a material can replace in-built material constitutive models in a FEM framework. We resort to Thermodynamics-based Artificial Neural Networks (TANNs), a physics-based data-driven machine learning algorithm introduced in [5] for material constitutive modelling. TANNs have been shown to guarantee the thermodynamic consistency of learnt material constitutive models. The first and second laws of thermodynamics are directly encoded in the architecture of TANNs through the definition of two scalar functions, an energy potential and a dissipation function, and the computation of their differentials [3].
 TANNs can be incorporated in FEM tools, in what is referred to as TANNxFEM in [6]. We present the application of the TANNxFEM framework to geomechanical reservoir modelling. This work aims to introduce a computationally efficient reservoir modelling framework, for which uncertainty quantification is possible. The proposed framework can maximise the use of information inherently contained in high-dimensional data, and significantly reduce computation demands necessary for accurate statistical evaluation, while warranting physical and geological realism.
 TANNs are first trained on analytical material data, computed by numerical integration of an incremental, thermodynamically consistent material model presented in [2]. The trained TANNs are then imported into a user material subroutine for the finite element package Abaqus. Through an input file, the parameters of the trained neural network are read as a set of material properties. The material subroutine then evaluates the incorporated trained neural network to construct the stress and elasticity tensors necessary for large-scale finite element reservoir simulation. The above proposed framework is validated against a large-scale finite element simulation with a user material subroutine implementing the constitutive model used to first generate the training data for TANNs. The free-energy, dissipation, and the stress-strain response of the two finite element simulations are compared for model verification.

Constitutive modeling of orthotropic nonlinear mechanical behavior of hardened 3D printed concrete

3D printing of concrete is a promising construction technology, offering the potential to build geometrically complex structures without the use of cost-intensive formwork. The layer-wise deposit of filaments during the 3D printing process results in an intrinsic orthotropic mechanical behavior in the hardened state. Beyond that, the material behavior of 3D printed concrete (3DPC) is governed by a highly nonlinear behavior, characterized by irreversible deformations, strain hardening, strain softening and a degradation of the material stiffness. In this contribution, a new constitutive model for describing the orthotropic and highly nonlinear material behavior of 3DPC will be presented. It is formulated by the extension of a well-established isotropic damage plasticity model for concrete to orthotropic material behavior by linear mapping of the stress tensor into a fictitious isotropic configuration. The performance of the new model will be evaluated by finite element simulations of three-point bending tests of 3DPC samples, performed for different orientations of the loading direction relative to the printing direction and comparison with experimental results. In addition, the applicability of the model to replicate the mechanical behavior of 3DPC, manufactured by the alternative 3D printing process of binder jetting of cementitious powders, will be demonstrated by 3D finite element simulations of an arch structure with varying orientations of the loading direction relative to the layering. Overall, the proposed model provides a computationally efficient modeling approach for large-scale finite element simulations of 3DPC structures, being a promising alternative to complex and computationally expensive finite element models considering distinct interfacial planes.

Evolution of Thin-Film Wrinkle Patterns on a Soft Substrate: Direct Simulations and the Effects of the Deformation History.

Surface wrinkling instability in thin films attached to a compliant substrate is a well-recognized form of deformation under mechanical loading. The influence of the loading history on the formation of instability patterns has not been studied. In this work, the effects of the deformation history involving different loading sequences were investigated via comprehensive large-scale finite element simulations. We employed a recently developed embedded imperfection technique which is capable of direct numerical predictions of the surface instability patterns and eliminates the need for re-defining the imperfection after each analysis step. Attention was devoted to both uniaxial compression and biaxial compression. We show that, after the formation of wrinkles, the surface patterns could still be eliminated upon complete unloading of the elastic film–substrate structure. The loading path, however, played an important role in the temporal development of wrinkle configurations. With the same final biaxial state, different deformation histories could lead to different surface patterns. The finding brings about possibilities for creating variants of wrinkle morphologies controlled by the actual deformation path. This study also offers a mechanistic rationale for prior experimental observations.

Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics.

The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms, such as damage, that occur during tissue deformation. Furthermore, implementation of sophisticated material models in finite element models is essential to improve medical devices and diagnostic tools. Building on previous work toward microstructure-driven models of collagenous tissue, here we show a constitutive model based on fiber orientation and waviness distributions for skin that captures not only the anisotropic strain-stiffening response of this and other collagen-based tissues, but, additionally, accounts for tissue damage directly as a function of changes in the microstructure, in particular changes in the fiber waviness distribution. The implementation of this nonlinear constitutive model as a user subroutine in the popular finite element package Abaqus enables large-scale finite element simulations for biomedical applications. We showcase the performance of the model in fracture simulations during pure shear tests, as well as simulations of needle insertion into skin relevant to auto-injector design.

Gaussian Processes for Transfer Path Analysis Applied on Vehicle Body Vibration Problems

<div class="section abstract"><div class="htmlview paragraph">Transfer path analyses of vehicle bodies are widely considered as an important tool in the noise, vibration and harshness design process, as they enable the identification of the dominating transfer paths in vibration problems. It is highly beneficial to model uncertain parameters in early development stages in order to account for possible variations on the final component design. Therefore, parameter studies are conducted in order to account for the sensitivities of the transfer paths with respect to the varying input parameters of the chassis components. To date, these studies are mainly conducted by performing sampling-based finite element simulations. In the scope of a sensitivity analysis or parameter studies, however, a large amount of large-scale finite element simulations is required, which leads to extremely high computational costs and time expenses. This contribution presents a method to drastically reduce the computational burden of typical sampling-based simulations. For this purpose, Gaussian processes are introduced to find a probabilistic function approximation of the transfer paths. Initial results reveal that a wider solution space can be explored by only observing a few transfer path samples. This entails a time-efficient and robust technique, which inherently incorporates the variability of the input parameters. As such, Gaussian processes offer a versatile solution strategy for transfer path analyses, where simulation data as well as experimental measurements can be holistically investigated.</div></div>

Modeling cyclic behavior of unbound aggregates using two-surface plasticity theory

Various empirical rutting models have been proposed to predict the permanent deformation of aggregate base/subbase layers in pavements. Nevertheless, an analytical model is required for large-scale finite element simulation of the pavement structure. A two-surface plasticity theory is used to predict the long-term cyclic behavior and provide path-dependent material responses of aggregates. The deviatoric stresses for each aggregate were determined based on the shear stress ratio and the shear strength properties at source and engineering gradations. The proposed rutting model was optimized and validated via repeated load triaxial tests using 11 aggregates. The numerical results demonstrate that the proposed model accurately describes aggregates with low-level permanent strain and thus enables the yield surface, long-term shear strain, and path-dependent resilient modulus to be assessed. Overall, the proposed physics-based modeling approach can help understand and predict the deformation behavior of aggregates subjected to moving-wheel loads.

Understanding and Controlling Hexagonal Patterns of Wrinkles in Neo-Hookean Elastic Bilayer Structures

A controlled surface wrinkling pattern has been widely used in diverse applications such as stretchable electronics, smart windows, and haptics. Here, we focus on hexagonal wrinkling patterns because of their great potentials in realizing anisotropic and tunable friction and serving as a dynamical template for making non-flat thin films through self-assembling processes. We employ large-scale finite element simulations of a bilayer neo-Hookean solid (e.g., a film bonded on a substrate) to explore mechanical principles that govern the formation of hexagonal wrinkling patterns and strategies for making nearly perfect hexagonal patterns. In our model, the wrinkling instabilities are driven by the confined film expansion. Our results indicate robust hexagonal patterns exist at a relatively small modulus mismatch (on the order of 10) between the film and substrate. Besides, the film expansion should not exceed the onset of wrinkling value too much to avoid post-buckling patterns. By harnessing the imperfection insensitivity of one dimension sinusoidal wrinkles, we apply a sequential loading to the bilayer structure to produce the nearly perfect hexagonal patterns. Lastly, we discuss the connection between the simple bilayer model and the gradient structures commonly existed in experiments.

Phase-field modeling of multivariant martensitic transformation at finite-strain: Computational aspects and large-scale finite-element simulations

Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a penalty-regularized double-obstacle potential, and viscous dissipation. The finite-element discretization of the model is performed in Firedrake and relies on the PETSc solver library. The large systems of linear equations arising are efficiently solved using GMRES and a geometric multigrid preconditioner with a carefully chosen relaxation. The modeling capabilities are illustrated through a 3D simulation of the microstructure evolution in a pseudoelastic CuAlNi single crystal during nano-indentation, with all six orthorhombic martensite variants taken into account. Robustness and a good parallel scaling performance have been demonstrated, with the problem size reaching 150 million degrees of freedom.

A globally convergent method to accelerate topology optimization using on-the-fly model reduction

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite element simulation, which dominates the computational cost, with ROMs that reduce the cost of objective function and gradient evaluations by orders of magnitude. To guarantee convergence, we first introduce a trust-region method that employs generalized trust-region constraints and prove it is globally convergent. We then devise a class of globally convergent ROM-accelerated topology optimization methods informed by two theories: the aforementioned trust-region theory, which identifies the ROM accuracy conditions required to guarantee the method converges to a critical point of the original topology optimization problem; a posteriori error estimation theory for projection-based ROMs, which informs ROM construction procedure to meet the accuracy conditions. This leads to trust-region methods that construct and update the ROM on-the-fly during optimization; the methods are guaranteed to converge to a critical point of the original, unreduced topology optimization problem, regardless of starting point. Numerical experiments on three different structural topology optimization problems demonstrate the proposed reduced topology optimization methods accelerate convergence to the optimal design by up to an order of magnitude.

Research on Response Characteristics of Hydraulic Gate Subjected to Non-contact Underwater Explosion Load

In this paper, the response characteristics of deep-hole planar steel gates under the separate induction of bubble pulsating load are studied. Through the large-scale finite element simulation software ABAQUS, using the explicit dynamic finite element analysis method, the contact surface of the gate and the water is taken into account by the fluid-solid coupling algorithm. When the water level is constant, the gate is subjected to explosion and the impact of the generated bubble impact on the gate structure and its anti-explosion ability are analyzed. The equivalent stress, displacement, and equivalent plastic strain of the gate under six different cases were simulated. Then, the effect of bubble pulsating load on the stress characteristics of the gate and the anti-explosion ability of the gate were summarized.

On-demand Direct Design of Polymeric Thermal Actuator by Machine Learning Algorithm

The design optimization of thermal-driven actuators is a challenging task because the performance depends on multiple materials parameters, structural parameters, and working conditions. In this work, we adopted large scale finite element simulation together with machine learning algorithm to fulfill the on-demand design of thermal actuators. Finite element analysis was used to simulate the performance of thermal actuator with two-layer structure, which generated large amount of dataset by considering the variation of parameters including the moduli, thermal expansion coefficient, sample thickness and length, and temperature. Support vector regression (SVR) was adopted to establish the relationship between multiple input parameters and the resulting contact pressure. Thereafter, a simple interior point algorithm was used to achieve the on-demand design based on the SVR model. The contact pressures of thermal actuator constructed from the optimized parameters deviated less than 15% of the target values.

Research on Deformation Model of Welding Material Based on Inherent Strain Finite Element Prediction Method

The paper first introduces the concept of inherent strain and the theory and method of predicting welding deformation by the inherent strain finite element method. Studies have shown that the inherent strain exists in the weld and the near seam area, and it is also related to factors such as welding heat input and plate thickness. Through the use of large-scale finite element simulation software ANSYS, the inherent strain finite element prediction method is applied to the welding deformation of the outer gantry assembly material of forklift, which provides effective reference data for future welding work of forklift gantry materials.

Bonding property and seismic behavior of reinforced concrete and finite element analysis

Reinforced concrete is one of the most widely used building materials in civil engineering, water conservancy and hydropower engineering, and construction engineering; in the course of its service, due to human or natural factors, reinforced concrete structures will gradually age, or be damaged or even destroyed. Therefore, in order to evaluate the durability of reinforced concrete structures, it is necessary and meaningful to study the problems of bonding and seismic performance. Based on the separation model and nonlinear constitutive relation, the finite element model of reinforced concrete beam specimens is established by using large-scale general finite element simulation software ANSYS. The corrosion rate, failure morphology, bond strength, and stress of steel bars are analyzed. The influence of slippage on the bonding properties of the test piece, and the effects of axial compression ratio, steel reinforcement ratio, steel bar strength, concrete strength, etc., on the seismic performance of the test piece were studied, in order to further utilize ANSYS on the bonding and resistance of reinforced concrete. A comprehensive study of performance provides a reference.

Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses

When a sample is cyclically loaded under a mean stress or strain, incremental strain ratcheting or mean stress relaxation phenomena are usually observed. Experiments show that for metallic materials there is generally no full mean stress relaxation as well as saturation of macroscopic strain ratcheting. In contrast, most macroscopic constitutive models produce both quantities in excess, and complex sets of additional internal variables must be introduced to improve the modeling. Little attention has been paid to model such phenomena using polycrystal aggregates especially going up to the regime of cyclic mechanical stability. In this work based on an elementary crystal plasticity model for FCC crystals and large scale finite element simulations, it is shown that the interaction between different grains is sufficient to cater for such complex phenomena. Light is shed on how different regions of the polycrystal accommodate each other and how the classical definition of constant rate strain ratcheting or a zero mean stress is nearly impossible to apply to a polycrystalline aggregate. In addition, it is shown that even if a macroscopic stable hysteresis stress strain loop is observed, ratcheting phenomena can still be observed at the local scale. The distributions of different constitutive quantities within a polycrystal are also analyzed which gives a new insight into what is happening inside a polycrystal in terms of stress and strain redistribution. In particular, the existence of evolving bimodal distributions of stress and accumulated plastic strain is evidenced and related to the occurrence of plastic shakedown and incomplete mean stress relaxation. Two numerical criteria to detect strain ratcheting are finally proposed and discussed.

Three-dimensional ultrasonic wave simulation in laminated CFRP using elastic parameters determined from wavefield data

A numerical modeling of ultrasonic testing (UT) for a carbon fiber reinforced plastic (CFRP) material is presented. Due to the heterogeneity caused by the several unidirectional lamina stacked at different angle, the CFRP shows unique mechanical properties and leads to ultrasonic wave skewing and scattering. In this paper, we present a large-scale finite element (FE) simulation based on the image-based modeling approach. We model the mesoscopic heterogeneity of the CFRP in the numerical discretization by using the voxel of the same size. The determination of the anisotropic elastic stiffness of each lamina is essential to the FE simulation. Here, we estimated the parameters via an inversion method using wavefield visualization data. The parameters were fed into the 3D wave propagation simulations in the laminated CFRPs. The simulation and experimental results showed good agreement with respect to the wave velocity and the spread of the ultrasonic waves. It was found that the mesoscopic modeling and parameterization of the elastic stiffness of the lamina were important for the UT simulation.

Large-scale magnetostatic field calculation in finite element micromagnetics withH2-matrices

Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element / boundary element method (FEM/BEM) by Fredkin & Koehler involves a densely populated matrix with unacceptable numerical costs for problems involving a large number of degrees of freedom $N$. By using hierarchical matrices of $\mathcal{H}^2$ type, we show that the memory requirements for the FEM/BEM method can be reduced dramatically, effectively converting the quadratic complexity $\mathcal{O}(N^2)$ of the problem to a linear one $\mathcal{O}(N)$. We obtain matrix size reductions of nearly $99\%$ in test cases with more than $10^6$ degrees of freedom, and we test the computed magnetostatic energy values by means of comparison with analytic values. The efficiency of the $\mathcal{H}^2$-matrix compression opens the way to large-scale magnetostatic field calculations in micromagnetic modeling, all while preserving the accuracy of the established FEM/BEM formalism.

Static and dynamic testing and modelling of aluminium joints with flow-drill screw connections

A new component test suited for quasi-static and dynamic testing of flow-drill screw connections is presented. The component specimen was made of two different aluminium alloys, and included connections with two material combinations. Large-scale finite element simulations were carried out of each test, in which the connections were modelled with a constraint-based macroscopic model. An improvement of the connection modelling technique is presented. The model was calibrated to cross tension, cross mixed and single lap-joint tests, and validated with peeling and the component tests.

A multiscale approach to modeling formability of dual-phase steels

A multiscale modeling approach is used to predict how the formability of dual-phase (DP) steels depend on the properties of their constituent phases and microstructure. First, the flow behavior of the steels is predicted using microstructure-based finite element simulations of their 3D representative volume elements, wherein the two phases (ferrite and martensite) are discretely modeled using crystal plasticity constitutive models. These results are then used to calibrate homogenized constitutive models which are then used in large-scale finite element simulations to compute the forming limit diagrams (FLDs). The multiscale approach is validated by predicting the FLDs of two commercial DP steels and comparing the predictions with experimental measurements. Subsequently, the approach is used to compute flow behavior and FLDs of a series of ‘virtual’ DP steels, constructed by varying the microstructural parameters in the commercial DP steels. The results of these computations suggest that combining the ferrite from one of the two commercial steels with the martensite of the other and optimizing the phase volume fractions can yield ‘virtual’ steels with substantially improved properties. These include a material with an FLD0 (plane strain) that exceeds those of the commercial steels by 75% without a degradation in strength; and a material with a flow strength (0.2% offset) that exceeds those of the commercial steels by ~30% without degradation of formability.