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Abstract: Abstract As a reduced order homogenization approach, the FEM-Cluster based reduced order Analysis method (FCA) proposed by Cheng et al. provides an efficient approach to predict the nonlinear effective properties of heterogeneous materials. In its improved version, the clustered Minimum Complementary Energy (MCE) approach is adopted for the computations of incremental strain–stress relation. This work mainly focuses on the mathematical foundations of FCA with clustered MCE. The completeness of the interaction matrix as the clustered self-equilibrium stress space is proved, and the prediction error of FCA solution is analyzed. The deductions also reveal that some bases of the clustered self-equilibrium stress space denoted by the interaction matrix may contradict the basic hypothesis of the cluster-based reduce order methods, and they are mainly responsible for the error of FCA. According to this observation, a spectral analysis algorithm is developed to refine the interaction matrix and improve the accuracy of FCA. PubDate: 2022-06-01
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Abstract: Abstract Forced vibration analysis is an indispensable process for the design of a rotating component. However, rather expensive nonlinear static and linear frequency response analyses are usually accompanied by a frequency domain analysis. The traditional mode-superposition method (MSM) effectively reduces the cost of the frequency response analysis. However, the nonlinear static analysis of earlier processes remains as the computational bottleneck. In this paper, the application of the hyper-reduction method will be proposed along with the model order reduction (MOR) framework for rotating component forced vibration analysis. The energy-conserving sampling and weighting (ECSW) method will be employed for the nonlinear iterative computation. The pre-stressed stiffness matrix of the reduced finite elements (FEs) resulting from the ECSW will be used for the post computation stage. Also, a variety of MOR will be attempted for the performance comparison, including MSM, proper orthogonal decomposition (POD)-based reduced order model (ROM), and a hybrid approach. It is found that the present ECSW-combined MOR will significantly relieve the computational bottleneck, provide a minimal loss of accuracy, and be compatible with both nonlinear and linear analyses of the rotating component forced vibration analysis. PubDate: 2022-06-01
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Abstract: Abstract In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis. PubDate: 2022-06-01
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Abstract: Abstract Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. PubDate: 2022-06-01
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Abstract: Abstract We construct two-dimensional, two-phase random heterogeneous microstructures by stochastic simulation using the planar Boolean model, which is a random collection of overlapping grains. The structures obtained are discretized using finite elements. A heterogeneous Neo-Hooke law is assumed for the phases of the microstructure, and tension tests are simulated for ensembles of microstructure samples. We determine effective material parameters, i.e., the effective Lamé moduli \(\lambda ^*\) and \(\mu ^*\) , on the macroscale by fitting a macroscopic material model to the microscopic stress data, using stress averaging over many microstructure samples. The effective parameters \(\lambda ^*\) and \(\mu ^*\) are considered as functions of the microscale material parameters and the geometric parameters of the Boolean model including the grain shape. We also consider the size of the Representative Volume Element (RVE) given a precision and an ensemble size. We use structured and unstructured meshes and also provide a comparison with the FE \(^2\) method. PubDate: 2022-06-01
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Abstract: Abstract This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials following the strategy developed by Boldrini et al. (Methods Appl Mech Eng 312:395–427, 2016). Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the assumption of finite strain, in terms of fractional derivatives. A novel degradation function, which properly couples stress response and damage evolution for viscoelastic materials, is proposed. We obtain a set of differential equations that accounts for the evolution of motion, damage, and temperature. In the present work, for simplicity, this model is numerically solved for isothermal cases by using a semi-implicit/explicit scheme. Several numerical tests, including fitting with experimental data, show that the developed model accounts appropriately for damage in viscoelastic materials for small and finite strains. Non-isothermal numerical simulations will be considered in future works. PubDate: 2022-06-01
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Abstract: Abstract The massive growth in data-centers has led to increased interest and regulations for management of waste heat and its utilization. This work seeks to develop a combined Digital-Twin and Machine-Learning framework to optimize such systems by controlling both the ventilation and the cooling of the bases of data units/processors in the system. This framework ascertains optimal cooling strategies to deliver a target temperature in the system using a minimum amount of energy. A model problem is constructed for a data-center, where the design variables are the flow rates and air-cooling at multiple ventilation ports and ground-level conduction-based base-cooling of processors. A thermo-fluid model, based on the Navier–Stokes equations and the first law of thermodynamics, for the data-center is constructed and a rapid, stencil-based, iterative solution method is developed. This is then combined with a genomic-based machine-learning algorithm to develop a digital-twin (digital-replica) of the system that can run in real-time or faster than the actual physical system, making it suitable as either a design tool or an adaptive controller. Numerical examples are provided to illustrate the framework. PubDate: 2022-06-01
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Abstract: Abstract We present a new scalar damage model for dynamic brittle fracture. In contrast to existing damage theories, the internal damage variable is alternatively derived based on energy limiter theory, directly tightening to its physical meaning. Finite element implementation for the developed approach at small strain towards localized brittle failure is given. We integrate the energy decomposition into the theory to eliminate nonphysical damaged phenomenon when cracks develop in compression domain, while the crack band theory is employed to treat mesh sensitivity. As a result, the current model does not involve any length scale parameter, and therefore nor diffusive equation of damage evolution characterizing the degradation of material stiffness is required. Two simple methods for estimating crack-tip velocity and dissipated energy are provided. Discrete forms of governing equation are solved by a simple staggered scheme in an effective manner. Several numerical examples for dynamic brittle fracture including crack branching are studied. PubDate: 2022-06-01
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Abstract: Abstract In this work, the geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) model is further generalized to study the mechanical responses and rate-dependent fracture behaviors of viscoelastic materials. The viscoelasticity is generated by directly incorporating the classical viscoelastic constitutive relation in the form of the Generalized Maxwell Model, which is expressed as Prony-series type expansion, into the GC-NOSBPD framework. A strain-based scalar damage variable only driven by elastic energy, whose evolution follows a rate-independent law, is proposed to describe the progressive growth of the mode-I crack. Combining the rate-independent damage variable and viscoelasticity results in a rate-dependent damage model in the hypothesis that the fracture of viscoelastic material is driven by both elastic and viscous components of the energy. The fidelity of this model is established in the absence of damage by comparison with the benchmark solution for the viscoelastic response of a 3D bar subjected to various load histories. Further, the proposed model is employed to simulate two quasi-static fracture tests under various loading rates: a three-point bend fracture test for concrete and a double-cantilever-beam delamination test for rubber interface. These numerical results agree well with experimental tests, showing that the proposed model can effectively capture rate-dependent crack propagation. PubDate: 2022-06-01
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Abstract: Abstract This work develops a systematic uncertainty quantification framework to assess the reliability of prediction delivered by physics-based material models in the presence of incomplete measurement data and modeling error. The framework consists of global sensitivity analysis, Bayesian inference, and forward propagation of uncertainty through the computational model. The implementation of this framework on a new multiphase model of novel porous silica aerogel materials is demonstrated to predict the thermomechanical performances of a building envelope insulation component. The uncertainty analyses rely on sampling methods, including Markov-chain Monte Carlo and a mixed finite element solution of the multiphase model. Notable features of this work are investigating a new noise model within the Bayesian inversion to prevent biased estimations and characterizing various sources of uncertainty, such as measurements variabilities, model inadequacy in capturing microstructural randomness, and modeling errors incurred by the theoretical model and numerical solutions. PubDate: 2022-06-01
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Abstract: Abstract Many drugs interact with ion channels in the cells of our heart and trigger heart rhythm disorders with potentially fatal consequences. Computational modeling can provide mechanistic insight into the onset and propagation of drug-induced arrhythmias, but the effect of drugs on the mechanical performance of the heart remains poorly understood. Here we establish a multiphysics framework that integrates the biochemical, electrical, and mechanical effects of drugs, from cellular excitation to cardiac contraction. For the example of the drug dofetilide, we show that drug concentrations of 5x and 8x increase the heart rate to 122 and 114 beats per minute, increase myofiber stretches by 5%, and decrease overall tissue relaxation by 6%. This results in inter-ventricular and atrial-ventricular dyssynchronies and changes in cardiac output by \(-2.5\) % and +7%. Our results emphasize the need for multiphysics modeling to better understand the mechanical implications of drug-induced arrhythmias. Knowing how different drug concentrations affect the performance of the heart has important clinical implications in drug safety evaluation and personalized medicine. PubDate: 2022-06-01
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Abstract: Abstract This work considers epistemic uncertainty in the form of fuzzy parameters in a multibody forward dynamics simulation of the human leg with a prosthetic foot. The thigh and shank are modelled as rigid bodies while the prosthetic foot, modelled after a carbon spring prosthesis, is represented by a predeformed geometrically exact beam model. A variational integrator is used to solve the equations of motion in the forward dynamics simulation and the Graph Follower algorithm is used to include epistemic uncertainty. Two cases are considered. Large movements are examined using a pendulum swing, similar to the swing phase during human gait. To validate the deformation of the prosthesis, a second case is examined, where the prosthesis is fixed in space and deforms under the weight of the body segments. Both cases consider a fuzzy Young’s modulus and determine the envelopes of the resulting uncertain target output. The Graph Follower algorithm was modified to substantially increase computational efficiency, enabling the propagation of fuzzy uncertainty through the complex multibody model with rigid and flexible bodies. PubDate: 2022-05-22
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Abstract: Abstract Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress–relaxation curves, pressure–volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic. PubDate: 2022-05-13
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Abstract: A Correction to this paper has been published: 10.1007/s00466-022-02145-2 PubDate: 2022-05-09
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Abstract: Abstract Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour. In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening. PubDate: 2022-05-09
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Abstract: Abstract Peridynamics is a non-local continuum theory which is able to model discontinuities in the displacement field, such as crack initiation and propagation in solid bodies. However, the non-local nature of the theory generates an undesired stiffness fluctuation near the boundary of the bodies, phenomenon known as “surface effect”. Moreover, a standard method to impose the boundary conditions in a non-local model is not currently available. We analyze the entity of the surface effect in ordinary state-based peridynamics by employing an innovative numerical algorithm to compute the peridynamic stress tensor. In order to mitigate the surface effect and impose Dirichlet and Neumann boundary conditions in a peridynamic way, we introduce a layer of fictitious nodes around the body, the displacements of which are determined by multiple Taylor series expansions based on the nearest-node strategy. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method. PubDate: 2022-05-09
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Abstract: Abstract From large scale structures such as bridges and cranes to small-scale structures such as lattices, mechanical structures today increasingly consist of “tuneable parts”: parts with a simple geometry described by a small set of strongly varying parameters. For example, although a bridge is a macroscale structure with a complex geometry, it is made from simple beams, bolts and plates, all of which depend on spatially varying, geometrical parameters such as their length-to-width ratio. Accelerating this trend is the concurrent improvement of, on one hand, Additive Manufacturing techniques that allow for increasingly complex parts to be manufactured and, on the other, structural optimization techniques that exploit this expanded design space. However, this trend also poses a challenge to current simulation techniques, as for example the Finite Element Method requires large amounts of elements to represent such structures. We propose to exploit the large conformity between parts inside the mechanical structure through construction of semi-analytic “Parametrized Superelements”, built by meshing with solid elements, reduction to a fixed interface and approximation of the reduced stiffness matrices. These new elements can be employed next to standard elements, enabling the simulation of more complex geometries. The technique we propose is applied to lattice structures and provides a flexible, differentiable, more accurate but still efficient way to simulate their elastic response. A net gain in total computation time occurs after simulating more than twenty lattices. As such, the proposed method enables large-scale parameter exploration and optimization of lattice structures for improved energy absorption, mass and/or stiffness. PubDate: 2022-05-07
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Abstract: Abstract In this contribution we propose an efficient and simple finite-element procedure for the approximation of open boundary problems for applications in magnetostatics. In these problems, the interaction of the solid with external space plays a crucial role because of the magnetic stray fields that arise. For this purpose, the infinite region under consideration is approximated by a sufficiently large domain. This region is then divided into a so-called interior domain and an exterior domain. As an essential prerequisite, we assume linear behavior of the (large) exterior domain. The latter is then reduced to the degrees of freedom of the connecting line (2D)/connecting surface (3D) of both domains via static condensation. The proposed finite element scheme can be seen as an alternative to established methods for infinite domains. These methods often require semi-analytical solutions to describe the behavior in the exterior domain, which can be difficult to obtain if heterogeneous structures are present. The proposed finite element procedure is not subject to any restrictions with regard to the topology of the exterior space. After a general introduction of the numerical scheme, we apply the method to problems of magnetostatics with nonlinear behavior in the interior domain. PubDate: 2022-05-06
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Abstract: Abstract When analysing complex structures with advanced damage or material models, it is important to use a robust solution method in order to trace the full equilibrium path. In light of this, we propose a new path-following solver based on the integral of the rate of dissipation in each material point, for solving problems exhibiting large energy dissipating mechanisms. The method is a generalisation and unification of previously proposed dissipation based path-following solvers, and makes it possible to describe a wider range of dissipation mechanisms, such as large strain plasticity. Furthermore, the proposed method makes it possible to, in a straightforward way, combine the effects from multiple dissipation mechanisms in a simulation. The capabilities of the solver are demonstrated on four numerical examples, from which it can be concluded that the proposed method is both versatile and robust, and can be used in different research domains within computational structural mechanics and material science. PubDate: 2022-05-05
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Abstract: Abstract Virtual element methods (VEM) provide great flexibility in solving numerical problems defined on arbitrarily shaped polygonal or polyhedral discretizations. In this paper, we develop a framework for two dimensional elastic problems defined on complex topology models using high-order virtual element methods from an engineering perspective. The VEM discrete formulations are detailedly derived following the rule used in standard FEM. An arbitrarily complex model is first embedded into a rectangular domain which is then discretized into a structured grid. The elements intersecting with the boundaries are further adaptively refined through a quad-tree refinement strategy controlled by a subdivision level or an approximation error. An optimization method is proposed to avoid the generation of tiny elements and two averaged schemes for stress recovery in post-processing are discussed. The behavior of the proposed VEM is thoroughly studied and the results are compared with analytical solutions and that obtained from FEM. The heavy burden placed on meshing complex CAD geometries is greatly alleviated and the convergence studies confirm the accuracy and convergence of the method. PubDate: 2022-05-05
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