Scipedia: 14th WCCM-ECCOMAS Congress 2020

A Bi-Fidelity DG-IMEX Method for the Linear Transport Equation with Random Parameters

Scipedia content — Thu, 11 Mar 2021 17:49:03 +0100

In this paper, we introduce a bi-fidelity stochastic collocation (SC) method for the linear transport equation with diffusive scaling and high-dimensional random inputs characterized by random variables. For the high-fidelity linear transport model, the asymptotic-preserving Discontinuous Galerkin implicit-explicit method in the micro-macro decomposition framework is used. We discuss different choices of low-fidelity models and conduct the corresponding uniform error estimates for the bi-fidelity method. Extensive numerical tests are presented to validate our bi-fidelity SC method.

A Class of Examination of Fiber Orientation Dependency and Failure with Multi-Scale Simulation

Scipedia content — Thu, 11 Mar 2021 17:37:02 +0100

This paper examines the mechanical behavior of the short fiber reinforced plastic (SFRP) considering the microstructure using multi-scale simulation. The SFRP, which the microstructure consists of resin and fiver, has a rate, thermal, and fiber orientation dependency. The mechanical property is predicted by matrix and fiber properties. However, the properties by material testing are different from the prediction. Thus, this paper decides each microscopic material parameter on microstructure by the least-square method using the experimental data. Comparing the macro simulation results using homogenized values and the experimental results shows microstructure influences the macroscopic behavior. Moreover, the numerical examples compare the results under two types of tensile speed and three fiber orientation types. The present work completes the multi-scale simulation using a simple microstructure considering fiber orientation and strain rate.

A Legendre-Based Displacement Field for Two-Dimensional Digital Image Correlation

Scipedia content — Thu, 11 Mar 2021 17:37:40 +0100

Two-dimensional digital image correlation (DIC) is one of the most commonly used measurement methods for displacement and deformation of specimen surfaces in the field of experimental mechanics. Since its presentation, DIC has been evolving with many new ideas and assets. This paper proposes a new displacement field, based on Legendre polynomials and compares it with conventional second-order polynomial, commonly used in DIC's method.

A Smeared Crack Modelling Approach for Aggregate Interlock and Mixed Mode Fracture of Concrete

Scipedia content — Thu, 11 Mar 2021 17:08:39 +0100

The intention of this contribution is the numerical description of the rarely investigated phenomenon of mixed mode fracture in plain concrete. Since cracks in concrete are typically subjected to both normal and shear displacements, a new material model called fictitious rough crack model (FRCM) is proposed which combines mode I fictitious crack models with aggregate interlock models. For modelling the mixed mode behavior as the result of coexisting cohesive concrete behavior and aggregate interlock stresses along concrete cracks, mode I behavior is considered as the main influence on crack formation at the crack tip and mode II behavior (aggregate interlock) is assumed to occur when translations are induced along the crack surfaces (slip). The combination of these tension-softening and shear-transfer laws and the resulting shear and normal stresses of both mechanisms in the crack characterizes the main idea of the model. Well-known experimental benchmark problems are solved both for validation of the proposed model as well as for comparison with renowned concrete models of commercial FE software. The analysis shows that the FRCM can simulate the transition from mode I fracture to mixed mode fracture in the structural response while the comparison with commercial numerical approaches demonstrates the lack of appropriate consideration of aggregate interlock and mixed mode behavior in commercial FE software.

A stable variational formulation for non-ordinary state-based peridynamics

Scipedia content — Thu, 11 Mar 2021 16:57:03 +0100

The paper builds a stable variational formulation for the non-ordinary state-based peridynamics (NOSB-PD). Firstly, a new force state vector is reformulated by introducing the first Piola-Kirchhoff stress in continuum mechanics. The consistency of the new governing equation of the proposed pridynamic model and classical continuum mechanics is proved. Secondly, a stable variational formulation of non-ordinary state based peridynamics is developed to unify the boundary conditions in peridynamcis and continuum mechanics. The zero mode oscillations of non-ordinary state based peridynamics is also eliminated by penalty method in numerical implementation. Numerical examples are illustrated to validate the proposed method. Numerical solutions obtained by the proposed method also indicate that the proposed method can well capture the general nonlinear behavior of solid materials.

An Electromechanical Micropolar Peridynamic Model for Isotropic and Orthotropic Materials

Scipedia content — Thu, 11 Mar 2021 17:19:06 +0100

A micropolar peridynamic model for in-plane electro-mechanical behavior of isotropic and orthotropic solids is presented. The analytical implicit formulation of the electrical part of the model is based on the definition of a proper microelectrical energy function and a specific electrical inelastic deformation parameter. A compatibility condition and a constitutive relationship has been derived and thus the electrical stiffness operator has been obtained. The electrical formulation is then coupled with a mechanical micropolar peridynamic formulation that accounts for full orthotropy and isotropy as special case. A distinctive aspect of the formulation is the use of continuous trigonometric functions, for the mechanical and electrical bond properties with respect to the principal material axes. The obtained unified model is capable to predict the mechanical response and the electrical conduction of elastic brittle materials taking into account the influence of cracks and other defects along with mechanical and/or electrical orthotropy. The proposed model has been applied to predict the electric field potential in isotropic and orthotropic square laminae, and to simulate a coupled electromechanical problem.

An improved bond-based peridynamic model based on Timoshenko beam theory

Scipedia content — Thu, 11 Mar 2021 16:42:12 +0100

An improved constitutive model based on Timoshenko beam theory is proposed for bond-based peridynamics. The motion and force governing equations of the bond are established by introducing Timoshenko beam element to simulate the interaction between the particles including the bond tension-rotation-shear coupling effects. Since the axial displacement, transverse displacement and relative rotation angle of the bond are considered in the model, it can overcome the limitation of Poisson’s ratio in the classical bond-based peridynamics model. Three kinds of peridynamic parameters, corresponding to the compressive, shear and bending stiffness of the bond, are introduced to keep the consistence between the strain energy of the peridynamic model and that of the continuum mechanics under arbitrary deformation field. Moreover, an energy-based failure criterion, involving the maximum stretch, shear strain and rotation angle limits of the bond, is proposed to capture the progressive failure of general quasi-brittle materials. The validation of the proposed model is verified by comparing the simulation results to the experiment observations and analytical solution. Numerical results show that this improved model can be widely used to predict the nonlinear deformation, crack propagation and progressive failure of materials with variable Poisson’s ratio under complex loading conditions.

Computational Modeling of the Seismic Response of Tensegrity Dissipative Devices Incorporating Shape Memory Alloys

Scipedia content — Wed, 10 Mar 2021 15:07:20 +0100

Infrastructures and buildings must have sufficient protection for design level earthquake excitations while minimizing major damage to comply with existing seismic design criteria. This paper explores the computational modeling of a tensegrity based brace, which helps dissipate energy while preventing inter-story drifts. The proposed brace integrates a D-bar tensegrity structure, shaped like a rhombus, with Shape-Memory Alloy (SMA) cables or tendons. These tendons grow austenitic-martensiticaustenetic (solid to solid) transformations, which make them more susceptible to mechanical stress when taking strain, and amplifying the stress into broad superelastic hysteresis, even after repeated mechanical cycles that require strains of up to 6% 8%. In addition in this article two special classes of the tensegrities are discussed namely 2D and 3D braces. 3D braces have been proven more efficient because of an enhaced capacity of energy dissipation, and also due to their improved safety against buckling. The effectiveness of the planned bracing paves the way to the development of innovative systems of seismic energy dissipation that combine tensegrity concepts with superelasticity.

Computational Modelling of Thermomechanical Behaviour of Cast Irons: Effect of Boundary Conditions

Scipedia content — Thu, 11 Mar 2021 16:41:41 +0100

In this work, a microstructure-based modelling approach is employed to investigate the performance of cast irons under thermal loading. Cast irons have a complex microstructure with graphite particles of different shapes, sizes and orientations embedded in an iron matrix. As a result of the mismatch in coefficients of thermal expansion of constituents, even a purely thermal load can cause failure. To evaluate this behaviour, representative volume elements of cast-iron microstructures are studied using finite-element simulations. Specific inputs in the models are provided based on statistical analysis of SEM micrographs. Further, the influence of boundary conditions is discussed. The obtained results demonstrate that the failure in the examined unit cells is sensitive to the adopted modelling assumptions, as well as the boundary conditions.

Contact Problems for Interface Cracks Under Harmonic Shear Loading

Scipedia content — Thu, 11 Mar 2021 17:46:36 +0100

The linear crack between two dissimilar elastic isotropic half-spaces under normal harmonic shear loading is considered. To take the crack faces interaction into account we assumed that the contact satisfies the Signorini constraints and the Coulomb friction law. The problem is solved numerically using the iterative process the solution changes until the distribution of physical values satisfying the contact constraints is found. The numerical convergence of the method with respect to the number of the Fourier coefficients and mesh size is analysed. The effects of material properties and values of the friction coefficient on the distribution of displacements and contact forces are presented and analysed. Special attention is paid to the size of the contact zone and the results are compared with the classical model solutions obtained for the static problems with and without friction.

Crack-Tracking In The Regularized XFEM: A Viable Alternative To Nonlocal And Cohesive Zone Models

Scipedia content — Thu, 11 Mar 2021 17:39:34 +0100

We have devised a crack-tracking methodology for general crack paths in elasto-damaging materials based on the regularized extended finite element method. The resulting procedure is in-between nonlocal models, where the discontinuity surface is replaced by a finite width zone, and cohesive zone models, where the discontinuous regime is governed by a traction-separation law.

Cyclic Behaviour of Beam-Column Dowel Connection in Precast Elements

Scipedia content — Thu, 11 Mar 2021 17:09:04 +0100

Disruption of structural continuity due to the inherent nature of the connections poses a challenge in seismic design of precast concrete structures. Seismic behaviour of portal frame systems typically used for industrial halls, is greatly influenced by the beam-column connections. Capacity design dictates that these connections should have an elastic behaviour under seismic horizontal actions to allow for the dissipation mechanisms to develop in the desired area, in this case the base of the columns. If this connection fails, the entire structure is compromised and may lead to a premature, partial, or even total collapse. Efforts are currently underway for a better understanding of the seismic response of precast structures (e.g. SAFECAST project). In this study, the test setups tried to replicate as closely as possible the behaviour of a commonly used beam-column assembly connected by steel dowels. The test specimens were designed as full scale precast concrete elements. This experimental campaign aimed to determine the failure mechanisms of the assemblies and to check if capacity design requirements were satisfied. Three setups have been tested according to the experimental protocol described in the SAFECAST report. The first test specimen was subjected to a unidirectional monotonic loading protocol with the aim of observing the maximum failure force and deformation. The resulted maximum displacement was used to determine the displacement step increment for the cyclic loading protocol of the following two specimens. In all the cases, failure has occurred in the region of the dowel connection. The failure mechanism was either because of dowel yielding, concrete spalling around the dowel, or a combination of both, consistent with results obtained by other researchers. The results have showed that the column was far from reaching its failure capacity and a premature failure has occurred in the connection area, which should be avoided in common practice. Marius G.L. Moldovan, Mihai Nedelcu and Zsolt Kovacs

Determination of Continuum Fracture Mechanics Parameters for Molecular Dynamics Simulations

Scipedia content — Thu, 11 Mar 2021 17:29:42 +0100

This study is aimed at determination of continuum fracture mechanics parameters such as stress intensity factors, T-stress and higher-order terms, from molecular dynamics simulation performed for copper plate with narrow diamond-like crack. For this purpose, an embedded atom potential (EAM) available in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics (MD) software is utilized to accurately describe mixed-mode crack growth. The stresses calculated from MD method using the virial theorem are used for over-deterministic method for extracting stress intensity factors, T-stress and higher order terms of Williams series expansion. It is shown that the algorithm of the over-deterministic method can be generalized for MD calculations and gives the reasonable value of continuum fracture mechanics parameters. The obtained value of stress intensity factors, T-stresses and higher order terms are compared with the theoretical values for an infinite plate with the central crack under Mode I loading and Mixed Mode loading conditions for several values of the mixity parameter which defines the type of Mixed Mode loading.

Effect of Climatic Actions On Buildings with Internal Insulation and Thermal Breaks: Multi-Scale Approach and Thermo-Hydro-Mechanical Modeling

Scipedia content — Thu, 11 Mar 2021 17:13:35 +0100

For buildings designed with internal insulation, thermal bridges at the junction between slabs and walls are a common issue, since they create heat loss from inside of the building. Thermal break systems (TBS), which are composed of structural elements (rebars and steel profiles) and insulation material, are used to reduce this heat loss and to transfer shear forces from the slab to the walls. Insulation system of TBS generates a temperature gap from wall to slab. As a consequence, while the wall is exposed to climatic actions and is repeatedly dilated and contracted, whereas the slab pertains a constant temperature and does not present any volumetric variation, thus the TBSs are submitted to large displacement constrains. The paper illustrates the effect of the thermal dilatation and contraction of the walls, which create a supplemental force in the TBSs, and consequently cracking of the walls. A numerical model of a quarter of a building's storey is submitted to the climatic actions computed at the location of Embrun city, in France. One side of the L-shape wall is supposed to face to the south, and the other one to the west. The thermal and mechanical analysis are performed with the software CASTEM. In thermal analysis, air temperature and flux of solar radiation signal are defined from databases of METEO FRANCE, and are applied on the exterior surface of the walls. The results of the first calculation, by thermo-hydro-mechanical analysis (THM) with elasticity behavior, confirm that a significant stress level in tension occurs in the concrete at the corner of the walls and the nearby interface elements of the TBS. Furthermore, the TBSs that are close to the corner of the walls pertain the highest horizontal and axial forces, and are at risk to exceed the limit strength. Based on those results, a second calculation, which includes the coupling of damage with shrinkage and creep model from the THM analysis, is made for determining more realistic forces in the TBSs, and analyzing the cracking pattern of the walls.

Knockdown Factors For Two Kinds of Stiffened Cylinders Under Axial Compression

Scipedia content — Thu, 11 Mar 2021 17:31:31 +0100

Stiffened cylinder is widely used in launch vehicle structures because its stiffener can prevent buckling wave to spread in the skin. However, it is still sensitive to shape imperfection more or less. Knockdown factors of stiffened cylinders have been researched all the time. However, comparison among different grid types is seldom. In this paper, both orthogrid stiffened cylinder and isogrid stiffened cylinder under axial compression are studied. Linear eigenvalue method and nonlinear implicit method are adopted to calculate the bearing capacities of the cylinders with ABAQUS. The sinusoidal function is used to model the imperfection. Given different imperfection parameters, the sensitive of bearing capacities to the shape imperfection is researched for two kinds of cylinders. Axial compression experiments are also implemented for the stiffened cylinders, and the results agree with numerical result. Knockdown factor of orthogrid cylinder is about 0.5~0.7. Meanwhile, it proves that when the stiffener is strong enough, the effects of shape imperfection on load capacity can be ignored for orthotropic grid, and its knockdown factor is nearly 1.

Micromechanics-Driven Variational Method for Diffuse-to-Localised Fracture in Quasi-Brittle Solids

Scipedia content — Thu, 11 Mar 2021 17:46:28 +0100

A novel multiscale variational method for modelling fracture propagation is proposed. The
method employs strong discontinuity kinematics enhancement, enabling macroscopic cracks to be modelled explicitly, while minimum remeshing is ensured. In addition, the response of quadrature points in the bulk is up-scaled using a Micromechanical continua, which enables the evolution of directional
micro-defects (e.g. microcracks) without venturing into prohibitive computational burden. Noticeably,
the method allows the Micromechanical continua to interact with macroscopic cracks. The framework is
conveniently formulated as a variational setting to provide a minimum energy solution. The new computational framework has been found to diagnose realistic failure mechanisms in quasi-brittle materials.

On Particle-in-Cell Approximations to Particle-in-Fourier Schemes

Scipedia content — Thu, 11 Mar 2021 17:38:53 +0100

The gridless Particle-In-Fourier method where particles are directly deposited onto a Fourier basis features excellent energy and momentum conservation properties, but is computationally expensive due to the global nature of its basis functions. In this paper, we investigate analytically and numerically how well a back-filtered spectral Particle-In-Cell method can approximate the Particle-In-Fourier method. The study is extended to a recent variational spectral PIC method which has a discrete Hamiltonian structure.

Peridynamic Finite Element Modelling of Quasibrittle Structures

Scipedia content — Thu, 11 Mar 2021 17:38:38 +0100

In a number of applications, large size structures subjected to loads that cause highly non-linear behavior need to be analyzed. With the peridynamic theory, proposed by Stewart Silling in 2000 and 2007, elasticity and damage in quasibrittle structures such as plain and reinforced concrete structures can be modeled with the peridynamic theory. To model these structures, lattice models with brittle beam elements are used to model concrete. A shortcoming of lattice and particle models is that they are highly demanding of computational power. Molecular dynamics may be, in some cases an appropriate tool for analyzing microcracks in quasibrittle materials in compression, but molecular dynamics becomes infeasible at scales larger than a few million atoms. For example, in masonry structures, cracks form in the brick mortar joints, and concrete blocks can be assumed to have a uniform displacement field. This allows us to use the peridynamic finite element model, which is an improvement over discrete lattice models. This model assumes a continuous displacement field within each finite element, with displacement discontinuities allowed to develop between finite elements. The objective of this work is to model cracks in quasibrittle structures, with the peridynamic model. The peridynamic finite element model is shown to be much more computer timeand memoryefficient than the similar discrete particle-based models. Results show that this implementation appears to be more computationally efficient than particle or lattice models.

Peridynamic Modelling of Harmonic Structured Materials Under High Strain Rate Deformation

Scipedia content — Thu, 11 Mar 2021 17:43:13 +0100

This paper applies the peridynamic continuum mechanics theory on a new type of material known as harmonic-structured materials. Using the Peridigm software, rapid uniaxial elongation is simulated on a peridynamic model of a thin bimodal harmonic-structured metal sheet. Mechanical wave initiation, propagation, and reflection, as well as fracture initiation and propagation are successfully simulated.

The Parametric High-Fidelity-Generalized-Method-of-Cells (PHFGMC) Micromechanical Model for Compression Failure of FRP Composites

Scipedia content — Thu, 11 Mar 2021 16:59:19 +0100

A multiscale model based on finite element (FE) and the Parametric High-Fidelity-GeneralizedMethod-of-Cells (PHFGMC) micromechanical model was formulated and implemented to solve the compression problem in unidirectional IM7/977-3 carbon epoxy composite. The nonlinear PHFGMC governing equations were obtained from a two-layered (local-global) virtual work principle and solved using a incremental-iterative formulation. In addition, the semi-analytical modified Lo and Chim failure criterion (based on the buckling of Timoshenko's beam) for unidirectional fiber-reinforced composite materials under compression [1] was adopted and combined with the FE-PHFGMC multiscale model. In this study, the criterion was employed for the general case of a multi-axial loading state accompanied with a nonlinear polymeric matrix behavior, where the local and thus effective properties of the composite change continuously throughout the loading path. Therefore the predicted lamina strength was incrementally reevaluated. In the present model, the use of the nonlinear constitutive model RambergOsgood was used for the matrix media and a linear-elastic transversely-isotropic law for the fiber, as common for carbon fibrous composites. This extends the existing criterion to account for the material microstructure with a refined parametric discretization, as well as the effect of a nonlinear constitutive law. The advantage of the proposed model is to predict the compressive damage (kink band formation and its width) and the compressive strength (within 11% of experimental data).

Validation of An Energy-Based Fatigue Life Model for Fibre Reinforced Plastics Under Different Stress Ratios

Scipedia content — Thu, 11 Mar 2021 17:32:50 +0100

The energy-based fatigue model presented in this work overcomes different shortcomings of existing model approaches, such as the need of separated assumptions for constant life diagrams. By using the range of the normalised strain energy density and a probabilistic based mode interaction approach, a failure mode dependent fatigue model for CFRP is established for directly predicting constant life diagrams and calculating the fatigue life for multiaxial loads with constant amplitude. In this contribution, the ply-based model and some of its main features, such as the consideration of residual stresses or of mode interactions at general threedimensional stress states, are shortly summarised. The stepwise model validation on different literature datasets is considered in more detail, including prediction of SN-curves with scatter band and constant life diagrams.