| 1. |
- Molavitabrizi, Danial, et al.
(författare)
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Computational model for low cycle fatigue analysis of lattice materials: Incorporating theory of critical distance with elastoplastic homogenization
- 2022
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Ingår i: European Journal of Mechanics, A/Solids. - : Elsevier BV. - 0997-7538 .- 1873-7285. ; 92
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Tidskriftsartikel (refereegranskat)abstract
- A novel numerical framework for low cycle fatigue analysis of lattice materials is presented. The framework is based on computational elastoplastic homogenization equipped with the theory of critical distance to address the fatigue phenomenon. Explicit description of representative volume element and periodic boundary conditions are combined for computational efficiency and elimination of the boundary effects. The proposed method is generic and applicable to periodic micro-architectured materials. The method has been applied to 2-D auxetic and 3-D kelvin lattices. The classical Coffin-Manson and Morrow models are used to provide fatigue life predictions (strain-life curves). Predicted fatigue lives for the auxetic lattice are shown to provide good correspondence to experimentally found fatigue lives from the literature.
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| 2. |
- Molavitabrizi, Danial, et al.
(författare)
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Damage-induced failure analysis of additively manufactured lattice materials under uniaxial and multiaxial tension
- 2022
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Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 252
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Tidskriftsartikel (refereegranskat)abstract
- Mechanical behavior of additively manufactured lattice materials has been mainly investigated under uniaxial compression, while their performance under uniaxial and multiaxial tension are yet to be understood. To address this gap, a generic elastoplastic homogenization scheme with continuum damage model is developed, and three different lattice materials, namely cubic, modified face-center cubic and body-center cubic, are analyzed under uniaxial, biaxial and triaxial tension. The influence of micro-architecture on the material's failure behavior as well as its macroscopic mechanical performance is thoroughly discussed. For validation, a set of uniaxial tensile experiments are conducted on functionally graded cubic lattice samples that are additively manufactured using Electron Beam Melting (EBM) process. Digital image correlation technique is employed to obtain the macroscopic stress-strain curves, and manufacturing imperfections are inspected using light omitting microscopy. It turns out that the behavior of as-built samples could substantially differ from numerical predictions. Thus, a defect-informed numerical model is employed to accommodate the effect of imperfections. The outcome is in a very good agreement with experimental data, indicating that with proper input data, the developed scheme can accurately predict the mechanical and failure behavior of a given lattice material.
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| 3. |
- Molavitabrizi, Danial, et al.
(författare)
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Elasticity of Anisotropic Low-Density Lattice Materials
- 2021
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Ingår i: Journal of engineering materials and technology. - : ASME International. - 0094-4289 .- 1528-8889. ; 143:2
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Tidskriftsartikel (refereegranskat)abstract
- Computational first-order homogenization theory is used for the elastic analysis of generally anisotropic lattice materials within classical continuum mechanics. The computational model is tailored for structural one-dimensional (1D) elements, which considerably reduces the computational cost comparing to previously developed models based on solid elements. The effective elastic behavior of lattice materials is derived consistently with several homogenization approaches including strain- and stress-based methods together with volume and surface averaging. Comparing the homogenization based on the Hill–Mandel Lemma and constitutive approach, a shear correction factor is also introduced. In contrast to prior studies that are usually limited to a specific class of lattice materials such as lattices with cubic symmetry or similarly situated joints, this computational tool is applicable for the analysis of any planar or spatial stretching- and bending-dominated lattices with arbitrary topology and anisotropy. Having derived the elasticity of the lattice, the homogenization is then complemented by the symmetry identification based on the monoclinic distance function. This step is essential for lattices with non-apparent symmetry. Using the computational model, nine different spatial anisotropic lattices are studied among which four are fully characterized for the first time, i.e., non-regular tetrahedron (with trigonal symmetry), rhombicuboctahedron type a (with cubic symmetry), rhombicuboctahedron type b (with transverse isotropy), and double-pyramid dodecahedron (with tetragonal symmetry).
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| 4. |
- Molavitabrizi, Danial, et al.
(författare)
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Hydrogen embrittlement in micro-architectured materials
- 2022
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Ingår i: Engineering Fracture Mechanics. - : Elsevier. - 0013-7944 .- 1873-7315. ; 274
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Tidskriftsartikel (refereegranskat)abstract
- Hydrogen embrittlement is a classical problem in bulk materials while it is rather untouched for advanced materials such as micro-architectured materials. This can be a barrier to industrial adoption of these materials where hydrogen is present as a popular source of energy. In this study, we developed a numerical scheme to assess the hydrogen degradation in metallic micro-architectured materials. The numerical scheme is built on the concept of elastoplastic homoge-nization and two hydrogen embrittlement theories, i.e. hydrogen enhanced decohesion (HEDE) and hydrogen enhanced localized plasticity (HELP). The use of homogenization allows for explicit definition of a unit-cell, drastically improving the computation time. The hydrogen degradation loci of two specific micro-architectured materials, that is cubic (with 10%, 20% and 30% relative densities) and body-center cubic (with 20% relative density), are numerically characterized. Additionally, the influence of unit-cell topology, relative density, and trap hydrogen on the degradation of homogenized macroscopic material is determined. Finally, a unique failure locus is provided for generic cubic unit-cell with arbitrary relative densities. This degradation law is in-dependent of the relative density and can be interpreted as a material property, contributing to the material design charts.
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| 5. |
- Molavitabrizi, Danial
(författare)
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Linear and Nonlinear Mechanics of Lattice Materials : Computational Modelling and Experiments
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Lattice materials are artificial materials made of repeating unit-cells. The internal architecture of these materials can be engineered for a specific application such as energy absorption, heat transfer, or acoustic damping. The advancements in additive manufacturing have enabled the design and fabrication of lattice materials with complex geometries, but the lack of understanding about their mechanical performance has limited their application. This thesis investigates the mechanics of lattice materials via numerical simulations and mechanical tests. We start with development of a discrete homogenization scheme for the elastic analysis of lattice materials with arbitrary level of complexity. Next, the method is extended to a continuum elastoplastic homogenization and accompanied with the theory of critical distances to assess the low cycle fatigue behaviour of lattice materials. Following that, the model is coupled with continuum damage mechanics to mimic the fracture initiation of the material unit-cell under quasi-static loads. The proposed model is calibrated using tensile tests, leading to a defect-informed numerical model that accommodates the manufacturing imperfections. Following this, an environmentally assisted failure known as hydrogen embrittlement is studied by incorporating hydrogen failure mechanisms into elastoplastic homogenization model. In the next step, numerical simulations and compression tests are employed to analyze the mechanical coupling and elastic anisotropy in the so-called non-regular tetrahedron lattice. The results show a good correspondence but the periodicity assumption in computational homogenization –mimicking an infinite cell number–should be considered when comparing numerical results with the data obtained from real samples. To capture the size effect, as the final step, we develop a homogenization scheme based on strain-gradient elasticity. The model is verified using numerical and experimental three-point bending tests and has shown to be more precise compared to classical elasticity. The methodologies proposed in this thesis are generic and can be used as guidelines for design of micro-architectured materials.
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| 6. |
- Molavitabrizi, Danial, et al.
(författare)
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Mechanical coupling and tuned anisotropic elasticity : Numerical and experimental material design for shear-normal and shear-shear interactions
- 2023
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Ingår i: Materials & design. - : Elsevier. - 0264-1275 .- 1873-4197. ; 230
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Tidskriftsartikel (refereegranskat)abstract
- Mechanical coupling in architectured materials has been traditionally investigated in the context of generalized continuum mechanics and is often assumed to be non-existent in the framework of classical continuum mechanics. In this paper, we challenge this misconception and study an anisotropic architectured material exhibiting shear-shear and shear-normal coupling from the standpoint of classical continuum mechanics. The material is non-regular tetrahedron lattice, a potential candidate for biomedical implants, but the lack of understanding about its anisotropic behavior and mechanical couplings has limited its application. We exploited the unit-cell definition with periodic boundary conditions and performed elastic and elastoplastic homogenizations. Non-zero coupling sub-matrices appeared in the homogenized elasticity matrix, which we further transformed into material’s natural coordinate system using elastic distance function. This allowed for anisotropy identification and determination of all the coupling parameters. Next, compression tests are conducted on laser powder bed fused Al-12Si (mass%) lattice samples with different relative densities and spatial orientations. Employing test data, mechanical anisotropy and shear-normal couplings are experimentally characterized. Both numerical and experimental results confirmed the presence of mechanical couplings and predicted a similar anisotropic tendency in the material. Finally, the role of manufacturing defects in deterioration of as-designed mechanical properties is discussed.
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| 7. |
- Molavitabrizi, Danial, et al.
(författare)
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Second-order homogenization of 3-D lattice materials towards strain gradient media : numerical modelling and experimental verification
- 2023
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959.
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Tidskriftsartikel (refereegranskat)abstract
- The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, acomputational homogenization scheme based on Mindlin (type II) strain gradient elasticity theory is developed here. The model is based on variational formulation with periodic boundary conditions, implemented in the open-source software FreeFEM to fully characterize the effective classical elastic, coupling, and gradient elastic matrices in lattice materials. Rigorous mathematical derivations based on equilibrium equations and Hill-Mandel lemma are provided, resulting in the introduction of macroscopic body forces and modifications in gradient elasticity tensors which eliminate the spurious gradient effects in the homogeneousmaterial. The obtained homogenized classical and strain gradient elasticity matrices are positive definite, leading to a positive macroscopic strain energy density value—an importantcriterion that sometimes is overlooked. The model is employed to study the size effects in 2-D square and 3-D cubic lattice materials. For the case of 3-D cubic material, the model is verified using full-field simulations, isogeometric analysis, and experimental three-point bending tests.The results of computational homogenization scheme implemented through isogeometric simulations show a good agreement with full-field simulations and mechanical tests. The developed model is generic and can be used to derive the effective second-grade continuum forany 3-D architectured material with arbitrary geometry. However, the identification of the proper type of generalized continua for the mechanical analysis of different cell architectures is yet an open question.
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