scholarly journals Variational-asymptotic homogenization of thermoelastic periodic materials with thermal relaxation

2021 ◽  
pp. 106566
Author(s):  
Deison Préve ◽  
Andrea Bacigalupo ◽  
Marco Paggi
Keyword(s):  
Thermal Relaxation ◽  
Asymptotic Homogenization ◽  
Variational Asymptotic ◽  
Periodic Materials

Variational asymptotic homogenization of finitely deformed heterogeneous elastomers

2019 ◽  
Vol 216 ◽  
pp. 379-391 ◽  
Author(s):  
Liang Zhang ◽  
Hamsasew M. Sertse ◽  
Wenbin Yu
Keyword(s):  
Asymptotic Homogenization ◽  
Variational Asymptotic

Finite Volume-Based Asymptotic Homogenization of Periodic Materials Under In-Plane Loading

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
Zhelong He ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Volume ◽  
Local Equilibrium ◽  
Shear Loading ◽  
Local Fields ◽  
Homogenization Theory ◽  
Asymptotic Homogenization ◽  
Plane Shear ◽  
Strain Gradients ◽  
Combination Approach ◽  
Periodic Materials

Abstract The previously developed finite volume-based asymptotic homogenization theory (FVBAHT) for anti-plane shear loading (He, Z., and Pindera, M.-J., “Finite-Volume Based Asymptotic Homogenization Theory for Periodic Materials Under Anti-Plane Shear,” Eur. J. Mech. A Solids (in revision)) is further extended to in-plane loading of unidirectional fiber reinforced periodic structures. Like the anti-plane FVBAHT, the present extension builds upon the previously developed finite volume direct averaging micromechanics theory applicable under uniform strain fields and further accounts for strain gradients and non-vanishing microstructural scale relative to structural dimensions, albeit with multidimensional in-plane loadings incorporated. The unit cell problems at different orders of the asymptotic field expansion are solved by satisfying local equilibrium equations and displacement and traction continuity in a surface-averaged sense which is unique among the existing asymptotic homogenization schemes, leading to microfluctuation functions that yield homogenized stiffness tensors at each order for use in macroscale problems. The newly extended multiscale theory is employed in the analysis of a structural boundary-value problem under in-plane loading, illustrating pronounced boundary effects. A combination approach proposed in the literature is subsequently employed to mitigate the boundary layer effects by explicitly accounting for the microstructural details in the boundary region. This combination approach produces accurate recovery of the local fields in both regions. The extension to in-plane problem marks FVBAHT as an alternative, self-contained asymptotic homogenization tool, with documented advantages relative to current numerical techniques, for the analysis of periodic materials in the presence of strain gradients produced by three-dimensional loading regardless of microstructural scale.

Variational asymptotic homogenization of magneto-electro-elastic materials with coated fibers

2015 ◽  
Vol 133 ◽  
pp. 300-311 ◽  
Author(s):  
Yifeng Zhong ◽  
Wenzheng Qin ◽  
Wenbin Yu ◽  
Xiaoping Zhou ◽  
Lichao Jiao
Keyword(s):  
Elastic Materials ◽  
Asymptotic Homogenization ◽  
Variational Asymptotic

Variational asymptotic homogenization of beam-like square lattice structures

2019 ◽  
Vol 24 (10) ◽  
pp. 3295-3318 ◽  
Author(s):  
Emilio Barchiesi ◽  
Sergei Khakalo
Keyword(s):  
Timoshenko Beam ◽  
Scaling Laws ◽  
Lattice Structure ◽  
Square Lattice ◽  
Scale Model ◽  
Asymptotic Homogenization ◽  
Macro Scale ◽  
Variational Asymptotic ◽  
Statics And Dynamics ◽  
Meso Scale

By means of variational asymptotic homogenization, using Piola’s meso-macro ansatz, we derive the linear Timoshenko beam as the macro-scale limit of a meso-scale beam-like periodic planar square lattice structure. By considering benchmarks in statics and dynamics, meso-to-macro convergence is numerically analyzed. At the finest micro-scale, a 2D assembly of elastic, geometrically linear, isotropic and homogeneous Cauchy continua in plane strain with different material parameters is considered. Using this description, we calibrate the meso-scale model using standard methodology and, by exploiting the meso-to-macro homogenization scaling laws, we recover bending and shear Timoshenko beam moduli. It turns out that the Timoshenko beam found in this way and the finest-scale description based on the Cauchy continuum are in excellent agreement.

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