Homogenization Methods and Multiscale Modeling

Zohdi, Tarek I.

doi:10.1002/9781119176817.ecm2034

Cited by 5 publications

(4 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, for every time step in the model, for the composite microstructure to reach a mechanical equilibrium state, the total mechanical energy stored in the whole microstructure should be minimized [12,13] 2 . Once the mechanical equilibrium state is reached, the volume averaged stress may be predicted through solving a series of elastic equations on the finite element mesh [32]. Then the composite moduli at this time step can be calculated with the predicted volume averaged stress and the known applied controlled strain.…”

Section: Finite Element Calculationmentioning

confidence: 99%

Computationally implemented modeling of creep of composite materials caused by phase dissolution

Rahman

Grasley

2016

Computational Materials Science

View full text Add to dashboard Cite

Multiphasic composites with time-evolving, transient microstructures exhibit time-dependent behavior under load. One mechanism leading to this behavior is the dissolution of loadbearing phases within such materials. When the dissolution process occurs inside one phase of the composite material, the stress transmitted by the dissolving phase transfers into the neighboring phases, resulting in additional deformation of the whole composite. This additional deformation of the macroscopic material manifests as time-dependent creep of the composite. The purpose of this paper is to provide a general kinematic framework for such dissolution induced creep for virtually any material class, and to mechanistically model the same utilizing a computationally-implemented approach that is consistent with the kinematic framework. Utilizing this modeling approach, two distinct processes are computationally simulated, namely 1) creep of a water saturated, porous, frozen body upon warming and 2) creep of cement paste due to hydration-induced dissolution of cement grains. The simulation results show that microstructure evolution induces significant creep behavior of the whole composite in these two simulated cases.

show abstract

Section: Finite Element Calculationmentioning

confidence: 99%

Computationally implemented modeling of creep of composite materials caused by phase dissolution

Rahman

Grasley

2016

Computational Materials Science

View full text Add to dashboard Cite

show abstract

“…At the mesoscale and above, a continuum model of mechanics is often required in practice. This fact creates the need for homogenized models that act at larger scales and that, combined with new advanced architectures, allow for fast and accurate predictions of material deformation and fracture [11][12][13][14][15][16][17][18][19][20][21] .…”

Section: Introductionmentioning

confidence: 99%

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

You

et al. 2023

Appl. Math. Mech.-Engl. Ed.

View full text Add to dashboard Cite

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

show abstract

“…Especially in composite materials, with fibers embedded in a matrix building a periodic substructure, micro-and macroscale behaviors are modeled by the same linear elastic model, also called a Cauchy continuum. The homogenization of such periodic structures toward an equivalent Cauchy continuum has been investigated thoroughly [20,45,56,65,67,96].…”

Section: Introductionmentioning

confidence: 99%

Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis

Yang

Abali

Timofeev

et al. 2019

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the macroscale as the mechanical characteristics deviate from the characteristics at the microscale. As a remedy, metamaterial is modeled by using additional parameters; we intend to determine them. A homogenization approach based on the asymptotic analysis establishes a connection between these different characteristics at micro-and macroscales. A linear elastic first order theory at the microscale is related to a linear elastic second order theory at the macroscale. Relation for parameters at the macroscale is derived by using the equivalence of energy at macro-and microscales within a so-called Representative Volume Element (RVE). Determination of parameters are succeeded by solving a boundary value problem with the Finite Element Method (FEM). The proposed approach guarantees that the additional parameters vanish if the material is purely homogeneous, in other words, it is fully compatible with conventional homogenization schemes based on spatial averaging techniques. Moreover, the proposed approach is reliable as it ensures that such resolved additional parameters are not sensitive to choices of RVE consisting in the repetition of smaller RVEs but depend upon the intrinsic size of the structure.

show abstract

Homogenization Methods and Multiscale Modeling

Cited by 5 publications

References 87 publications

Computationally implemented modeling of creep of composite materials caused by phase dissolution

Computationally implemented modeling of creep of composite materials caused by phase dissolution

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis

Contact Info

Product

Resources

About