Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
8
4
2010
Creep of a C-S-H Gel: Micromechanical Approach
357-368
Julien
Sanahuja
Lafarge Centre de Recherche, 95 rue du Montmurier, BP 15, 38291 Saint-Quentin Fallavier cedex, France; Presently at EDF R&D, Departement MMC, Site des Renardieres, Avenue des Renardieres, E´cuelles, 77818 Moret sur Loing cedex, France
Luc
Dormieux
LMSGC, Institut Navier, Ecole Nationale des Ponts et Chaussees
Both clays and calcium silicate hydrates (the main hydration products of Portland cements) exhibit a microstructure made up of lamellar particles. The microscopic mechanism responsible for the macroscopic creep of such materials is often described as the sliding of the sheets one onto the other. This paper proposes a micromechanical approach to estimate the macroscopic creep behavior rising from this microscopic mechanism. The asymptotic evolution of effective creep at both short and large times is especially investigated. The influence of the shape of the particles is also quantitatively discussed.
Mathematical and Biological Scientists Assess the State of the Art in RNA Science at an IMA Workshop, RNA in Biology, Bioengineering, and Biotechnology
369-378
Tamar
Schlick
New York University
Highlights of the IMA workshop RNA in Biology, Bioengineering, and Biotechnology are summarized, including recent developments in RNA secondary structure prediction and RNA design, innovative mathematical constructs for RNA structure, bioinformatics advances in RNA structure analysis and prediction, and experimental progress in RNA folding and imaging.
Multiscale Modeling of Viscoelastic Plant Tissue
379-396
P.
Ghysels
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
G.
Samaey
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
P.
Van Liedekerke
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
E.
Tijskens
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
H.
Ramon
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
D.
Roose
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
We present a multiscale method for the simulation of large viscoelastic deformations and show its applicability to biological tissue such as plant tissue. At the microscopic level we use a particle method to model the geometrical structure and basic properties of individual cells. The cell fluid, modeled as a viscoelastic fluid by means of smoothed particle hydrodynamics (SPH), is enclosed in an elastic cell wall, modeled by discrete elements. The macroscopic equation and stress tensor are derived from the SPH model by means of the generalized mathematical homogenization (GMH) technique. The macroscopic domain is discretized using standard finite elements, where the stress tensor is evaluated from microscopic simulations in small sub-domains, called representative volume elements (RVEs). Our emphasis is on reconstructing the microscopic state inside the RVE for a given macroscopic deformation and velocity gradient. We propose a scheme to initialize the RVE consistently, not only with the macroscopic variables, but also with the microscopic dynamics.
Adaptive Multiwavelet-Hierarchical Method for Multiscale Computation
397-409
Youming
Wang
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049
Xuefeng
Chen
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049
Zhengjia
He
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049
An adaptive multiwavelet-hierarchical method characterized by high convergent rate and flexible adaptive strategy is proposed for multiscale computation of field problems. According to the Strang--Fix condition, the convergence rate of the finite element multiwavelet method is determined by the approximation order of scaling functions in the same level of multiwavelet refinement. To raise the approximation order of scaling functions, finite element multiwavelets are combined with hierarchical bases to construct a new multilevel multiwavelet-hierarchical space. An adaptive strategy for multiwavelet-hierarchical refinement is presented based on new error estimation in the form of multiwavelets and hierarchical bases, which leaves much freedom for the problem-oriented selection of multiwavelets or hierarchical functions. Numerical examples demonstrate that the proposed method is an accurate and efficient tool in solving the field problems with singularities or changes in high gradients.
Coarse Implicit Time Integration of a Cellular Scale Particle Model for Plant Tissue Deformation
411-422
P.
Ghysels
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
G.
Samaey
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
P.
Van Liedekerke
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
E.
Tijskens
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
H.
Ramon
K.U. Leuven, Department of Biosystems, Kasteelpark Arenberg 30, bus 2456, B-3001 Heverlee, Belgium
D.
Roose
K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, B-3001 Heverlee, Belgium
We describe a multiscale method to simulate the deformation of plant tissue. At the cellular scale we use a combination of smoothed particle hydrodynamics and discrete elements to model the geometrical structure and basic properties of individual plant cells. At the coarse level, the material is described by the standard continuum approach without explicitly constructing a constitutive equation. Instead, the coarse scale finite element model uses simulations with the fine (cellular) scale model in small subdomains, called representative volume elements (RVEs), to determine the necessary coarse scale variables, such as stress and the elasticity and viscosity tensors. We present an implicit time integration scheme for the coarse finite element model, allowing much larger time steps than possible with explicit methods. Computation of the Cauchy stress from an RVE is straightforward by volume averaging over the RVE. In this work, we use forward finite differencing of the objective Truesdell stress rate to estimate both the fourth-order elasticity and viscosity tensors. These tensors are then used to construct the coarse scale stiffness and damping matrices required for implicit integration.
Equation-Free Accelerated Simulations of the Morphological Relaxation of Crystal Surfaces
423-439
Gregory J.
Wagner
Sandia National Laboratories, Livermore, California, and Albuquerque, New Mexico
Xiaowang
Zhou
Sandia National Laboratories, Livermore, California, and Albuquerque, New Mexico
Steven J.
Plimpton
Sandia National Laboratories, Livermore, California, and Albuquerque, New Mexico
A method for accelerating kinetic Monte Carlo simulations of solid surface morphology evolution, based on the equationfree projective integration (EFPI) technique, is developed and investigated. This method is demonstrated through application to the 1+1 dimensional solid-on-solid model for surface evolution. EFPI exploits the multiscale nature of a physics problem, using fine-scale simulations at short times to evolve coarse length scales over long times. The method requires identification of a set of coarse variables that parameterize the system, and it is found that the most obvious coarse variables for this problem, those related to the ensemble-averaged surface position, are inadequate for capturing the dynamics of the system. This is remedied by including among the coarse variables a statistical description of the fine scales in the problem, which in this case can be captured by a two-point correlation function. Projective integration allows speedup of the simulations, but if speed-up of more than a factor of around 3 is attempted the solution can become oscillatory or unstable. This is shown to be caused by the presence of both fast and slow components of the two-point correlation function, leading to the equivalent of a stiff system of equations that is hard to integrate. By fixing the fast components of the solution over each projection step, we are able to achieve speedups of a factor of 20 without oscillations, while maintaining accuracy.
Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures
441-446
H.
Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
S.
Arabnejad
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran
Size-dependent effects can significantly be indicated in experimental deformation of microstructures. In accordance with statistic behavior of size-dependent parameters, it is predictable that finite deformation and nonlinear forms of equations may obtain more appropriate computational results for microstructures. In this paper, classic couple stress theory is used to explain size dependency in strain gradient theory. Based on results obtained from couple stress in strain gradient theory, the theory is extended in nonlinear form. In this case, a length scale parameter is used in this model as a Lagrangian coefficient and a strain gradient is attested in a classic constitutive equation as a constraint. Finally, a nonlinear form of equation is used for a cylinder in micron order subjected to torsion, and results are compared with a linear model, the model expressed by Yang et al. (Int. J. Solids Struct., 39, pp. 2731-2743, 2002), and the finite element model of bone.