Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
17
2
2019
PREFACE: MULTISCALE PLASTICITY AND RELATED TOPICS
v
Klaus
Hackl
Ruhr University Bochum, Bochum, Germany
Jörg
Schröder
Institut für Mechanik, Fachbereich für Ingenieurwissenschaften/Abtl. Bauwissenschaften; Universitat Duisburg-Essen, Germany
THERMODYNAMICALLY CONSISTENT HOMOGENIZATION IN FINITE STRAIN THERMOPLASTICITY
99-120
Marko
Canadija
University of Rijeka, Faculty of Engineering, Department of Engineering Mechanics,
Vukovarska 58, HR-51000 Rijeka, Croatia
N.
Munjas
University of Rijeka, Faculty of Engineering, Department of Engineering Mechanics,
Vukovarska 58, HR-51000 Rijeka, Croatia
J.
Brnic
University of Rijeka, Faculty of Engineering, Department of Engineering Mechanics,
Vukovarska 58, HR-51000 Rijeka, Croatia
The present research aims to develop a thermodynamically consistent framework for the application in the homogenization of finite strain thermoplasticity. The focus is set on the metallic materials, but the framework can be applied to other classes of materials as well. The cornerstone of the current research is the amount already existing results developed for the multiscale thermoelasticity. The essential part of the procedure is enforcement of consistency between thermodynamical
quantities at macroscale and microscale levels. As will be demonstrated in the paper, such a consistency places
additional constraints that are usually not accounted for in the literature. The developed procedure is implemented into
the finite element framework, and performance is illustrated on two examples, one mechanically driven and the other
thermally driven.
A MULTIPHASE HOMOGENIZATION MODEL FOR THE VISCOPLASTIC RESPONSE OF INTACT SEA ICE: THE EFFECT OF POROSITY AND CRYSTALLOGRAPHIC TEXTURE
121-150
Shuvrangsu
Das
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania,
Philadelphia, PA 19104-6315
Pedro Ponte
Castaneda
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania,
Philadelphia, PA 19104-6315
Sea ice is a multiphase composite material with complex microstructure and viscoplastic rheology. At length scales
much smaller than the size of a typical floe, sea ice consists of aggregates of hexagonal closed packed (HCP) ice crystals with embedded inclusions of brine and air. Although there can be significant variations depending on the age and
depth of the ice, the dominant structure at this scale consists of columnar grains displaying a pronounced texture
where the (c)-symmetry axes of the single crystal grains lie in the horizontal plane, but with random orientations in
this plane. Because the HCP ice crystals exhibit highly anisotropic viscoplastic behavior, with "easy" glide on basal planes orthogonal to the (c)-axis and "hard" slip on nonbasal systems, this strong texture has significant implications for the anisotropy of the macroscopic response of intact sea ice. On the other hand, the brine-air inclusions, which are modeled as voids with elongated shapes in the vertical direction, are also expected to have significant implications for the rheological response of sea ice, most importantly, by endowing sea ice with overall compressibility. In this work, use is made of the iterated fully optimized second-order homogenization method to develop a constitutive model for the macroscopic viscoplastic response of sea ice accounting for the abovementioned microstructural variables. Comparisons to experimental results from the literature demonstrate the capabilities of the model, especially in terms of capturing the dilatational response of intact sea ice under combined hydrostatic and deviatoric mechanical loading.
A FAST AND ROBUST NUMERICAL TREATMENT OF A GRADIENT-ENHANCED MODEL FOR BRITTLE DAMAGE
151-180
Philipp
Junker
Ruhr University Bochum, Bochum, Germany
Stephan
Schwarz
Ruhr University Bochum, Bochum, Germany
Dustin R.
Jantos
Ruhr University Bochum, Bochum, Germany
Klaus
Hackl
Ruhr University Bochum, Bochum, Germany
Damage processes are modeled by a softening behavior in a stress/strain diagram. This reveals that the stiffness loses
its ellipticity and the energy is thus not coercive. A numerical implementation of such ill-posed problems yields results that are strongly dependent on the chosen spatial discretization. Consequently, regularization strategies have to be employed that render the problem well-posed. A prominent method for regularization is a gradient enhancement of the free energy. This, however, results in field equations that have to be solved in parallel to the Euler-Lagrange equation for the displacement field. An usual finite element treatment thus deals with an increased number of nodal unknowns, which remarkably increases numerical costs. We present a gradient-enhanced material model for brittle damage using Hamilton's principle for nonconservative continua. We propose an improved algorithm, which is based on a combination of the finite element and strategies from meshless methods, for a fast update of the field function. This treatment keeps the numerical effort limited and close to purely elastic problems. Several boundary value problems prove the mesh-independence of the results.
VIRTUAL ELEMENT FORMULATION FOR PHASE-FIELD MODELING OF DUCTILE FRACTURE
181-200
Fadi
Aldakheel
Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstrasse 11, 30167
Hannover, Germany
Blaž
Hudobivnik
Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstrasse 11, 30167
Hannover, Germany
Peter
Wriggers
Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstrasse 11, 30167
Hannover, Germany
An efficient low-order virtual element method (VEM) for the phase-field modeling of ductile fracture is outlined within
this work. The recently developed VEM is a competitive discretization scheme for meshes with highly irregular shaped elements. The phase-field approach is a very powerful technique to simulate complex crack phenomena in multi-physical environments. The formulation in this contribution is based on a minimization of a pseudo-potential density functional for the coupled problem undergoing large strains. The main aspect of development is the extension toward the virtual element formulation due to its flexibility in dealing with complex shapes and arbitrary number of nodes. Two numerical examples illustrate the efficiency, accuracy, and convergence properties of the proposed method.
ELASTO-PLASTIC PHASE-FIELD MODEL OF HYDRAULIC FRACTURE IN SATURATED BINARY POROUS MEDIA
201-221
Mangesh
Pise
Institut für Mechanik, Fachbereich für Ingenieurwissenschaften/Abtl. Bauwissenschaften
Joachim
Bluhm
Institut für Mechanik, Fachbereich für Ingenieurwissenschaften/Abtl. Bauwissenschaften
Jörg
Schröder
Institut für Mechanik, Fachbereich für Ingenieurwissenschaften/Abtl. Bauwissenschaften; Universitat Duisburg-Essen, Germany
In many fields of engineering, especially in geo sciences and rock mechanics, the theoretical and numerical modeling of hydraulic fracturing of porous materials plays an important role. Hydraulic fracturing is a well-known technology in which porous materials are fractured by a pressurized liquid. The process involves the pressure injection of a fracking fluid (primarily water, often enriched with filling materials and thickening agents) and accompanied by crack nucleation and propagation, as well as mass transport. This article presents a macroscopic model based on the Theory of Porous Media (TPM). For simplification, an incompressible binary model consisting of the solid and liquid phases is used. The development of the damage of the elastic-plastic solid phase is controlled by an evolution equation, which corresponds to known diffusive phase-field models within a continuum mechanical framework. A numerical example shows that the simplified model is indeed capable of simulating hydraulic fracturing of porous media.
ON PRESSURIZED FUNCTIONALIZED PARTICLE-LADEN FLUID INFILTRATION INTO POROUS MEDIA
223-237
Tarek I.
Zohdi
Department of Mechanical Engineering, University of California, 94720-1740, Berkeley, CA
Eduardo M. B.
Campello
Department of Structural and Geotechnical Engineering, University of São Paulo, P.O. Box
61548, 05424-970, São Paulo, SP, Brazil
In many emerging applications, the controlled infiltration of specially designed particle-laden fluids into porous media is critical. The added materials are often chosen with the objective to mechanically, electrically, or magnetically
functionalize the overall material. Because of the increased viscosity of particle-laden fluids and the pore-dependent
permeability of the medium to be infiltrated, there is a rich choice of parameters that govern the overall process: (i) the base viscosity of the solvent, (ii) the volume fraction of particles in the fluid, (iii) the pore volume fraction of the porous medium, and (iv) the absolute permeability of the medium. This paper develops Darcy-law–like expressions relating the infiltration flow rate of particle-laden fluids to the pressure gradient on porous solids, as a function of the four above parameters. General trends of the process may be satisfactorily described with the derived analytical expressions, yet at an affordable cost on accuracy for rapid daily design analysis. The paper then develops direct, large-scale numerical simulations based on the discrete element method to illustrate the practical use of the proposed relations.