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  • Articles  (9,050)
  • PAMM - Proceedings in Applied Mathematics and Mechanics  (1,050)
  • 24702
  • Mathematics  (9,050)
  • 1
    Publication Date: 2015-10-22
    Description: A Fluid–Structure Interaction (FSI) problem can be reinterpreted as a heterogeneous problem with two subdomains. It is possible to describe the coupled problem at the interface between the fluid and the structure, yielding a nonlinear Steklov–Poincaré problem. The linear system can be linearized by Newton iterations on the interface and the resulting linear problem can be solved by the preconditioned GMRES method. In this work we investigate the behavior of preconditioners of Neumann–Neumann and Dirichlet–Neumann type. We find that, in the context of hemodynamics, the Dirichlet– Neumann, i.e., using Dirichlet boundary conditions on the fluid side and Neumann on the structure side, outperforms the Neumann–Neumann method, except when a weighting is used such that it basically reduces to the Dirichlet–Neumann method. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
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  • 2
    Publication Date: 2015-10-22
    Description: An algorithmic strategy for the modelling and simulation of bone healing is presented. The algorithm works directly on the computed tomography data and simulates, after an appropriate volume meshing, a mechainically driven healing concept which is based on competitive and dynamical mechanical parameters. The finite element simulations are done with realistic boundary conditions from patient-specific OpenSim simulations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 3
    Publication Date: 2015-10-22
    Description: In the current contribution, we present a multi-scale constitutive model capturing macroscopic inelastic effects (like stress softening and permanent set) in soft tissues under cyclic loading. Soft biological tissues can be described as a biological composite material. The extracellular matrix is hereby reinforced by collagen fibers which themself are an assembly of collagen fibrils embedded in a proteoglycan (PG) rich matrix. Micro-damage induced by cyclic loading is treated by an interaction scenario between the fibrils and the PGs. At the low strain regime PGs promote sliding between fibrils [1] which leads to the yielding of statistical distributed overlapping segments. The breakage of the PG-bridges is defined by a decreasing PG-density. Due to the accumulated damage of the PG connections at high tissue strains, the strains at the fibril level increases. This finally drives the over-stretching of the fibrils, which is associated with a permanent rupture of the hydrogen bonds inside of the tropocollagen molecules [2]. The so obtained model is in line with recent experimental findings [1, 2] and was additionally validated against experimental data available in literature. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 4
    Publication Date: 2015-10-22
    Description: We present an application of the phase-field method of fracture to the simulation of artery rupture at large strains. To achieve this, the crack driving force function associated with the evolution of the crack phase-field is modified to account for the inherent anisotropy of the soft biological tissues. The phase-field methods present a promising and innovative approach to the thermodynamically consistent modeling of fracture. A key advantage lies in the prediction of the complex crack topologies where the cohesive zone approaches to fracture are known to suffer. A regularized crack surface functional is introduced that Γ-converges to a sharp crack topology for vanishing length scale parameter. The evaluation of the phase-field follows the minimization of this crack surface functional. The phase-field variable can be treated as a geometric quantity whose evolution is coupled to the anisotropic bulk response in a modular format in terms of a crack driving state function. A stress-based anisotropic failure criterion is introduced whose maximum value from the deformation history drives the irreversible crack phase-field. The formulation is verified by the finite element based simulation of a real arterial cross-section undergoing rupture in a two-dimensional setting when subjected to inflation pressure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 5
    Publication Date: 2015-10-22
    Description: The growth of metastases in the brain increases the state of stress, create leaky blood vessels and disrupt regular brain cells. Essential steps during the development of metastases are the infiltration of the tissue, the nutrient-dependent growth and the stimulation of blood-vessel sprouting. A promising medical treatment can be obtained by the direct infusion of a therapeutic solution into the tissue. Besides experiments, computational models can improve the understanding of brain metastases. In this regard, the liquid-saturated brain tissue represents a porous material. Therefore, the framework of the Theory of Porous Media (TPM) provides an excellent tool for its description. The continuum-mechanical theory of a multi-constituent model and mechanisms of metastases growth are presented in this contribution. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 6
    Publication Date: 2015-10-22
    Description: A recent computational model for tumor growth is presented. The mathematical model, based on thermodynamically constrained averaging theory (TCAT), is shortly summarized in the first part; then the attention is focused on modeling hypothesis and their impact on numerical results. Perspectives for future developments of the presented multiphase model are outlined at the end of the paper. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 7
    Publication Date: 2015-10-22
    Description: A surgical intervention is often required if the functionality of the sensitive human brain tissue is seriously compromised, e. g., due to the occurrence of malignant brain tumours. A promising method for an effective tumour-treatment procedure is given by the so-called convection-enhanced drug delivery (CED), cf. [1]. In this regard, the aim of this contribution is to simulate the expected effects as well as coupled impacts of a (scheduled) CED-procedure with the help of numerical computations, which base on a sophisticated multiphasic and multi-physical modelling strategy applied to human brain tissue. In particular, a quaternary porous-media model, cf. [3–5], is used for the discussion of selected numerical examples and demonstrates the applicability of the model. In detail, the optimal catheter placement and the application of multiple infusion catheters are studied in terms of the occurring anisotropic therapeutic spreading of the infused drug. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 8
    Publication Date: 2015-10-22
    Description: Recently, a scaled boundary finite element (SBFE) formulation for geometrically and physically nonlinear materials has been developed using the scaled boundary finite element method (SBFEM). The SBFE formulation has been employed to describe plane stress problems of notched and unnotched hyperelastic elastomer specimens. In this contribution, the derived SBFE formulation is extended to nonlinear time- and temperature-dependent material behavior. Subsequently, the SBFE formulation is incorporated into a crack propagation scheme to model crack propagation in cyclically loaded elastomer specimens of the so-called tear fatigue analyzer (TFA). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 9
    Publication Date: 2015-10-22
    Description: Masonry arch structures, and, more generally, vaulted structures, are traditionally assessed using a well-established approach, such as linear elasticity or limit analysis, whereby system behaviour at the intermediate stage – which occurs when the material's tensile strength has been exceeded but the collapse mechanism has not yet formed – is disregarded. A more accurate interpretation requires a thorough analysis that can take into account the intermediate cracking stage and uses a constitutive law providing a closer approximation to the actual behaviour of the material. In this paper, an evolutionary fracturing process analysis for the stability assessment of masonry arches is presented. This method makes it possible to capture the damaging process that takes place when the conditions evaluated by means of linear elastic analysis no longer apply and before the conditions assessed through limit analysis set in. Furthermore, the way the thrust line is affected by the opening of cracks and the redistribution of internal stresses can be checked numerically. The results obtained with the described approach are compared with a numerical simulation performed with the finite element code Diana (TNO, The Netherlands) adopting discrete cracking with cohesive laws. Finally, the case study of the arch of the Mosca Bridge over the Dora River in Turin, Italy, is described. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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  • 10
    Publication Date: 2015-10-22
    Description: There is currently a gap in the understanding of how crack propagation by intergranular versus transgranular fracture varies with changes in material properties and grain size. Much of the prior work in this area has been in terms of LEFM and criterion based on toughness alone. More recent work has shown that a toughness-and-strength approach is required. In this study a strength-and-energy approach is applied to intergranular-versus-transgranular fracture through a cohesive-zone approach implemented in a finite element model. Results show that intergranular fracture becomes more likely, and has an increasing shear component, as grain toughness increases and grain stiffness and grain size decrease. These results can help guide material development. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
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