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Sökning: WFRF:(Waffenschmidt Tobias)

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1.
  • Kiefer, Bjoern, et al. (författare)
  • A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts
  • 2018
  • Ingår i: International Journal of Damage Mechanics. - : SAGE Publications. - 1056-7895 .- 1530-7921. ; 27:2, s. 253-295
  • Tidskriftsartikel (refereegranskat)abstract
    • A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.
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2.
  • Menzel, Andreas, et al. (författare)
  • A microsphere-based remodelling formulation for anisotropic biological tissues
  • 2009
  • Ingår i: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science. - : The Royal Society. - 1364-503X .- 1471-2962. ; 367:1902, s. 3499-3523
  • Tidskriftsartikel (refereegranskat)abstract
    • Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material's anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.
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4.
  • Polindara, César, et al. (författare)
  • A computational framework for modelling damage-induced softening in fibre-reinforced materials - Application to balloon angioplasty
  • 2017
  • Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 118-119, s. 235-256
  • Tidskriftsartikel (refereegranskat)abstract
    • A computational framework for modelling damage-induced softening in fibre-reinforced materials is presented. The main aspect of this framework is the proposed non-local gradient-enhanced continuum damage formulation. At the material level, the elastic constitutive behavior is defined by a hyperelastic functional including a volumetric and an isochoric contribution. The isochoric contribution is subdivided into three contributions associated to three different phases i=0,1,2. Phase 0 is represented by an incompressible neo-Hookean material, whereas phases 1 and 2 are represented by an exponential format that accounts for the stretching along two preferred anisotropy directions, i.e. two fibre families. Furthermore, a 1-di-type damage function, is introduced to reproduce the loss of stiffness in each phase i. Following the ideas discussed in Dimitrijeciv and Hackl (2008) Waffenschmidt et al. (2014), and references cited therein, the model is built around the enhancement of the local free energy function by means of terms that contain the referential gradients of the non-local damage variables ϕ(symbol)i The inclusion of these terms ensures an implicit regularisation of the finite element implementation. A finite element implementation of the non-local gradient-enhanced continuum damage model is presented. To this end we develop an 8-noded Q1Q1P0 hexahedral element following a variational approach, in order to efficiently model the quasi-incompressible behaviour of the hyperelastic material. This element is implemented in Abaqus by means of a user subroutine UEL. Three boundary value problems are studied: an anisotropic plate with a hole, a balloon angioplasty and a full-3D artery-like tube. These computational experiments serve to illustrate the main capabilities of the proposed model.
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5.
  • Polindara, César, et al. (författare)
  • Simulation of balloon angioplasty in residually stressed blood vessels-Application of a gradient-enhanced fibre damage model.
  • 2016
  • Ingår i: Journal of Biomechanics. - : Elsevier BV. - 1873-2380 .- 0021-9290.
  • Tidskriftsartikel (refereegranskat)abstract
    • In this contribution we study the balloon angioplasty in a residually stressed artery by means of a non-local gradient-enhanced fibre damage model. The balloon angioplasty is a common surgical intervention used to extend or reopen narrowed blood vessels in order to restore the continuous blood flow in, for instance, atherosclerotic arteries. Inelastic, i.e. predominantly damage-related and elastoplastic processes are induced in the artery during its inflation resulting in an irreversible deformation. As a beneficial consequence, provided that the inelastic deformations do not exceed a specific limit, higher deformations can be obtained within the same pressure level and a continuous blood flow can be guaranteed. In order to study the mechanical response of the artery in this scenario, we make use of the non-local gradient-enhanced model proposed in Waffenschmidt et al. (2014). In this contribution, we extend this model to make use of an incompressible format in connection with a Q1Q1P0 finite element implementation. The residual stresses in the artery are also taken into account following the framework presented in Waffenschmidt (2015). From the results it becomes apparent that, when the artery is subjected to radial stresses beyond the physiological range, damage evolution is triggered in the collagen fibres. The impact of the residual stresses on the structural response and on the circumferential stress distribution along the thickness of the arterial wall is also studied. It is observed that the residual stresses have a beneficial effect on the mechanical response of the arterial wall.
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6.
  • Tobias, Waffenschmidt, et al. (författare)
  • A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials
  • 2014
  • Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 268, s. 801-842
  • Tidskriftsartikel (refereegranskat)abstract
    • A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed.
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8.
  • Tobias, Waffenschmidt, et al. (författare)
  • Extremal states of energy of a double-layered thick-walled tube – application to residually stressed arteries
  • 2014
  • Ingår i: Journal of the Mechanical Behavior of Biomedical Materials. - : Elsevier BV. - 1751-6161. ; 29, s. 635-654
  • Tidskriftsartikel (refereegranskat)abstract
    • Various biological tissues are designed to optimally support external loads for complex geometries and mechanobiological structures. This results in complex microstructures of such materials. The design of, for instance, (healthy) arteries, which are in the focus of this work, is characterised by a residually stressed fibre-reinforced multi-layered composite with highly non-linear elastic response. The complex interaction of material properties with the geometry and residual stress effects enables the optimal support under different blood pressures, respectively blood flow, within the vessel. The fibres reinforcing the arterial wall, as well as residual stresses present in the vessel, strongly influence its overall behaviour and performance. Turn-over and remodelling processes of the collagenous fibres occurring in the respective layers – either resulting from natural growth phenomena or from artificially induced changes in loading condition such as stent deployment – support the optimisation of the multi-layered composite structure of arteries for the particular loading conditions present in the artery. Within this contribution, the overall energetic properties of an artery are discussed by means of the inflation, bending and extension of a double-layered cylindrical tube. Different states of residual stresses and different fibre orientations are considered so that, for instance, representative fibre angles that result in extremal states of the total potential energy can be identified. In view of turn-over and remodelling processes, these orientations are considered to constitute preferred directions of fibre alignment. In summary, the main goal of this work is to calculate optimal material, structural and loading parameters by concepts of energy-minimisation. Several numerical studies show that the obtained values – such as the fibre orientations, the residual axial stretch and the opening angle – are in good agreement with respective physiological parameters reported in the literature.
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9.
  • Waffenschmidt, Tobias, et al. (författare)
  • A Gradient-Enhanced Continuum Damage Model for Residually Stressed Fibre-Reinforced Materials at Finite Strains
  • 2015
  • Ingår i: Biomedical Technology. - Cham : Springer International Publishing. - 1613-7736. - 9783319109800 ; 74, s. 19-40
  • Bokkapitel (refereegranskat)abstract
    • The modelling of damage effects in materials constitutes a major challenge in various engineering-related disciplines. However, the assumption of purely local continuum damage formulations may lead to ill-posed boundary value problems and—with regard to numerical methods such as the finite element method—to mesh-dependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, we present a non-local gradient-enhanced damage model at finite strains. We additively compose the hyperelastic constitutive response at local material point level of an isotropic matrix and of an anisotropic fibre-reinforced material. The inelastic constitutive response is characterised by a scalar [1– d]-damage model, where we assume only the anisotropic elastic part to damage. Furthermore, we enhance the local free energy by a gradient-term. This term essentially contains the gradient of the non-local damage variable which we introduce as an additional global field variable. In order to guarantee the equivalence between the local and non-local damage variable, we incorporate a penalisation term within the free energy. Based on the principle of minimum total potential energy, we obtain a coupled system of variational equations. The associated non-linear system of equations is symmetric and can conveniently be solved by standard incremental-iterative Newton-Raphson schemes or arc-length-based solution methods. As a further key aspect, we incorporate residual stresses by means of a multiplicative composition of the deformation gradient. As a three-dimensional finite element example, we study the material degradation of a fibre-reinforced tube subjected to internal pressure. This highlights the mesh-objective and constitutive properties of the model and illustratively underlines the capabilities of the formulation with regard to biomechanical application such as the simulation of arteries.
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