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Christian Miehe - One of the best experts on this subject based on the ideXlab platform.
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an incremental variational formulation of dissipative magnetostriction at the macroscopic continuum level
International Journal of Solids and Structures, 2011Co-Authors: Christian Miehe, Bjorn Kiefer, Daniele RosatoAbstract:This paper outlines a new variational-based modeling and computational implementation of macroscopic continuum magneto-mechanics involving non-linear, Inelastic Material behavior, with a special focus on dissipative magnetostriction. It is based on a constitutive variational principle that optimizes a generalized incremental work function with respect to the internal state variables. In an incremental setting at finite time steps, this variational problem defines a quasi-hyper-magnetoelastic potential for the stresses and the magnetic induction, and incorporates energy storage as well as dissipative mechanisms. The existence of this potential further allows the incremental boundary-value problem of quasi-static Inelastic magneto-mechanics to be recast into a principle of stationary incremental energy. The second focus of this paper is on the careful construction of the energy storage and dissipation functions for the model problem of hysteretic magnetostriction at the macroscopic level. It is then demonstrated that the proposed model is capable of predicting the ferromagnetic and field-induced strain hysteresis curves characteristic of magnetostrictive Material response in good agreement with experiments. The numerical solution of the coupled non-linear boundary-value problem is based on a monolithic multi-field finite element implementation. As a consequence of the proposed incremental variational principle, the discretization of the multi-field problem appears in a compact symmetric format. In this sense, the proposed formulation provides a canonical framework for the simulation of boundary-value-problems in dissipative magnetostriction at the macro-level. The performance of the proposed algorithm is tested by application to relevant numerical examples.
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on multiscale fe analyses of heterogeneous structures from homogenization to multigrid solvers
International Journal for Numerical Methods in Engineering, 2007Co-Authors: Christian Miehe, C G BayreutherAbstract:Heterogeneous structures like composites often need a fine-scale resolution of micro-effects which influence the macroscopic overall response. This is of particular relevance in the fully non-linear range of large strains and Inelastic Material response of the constituents. Suitable solution methods introduce a multifield scenario of hierarchically superimposed states on different length scales. For big differences of micro- and macro-scales, the argument of scale separation induces the application of homogenization methods. Such types of physical multiscale approaches can be treated by nested multilevel finite element analyses that discretize both the fine-scale micro-structure as well as the macroscopic boundary-value problem. In contrast, small-scale differences require full resolution of the heterogeneous structure. Effective solution methods for the resulting large-scale problems with strongly oscillating properties are suitably designed geometric multigrid techniques, which may be considered as numerical multiscale approaches. In both scenarios, a key ingredient is the suitable formulation of scale bridging algorithms that govern the transfer between different scales. The paper outlines new mesh-bridging techniques in a deformation-driven context for fully non-linear response, which exploit in a non-trivial manner weak constraints on the average deformation in typical finite element patches. The framework is based on an incremental variational structure of finite Inelasticity. The proposed new formulations provide variational-based homogenization algorithms for physical multiscale scenarios and problem-dependent optimal finite element grid transfers for numerical multiscale scenarios of heterogeneous Materials. Copyright © 2007 John Wiley & Sons, Ltd.
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analysis of Material instabilities in Inelastic solids by incremental energy minimization and relaxation methods evolving deformation microstructures in finite plasticity
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: Christian Miehe, Marc Lambrecht, Ercan GursesAbstract:Abstract We propose an approach to the definition and analysis of Material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative Materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic stress potential. The existence of this potential allows to be recast a typical incremental boundary-value problem of quasi-static Inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the Material stability of the Inelastic Material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental Material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental stress potential . This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable Inelastic Materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex stress potentials for standard dissipative solids . The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size.
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a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric
International Journal of Solids and Structures, 1998Co-Authors: Christian MieheAbstract:Abstract The article presents a constitutive framework of large-strain elastoplasticity in both the Lagrangian and the Eulerian geometric setting which takes into account anisotropic Material response. In summary, the key ingredients of this framework are: (i) the introduction of a plastic metric which is assumed to describe locally the history-dependent Inelastic Material response in the sense of an internal variable formulation. (ii) The definition of a convex elastic domain in the space of the local stress-like variable conjugate to the plastic metric, denoted as the plastic force. (iii) An equivalent Lagrangian and Eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments, denoted as anisotropy variables. (iv) The set-up of normality rules for the evolution of the plastic metric and the anisotropy variables, yielding a canonical symmetric form of the elastoplastic tangent moduli. (v) A geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions. Applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic, initial anisotropic and induced anisotropic elastoplastic response.
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a formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric
Computer Methods in Applied Mechanics and Engineering, 1998Co-Authors: Christian MieheAbstract:The article presents a new formulation of isotropic elastoplasticity at large strains in both the Lagrangian and the Eulerian geometric setting and addresses aspects of its numerical implementation. The key ingredients on the theoretical side are the introduction of a plastic metric for the description of the local history-dependent Inelastic Material response, the definition of a convex elastic domain in the space of the local stress-like variable conjugate to the plastic metric, denoted as the plastic force, and a fully equivalent Lagrangian and Eulerian representation of all constitutive functions in spectral form for general non-Cartesian coordinate charts in terms of dual co- and contra-variant eigenvector triads which are normalized with respect to the plastic metric. On the numerical side, we propose a stress update algorithm for general non-associative isotropic elasto(visco)plastic response with an arbitrary number of scalar internal variables. The algorithm is based on an exponential map integrator and is recast into a general return mapping scheme, methodically organized with tensorial pre- and postprocessing and a constitutive box in the eigenvalue space. Furthermore, we propose a new perturbation stabilization technique which dramatically enhances the convergence of the general return algorithm. The theoretical and numerical developments are applied to a constitutive model problem with large elastic and large plastic strains: the von Mises-/Tresca-type associative plastic flow in Ogden-type large-strain elastic Materials.
Ali S Mirza - One of the best experts on this subject based on the ideXlab platform.
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equivalent uniform moment diagram factor for composite columns in major axis bending
Journal of Structural Engineering-asce, 2005Co-Authors: Timo K. Tikka, Ali S MirzaAbstract:The ACI Building Code permits the use of the equivalent uniform bending moment diagram factor ( Cm ) for computing the effect of moment gradient, along the column height, caused by unequal column end moments. The concept of equivalent uniform moment diagram was introduced into design practice to eliminate the need for extensive calculations based on the solution to a differential equation. The expression currently used by the ACI Building Code is a simplified equation based on the elastic behavior of columns, and does not include the Inelastic Material behavior. This study was conducted to investigate the influence of different variables on Cm of slender, tied, rectangular composite columns in which steel shapes are encased in concrete and to examine existing expressions for Cm . Approximately, 11,000 square composite columns, each with a different combination of specified values of variables, were simulated. The columns studied were subjected to short-term ultimate loads and unequal end moments causing m...
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equivalent uniform moment diagram factor for composite columns in minor axis bending
Aci Structural Journal, 2005Co-Authors: Timo K. Tikka, Ali S MirzaAbstract:The equivalent uniform moment diagram factor C m was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, to compute the effect of moment gradient, along the column height, caused by unequal column end moments. The C m expressions currently used by North American structural codes are based on the elastic behavior of columns, and do not include Inelastic Material behavior. This study was undertaken to determine the influence of different variables on C m of slender, tied, rectangular composite columns in which steel shapes are encased in concrete and to examine existing expressions for C m . Approximately 11,000 simulated columns, each with a different combination of specified values of variables, were used to generate the C m data. The columns studied were subjected to short-term ultimate loads and unequal end moments causing moment gradient in single curvature and double curvature bending about the minor axis of the encased steel section. Two C m design equations are proposed in this paper.
P. Wriggers - One of the best experts on this subject based on the ideXlab platform.
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Numerical homogenization of hardened cement paste
Computational Mechanics, 2008Co-Authors: M. Hain, P. WriggersAbstract:Based upon a three-dimensional computer-tomography of hardened cement paste, a finite-element mesh at micrometer length scale is introduced. Effective Material properties are obtained through numerical homogenization techniques using representative volume elements. Statistical tests, two- and three-dimensional computations and a comparison with experimental data are shown. For the hydration products of hardened cement paste a visco-plastic constitutive equation of P erzyna type including isotropic damage is introduced. The Inelastic Material parameters are identified solving an optimization problem through a combination of a stochastic genetic algorithm and the deterministic L evenberg -M arquardt method. The time-consuming evaluations of the corresponding objective function are distributed within a network environment automatically.
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computational homogenization of micro structural damage due to frost in hardened cement paste
Finite Elements in Analysis and Design, 2008Co-Authors: M. Hain, P. WriggersAbstract:Based on a micro-structural finite-element model using computer-tomography scans at micrometer length-scale, damage due to frost within hardened cement paste (HCP) is evaluated. In order to verify the microscopic constitutive equations, a multi-scale model is introduced which allows a comparison with experimental data at macro-level. Subsequently, damage due to frost is simulated numerically: the water-filled pores of HCP increase in volume during a freezing process which yields an Inelastic Material behavior. Numerical simulations at micro-structural level are performed for different moistures and temperatures, and an effective correlation between moisture, temperature and the Inelastic Material behavior is obtained. Finally, thermo-mechanical coupling is introduced and an effective constitutive equation for HCP is developed using the abovementioned temperature-moisture-damage correlation.
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analysis and simulation of contact problems
Published in 2006, 2006Co-Authors: P. Wriggers, Udo NackenhorstAbstract:Numerical methods.- Mortar-based surface-to-surface contact algorithms in large deformation solid mechanics.- From inexact active set strategies to nonlinear multigrid methods.- On a geometrical approach in contact mechanics.- On the discretization of contact problems in elastodynamics.- Mortar methods for contact problems.- Contact mechanics for analysis of fracturing and fragmenting solids in the combined finite-discrete element method.- Numerical analysis of a dynamic viscoelastic contact problem with damage.- An energy-conserving algorithm for nonlinear elastodynamic contact problems - Extension to a frictional dissipation phenomenon.- DDM-based sensitivity analysis and optimization for smooth contact formulations.- On the modeling of contact/impact problems between rubber Materials.- The quadrilateral parametric contact element based on the moving friction cone formulation.- 3D beam-to-beam contact within coupled electromechanical fields: a finite element model.- A study of symbolic description, numerical efficiency and accuracy of 2D and 3D contact formulations.- Mathematical analysis.- Existence theorems for noncoercive incremental contact problems with Coulomb friction.- Local uniqueness results for the discrete friction problem.- Analysis of a class of dynamic unilateral contact problems with friction for viscoelastic bodies.- Sthenic incompatibilities in rigid bodies motion.- Study of two quasistatic viscoplastic contact problems with adhesion.- A uniqueness criterion for the Signorini problem with Coulomb friction.- Finite element/boundary element coupling for two-body elastoplastic contact problems with friction.- Contact models, results and applications.- On the numerical simulation of non-smooth, resonant vibrations of delaminated structures.- Mesoscopic particles - a new approach for contact and friction dynamics.- On wedged configurations with Coulomb friction.- A genetic algorithm approach for wedged configurations with Coulomb friction.- Friction and contact between rough surfaces based on elastic-plastic sphere and rigid flat interaction.- TEDI (ThermoElasto-Dynamic Instability): a new mechanism for squeal & TEI.- Contact behaviour of a sliding rubber element.- Sliding friction and contact mechanics of elastomers on rough surfaces.- Unsteady rolling contact of rubber wheels.- A physicist view to tire traction.- Friction coefficient prognosis for the Grosch-wheel.- Numerical modelling of reinforced geoMaterials by wires using the non smooth contact dynamics.- A unified interface constitutive law for the study of fracture and contact problems in heterogeneous Materials.- Elasto-plastic contact of fractal surfaces.- A 3D study of the contact interface behavior using elastic-plastic constitutive equations.- Micromechanical analysis of deformation and temperature inhomogeneities within rough contact layers.- Micro-slip of rough surfaces under cyclic tangential loading.- Stability.- Stability of discrete systems involving shocks and friction.- On the stability of quasi-static paths of a linearly elastic system with friction.- The T.G.V. disk brake squeal.- Poster session.- Sliding path curvature dependent friction and wear.- Composition duality methods in contact mechanics.- Modeling of behaviour of the flat friction lining under the external.- The non smooth contact dynamic method: recent LMGC90 software developments and application.- Frictional contact of elastomer Materials on rough rigid surfaces.- Micromechanics of internal friction stress softening and hysteresis of reinforced rubbers.- Selected contact problems in human joints after arthroplasty.- Optimal impulsive control of dynamical system in an impact phase.- Tribometric analysis of two tribo-Materials with different contact geometries-critical reflection and simulation of the results.- Solvability and limit analysis of masonry bridges.- On the treatment of Inelastic Material behavior in an ALE-description of rolling contact.- A formulation to define the contact surface in the 2D mortar finite element method.
Terry Bennett - One of the best experts on this subject based on the ideXlab platform.
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geometrically nonlinear Inelastic analysis of steel concrete composite beams with partial interaction using a higher order beam theory
International Journal of Non-linear Mechanics, 2018Co-Authors: Md Alhaz Uddin, A H Sheikh, David Brown, Terry BennettAbstract:Abstract A comprehensive finite element model based on a higher-order beam theory (HBT) is developed for an accurate prediction of the response of steel–concrete composite beams with partial shear interaction. The formulation of the proposed one dimensional finite element model incorporated nonlinearities due to large deformations of the beam as well as Inelastic Material behaviour of its constituent components. The higher-order beam model is achieved by taking a third order variation of the longitudinal displacement over the beam depth for the steel and concrete layers separately. The deformable shear studs used for connecting the concrete slab with the steel girder are modelled as distributed shear springs along the interface between these two Material layers. The Green–Lagrange strain vector is used to capture the effect of geometric nonlinearity due to large deflections. The von Mises plasticity theory with an isotropic hardening rule and a damage mechanics model are incorporated within the proposed finite element model for simulating the Inelastic response of the beam Materials. The nonlinear governing equations are solved by an incremental-iterative technique following the Newton–Raphson method. A dissipation based arc-length method is employed to capture the post peak response of these beams successfully. The capability of the proposed model is assessed through its validation and verification using existing experimental results and numerical results produced by detailed finite element modelling of these beams.
Timo K. Tikka - One of the best experts on this subject based on the ideXlab platform.
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equivalent uniform moment diagram factor for composite columns in major axis bending
Journal of Structural Engineering-asce, 2005Co-Authors: Timo K. Tikka, Ali S MirzaAbstract:The ACI Building Code permits the use of the equivalent uniform bending moment diagram factor ( Cm ) for computing the effect of moment gradient, along the column height, caused by unequal column end moments. The concept of equivalent uniform moment diagram was introduced into design practice to eliminate the need for extensive calculations based on the solution to a differential equation. The expression currently used by the ACI Building Code is a simplified equation based on the elastic behavior of columns, and does not include the Inelastic Material behavior. This study was conducted to investigate the influence of different variables on Cm of slender, tied, rectangular composite columns in which steel shapes are encased in concrete and to examine existing expressions for Cm . Approximately, 11,000 square composite columns, each with a different combination of specified values of variables, were simulated. The columns studied were subjected to short-term ultimate loads and unequal end moments causing m...
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equivalent uniform moment diagram factor for composite columns in minor axis bending
Aci Structural Journal, 2005Co-Authors: Timo K. Tikka, Ali S MirzaAbstract:The equivalent uniform moment diagram factor C m was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, to compute the effect of moment gradient, along the column height, caused by unequal column end moments. The C m expressions currently used by North American structural codes are based on the elastic behavior of columns, and do not include Inelastic Material behavior. This study was undertaken to determine the influence of different variables on C m of slender, tied, rectangular composite columns in which steel shapes are encased in concrete and to examine existing expressions for C m . Approximately 11,000 simulated columns, each with a different combination of specified values of variables, were used to generate the C m data. The columns studied were subjected to short-term ultimate loads and unequal end moments causing moment gradient in single curvature and double curvature bending about the minor axis of the encased steel section. Two C m design equations are proposed in this paper.