Development of a generalized material interface for the simulation of finite elasto-plastic deformations

Bucher, Anke; Görke, Uwe–Jens; Kreißig, R.

doi:10.1016/s0020-7683(01)00131-7

Cited by 10 publications

(7 citation statements)

References 15 publications

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“…The equations necessary to integrate the stress increment usually lead to a differential-algebraic equation system (Hartmann et al 1997;Bucher et al 2001) of the form…”

Section: Discretisation Of the Weak Formmentioning

confidence: 99%

On advantages of the Kelvin mapping in finite element implementations of deformation processes

et al. 2016

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Classical continuum mechanical theories operate on three-dimensional Euclidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapping is that Kelvin's method preserves tensor character, and thus the numerical matrix notation directly corresponds to the original tensor notation. Further benefits in numerical implementations are that tensor norms are calculated identically without distinguishing stress-or strain-type quantities, and tensor equations can be directly transformed into matrix equations without additional considerations. The only implementational changes are related to a scalar factor in certain finite element matrices, and hence, harvesting the mentioned benefits comes at very little cost.

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“…The equations necessary to integrate the stress increment usually lead to a differential-algebraic equation system (Hartmann et al 1997;Bucher et al 2001) of the form…”

Section: Discretisation Of the Weak Formmentioning

confidence: 99%

On advantages of the Kelvin mapping in finite element implementations of deformation processes

et al. 2016

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“…Defining suitable evolutional equations for special scalar and tensor-valued internal variables the constitutive equations are capable to describe isotropic as well as kinematic and distorsional hardening with an additional initial anisotropy. The thermodynamical consistency of the material model has been proven analyzing the Clausius-Duhem inequality (for details see Bucher et al [8,9,10]). …”

Section: Materials Modelmentioning

confidence: 99%

Identification and estimation of constitutive parameters for material laws in elastoplasticity

et al. 2007

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MSC (2000) 49Q12, 74P10, 74S05The paper summarizes the comprehensive experience of the authors in the numerical identification and estimation of parameters for anisotropic elastoplastic material laws analyzing inhomogeneous mechanical fields. Generally, the constitutive model under consideration represents a system of differential and algebraic equations. It distinguishes itself by a strictly thermodynamically consistent foundation, and an identical structure in case of small as well as finite deformations. Different rules for the evolution of internal variables describing various hardening effects are proposed. The nonlinear inverse problem of the identification of material parameters is solved with deterministic optimization methods. Basically, the least squares type objective function contains several local and global variables for the comparison of experimental and numerical data. Within this context, the numerical values of the comparative quantities are calculated either using the local integration of the initial value problem at suitably chosen material points or analyzing the entire initial-boundary value problem (e.g. with the Finite Element Method). In order to obtain the gradient of the objective function within the framework of a sensitivity analysis a semianalytical approach based on the implicit differentiation of the equilibrium conditions and the discretized constitutive relations is presented. The numerical algorithms for the direct as well as the inverse problem are implemented into in-house Finite Element codes. Some examples based on real and numerical experiments analyzing selected constitutive approaches are presented.

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“…In accordance with the considered number of stress components the matrixG is composed of a corresponding number of vectors N analogously to (13). The calculation of the smoothed stresses σ is based on an assembly of all adjacent elements (the patch) around a vertex node.…”

Section: Patch-oriented Transfer Of History-dependent State Variable mentioning

confidence: 99%

“…Applying a generalized implicit single step discretization scheme (Euler, CrankNicolson as special cases) for the solution of differential equations we get a non-linear system of algebraic equations which is solved by Newtons method. For details we refer to [12][13][14].…”

Section: Integration Of the Materials Law At Element Nodesmentioning

confidence: 99%

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A Comparison of Mapping Algorithms for Hierarchical Adaptive FEM in Finite Elasto-Plasticity

et al. 2006

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The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.

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Development of a generalized material interface for the simulation of finite elasto-plastic deformations

Cited by 10 publications

References 15 publications

On advantages of the Kelvin mapping in finite element implementations of deformation processes

On advantages of the Kelvin mapping in finite element implementations of deformation processes

Identification and estimation of constitutive parameters for material laws in elastoplasticity

A Comparison of Mapping Algorithms for Hierarchical Adaptive FEM in Finite Elasto-Plasticity

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