Theory and numerics of ductile micropolar elastoplastic damage

Abstract

SUMMARYThe aim of this work is to extend an isotropic elastoplastic damage concept for ductile materials within a generalized micropolar continuum framework. The underlying motivation is on the one hand to model softening behaviour by damage evolution and on the other hand to regularize the impending loss of ellipticity which results in strong mesh dependence of localization computations. To this end, the classical displacement field is supplemented by an independent rotation field to yield an enhanced continuum. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. Special emphasis is directed towards the numerical implementation of the constitutive model within the framework of finite element analysis of inelastic boundary value problems.To compare damage evolution and standard strain softening the results are contrasted to the outcome of an analysis with the micropolar version of the classical von Mises model. Thereby, the intriguing correspondence of strain softening and damage evolution is highlighted. Additionally, several planar micropolar finite element formulations are derived within mixed variational principles to enhance the poor performance of the standard bilinear displacement and rotation expansions used so far in the literature. The merits of these new element developments are demonstrated for the example of localization within a compression problem.

Towards dense, realistic granular media in 2D

“…[3,77,78], nor the possibility of additional (micro-polar) terms (like in the Cosserat approach [15,[79][80][81][82][83][84][85][86], see also Refs. [87][88][89][90][91][92][93][94] among many others), asymmetric terms in general, or the presence of anisotropy in the constitutive relations, e.g., for stress in Eq. (4), [73,77,95].…”

Numerical investigations of shear localization in a micro‐polar hypoplastic material

“…Among them, de Borst [27] presented a tangent operator for Cosserat elastoplasticity following Simo and Taylor's concept of consistent linearization of the response function resulting from the integration algorithm. In cases where deformations under almost constant volume are dominant, the performance of the four-noded quadrilateral element with standard bilinear displacement and rotation interpolation and with full element integration is poor [29] and can lead to the so-called volumetric locking as first discussed in the framework of the non-polar continuum by Nagtegaal et al [42]. It was shown by Steinmann [29] that the performance of the standard quadrilateral finite element with bilinear displacement and rotation interpolation can be improved based on mixed variational principles.…”

“…u uhlhaus [23], de Borst [27], Tejchman and Wu [26], Tejchman [28], Steinmann [29], Ehlers and Volk [30], who used a micro-polar elasto-plastic law, and by Tejchman [28], Bauer and Tejchman [31], Tejchman and Bauer [32], Bauer and Huang [33], Tejchman and Gudehus [34], who used a micro-polar hypoplastic model. Although there is a wide interest in micro-polar continuum theories as a tool for the regularization of shear localization a critical perusal of the relevant literature reveals that the development of constitutive models for granular materials is still in progress.…”

“…It may be noted that although many numerical investigations using micro-polar continuum models have been published only a few publications deal with questions of the finite element implementation (e.g. References [27,40,29,41]). Among them, de Borst [27] presented a tangent operator for Cosserat elastoplasticity following Simo and Taylor's concept of consistent linearization of the response function resulting from the integration algorithm.…”

An isotropic damage model to simulate collapse in reinforced concrete elements

“…In finite elements computations spurious mesh sensitivity problems occur, strain localizes into a narrow band whose width depends on the element size, the corresponding load-displacement curve always shows snapback for a fine mesh and the dissipate fracture energy converges to zero. To overcome the shortcomings of local theories for modelling strain softening, some alternatives have been proposed such as: non-local modelling of the constitutive behaviour (Costa Mattos et al 1992, Costa Mattos and Sampaio 1995, Da Costa Mattos et al 2009), gradient material description (Triantafylidis andAifantis 1986, Peerlings et al 1996), micropolar continuum theory (de Borst 1991, Steinmann 1995, viscous regularization (de Borst and Mühlhaus 1992) and local manipulations of the material properties depending on the element size (Bazant and Oh 1983, Crisfield 1986, Oliver 1989. Recently, Da Costa- Mattos et al (2009) proposed a special gradient-enhanced damage theory in which the material is considered to possess a substructure or microstructure, where the free energy is supposed to depend not only on the strain and the damage variable but also on the damage gradient.…”