A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identificati
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O R I G I NA L PA P E R
L. Sprave
· A. Menzel
A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification
Received: 21 February 2020 / Revised: 7 July 2020 © The Author(s) 2020
Abstract A gradient-enhanced ductile damage model at finite strains is presented, and its parameters are identified so as to match the behaviour of DP800. Within the micromorphic framework, a multi-surface model coupling isotropic Lemaitre-type damage to von Mises plasticity with nonlinear isotropic hardening is developed. In analogy to the effective stress entering the yield criterion, an effective damage driving force— increasing with increasing plastic strains—entering the damage dissipation potential is proposed. After an outline of the basic model properties, the setup of the (micro)tensile experiment is discussed and the importance of including unloading for a parameter identification with a material model including damage is emphasised. Optimal parameters, based on an objective function including measured forces and the displacement field obtained from digital image correlation, are identified. The response of the proposed model is compared to a tensile experiment of a specimen with a different geometry as a first approach to validate the identified parameters. Keywords Ductile damage · Gradient-enhanced formulation · Micromorphic model · Parameter identification · DIC measurements · Multi-surface formulation
1 Introduction The design of metal forming processes requires increasingly more accurate models to predict material behaviour in order to use more of the forming capability of the material and to more accurately predict safety margins, ultimately saving costs and energy. To this end, the description of damage, particularly damage preceding failure, needs to be improved together with the development of predictive simulation tools and models, e.g. by means of a regularised continuum damage formulation coupled to finite plasticity. The field of damage mechanics dates back to the original findings from Kachanov [22] and further development by Rabotnov [50], who proposed a single scalar damage variable to model the effects of creep damage. For many years, only isotropic damage was considered, which, however, is in contrast to the anisotropic nature of damage mechanisms. In order to capture anisotropic damage phenomena, a tensorial damage variable may be introduced [9,13,23,30]. Damage evolves with increased loading, and the form of anisotropy can change during loading. These changes may be captured by an approach which, by means of related mappings, introduces a fictitious undamaged configuration and which defines a tensorial damage variable, see [17,41–43] L. Sprave (B)· A. Menzel Institute of Mechanics, TU Dortmund, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany E-mail: [email protected] A. Menzel Division of Solid Mechanics, Lund University, P.O. Box 118, 221 00 Lund, Sweden
L. Sprave, A. Menzel
amongst others. Research on anisotropic damage formulatio
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