| 1. |
- Heitbreder, Tim, et al.
(författare)
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Consistent elastoplastic cohesive zone model at finite deformations – Variational formulation
- 2017
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 106-107, s. 284-293
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Tidskriftsartikel (refereegranskat)abstract
- Cohesive zone models based on classical interface-type formulations at finite deformations are subjected to fundamental physical principles such as thermodynamical consistency, balance equations and material frame indifference. However, these restraints are often ignored and in that respect such formulations are inconsistent. By way of contrast, a consistent cohesive zone framework suitable for the analysis of localized elastoplastic deformations which only depends on the displacement jump was recently advocated in Ottosen et al. (2015). A certain subclass of this consistent framework is analyzed here, further extended and finally, an efficient numerical implementation is proposed. Conceptually, the considered cohesive zone model is a fiber-like model where the fiber direction is defined by the direction of the displacement discontinuity. A novel unloading model is advocated where the key idea is to assign a vanishing bending stiffness to the fibers and they therefore buckle when compressive stresses are initiated. Following ideas known from wrinkling in membranes, it is shown that the resulting framework can be rewritten into a variationally consistent format such that all unknowns follow jointly from minimizing a time-dependent potential whose discretization leads to an efficient implementation in terms of an efficient variational constitutive update. The physical properties of the final constitutive framework are analyzed by means of numerical examples. This analysis shows that although the framework is based on elastoplasticity, it predicts for the L-shaped structure investigated a mechanical response similar to that of damage theory even during unloading.
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| 2. |
- Heitbreder, Tim, et al.
(författare)
-
On damage modeling of material interfaces : Numerical implementation and computational homogenization
- 2018
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 337, s. 1-27
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Tidskriftsartikel (refereegranskat)abstract
- A novel constitutive framework suitable for material interfaces undergoing large deformations in a geometrically exact setting was developed in Ottosen et al. (2016). In contrast to previous works, it permits the description of arbitrary material anisotropies by fulfilling all fundamental balance laws in physics as well as the principle of material objectivity. This paper deals with an efficient finite element implementation of the aforementioned framework in terms of the natural basis vectors. To be more precise, a different, more compact and more direct derivation of this framework is outlined first. It relies on the variational structure of the underlying problem. Subsequently, the aforementioned finite element approximation is elaborated which is finally embedded into a computational homogenization scheme. This scheme allows the analysis of the influence of the novel interface model on the resulting macroscopic (effective) material response. It is shown by numerical examples that the interaction of bulk energies and interface energies leads, in a very natural manner, to a complex size effect. It includes the frequently observed “the smaller the stiffer” relation, but also the less often observed “the smaller the softer” relation. However, since the overall response is usually a superposition of such relations, the effective properties cannot generally be characterized by one of the aforementioned limiting relations.
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