13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The interphase elasto-plastic damaging model Giuseppe Giambanco1,*, Giuseppe Fileccia Scimemi1, Antonino Spada1 1 Department of Civil, Environmental, Aerospace and Materials’ Engineering, University of Palermo, 90128, Italy * Corresponding author: giuseppe.giambanco@unipa.it Abstract Heterogeneous materials present a mechanical response strongly dependent on the static and kinematic phenomena occurring in the constituents and at their joints. In order to analyze this kind of materials it is a common practice to distinguish a macroscopic length scale of interest from a mesoscopic one, where the mesoscopic length scale is of the order of the typical dimensions of the constituents. At the mesoscopic level the interaction between the units is simulated by mean of apposite mechanical devices. Among these devices is popular the zero thickness interface model where contact tractions and displacement discontinuities are the primary static and kinematic variables respectively. However, in heterogeneous materials the response also depends on joint internal stresses as much as on contact stresses. The introduction of internal stresses brings to the interphase model or an enhancement of the classical zero-thickness interface. With the term ‘interphase’ we shall mean a layer separated by two physical interfaces from the bulk material or a multilayer structure with varying properties and several interfaces. Different failure conditions can be introduced for the physical interfaces and for the joint material. The interphase model has been implemented in an open-source research-oriented finite element analysis program for 2D applications. Numerical simulations are provided to show the main features of the model. Keywords Interphase element, Damage, Elastoplasticity, Finite element 1. Introduction The mechanical response of all those structures that are constituted by heterogeneous materials is dependent by different static and kinematic phenomena occurring in each constituent and at their joints. Material degradation due to nucleation, growth and coalescence of microvoids and microcracks is usually accompanied by plastic deformations as decohesion and sliding that cause strain softening and induced anisotropy. The mesoscopic approach is by now the most diffused technique to understand this kind of materials, because it overcomes the problems associated with the strong simplifications that have to be introduced when the macroscopic approach is applied. In particular, with the mesoscopic approach all the material constituents are modelled individually and their interactions are regulated by using appropriate devices able to reproduce the inelastic phenomena that usually occur at the physical interfaces. In literature, these mechanical devices are generally called contact elements, normally distinguished between link elements, thin layer elements and zero-thickness interface elements (ZTI). In the last decades interface elements have been applied in several engineering applications due to their simple formulation and to their easiness to be implemented in finite element codes [1-10]. The interface constitutive laws are expressed in terms of contact tractions and displacement discontinuities which are considered as generalized joints strains. In order to model the nonlinear behaviour caused by plastic deformations and damage evolution the constitutive laws of the interface elements are formulated making use of concepts borrowed by theory of Plasticity and Continuum Damage Mechanics. In many cases the structural response depends also on internal stresses and strains within the joint. It is sufficient to think to the fracture that appears in the middle of masonry blocks caused by the horizontal tangential contact stresses between the mortar and the block when a masonry assembly is subjected to a pure compressive load. These tangential stresses cannot be captured by the classical ZTI model. Therefore, the usual assumption used in zero-thickness interface elements, where the response is governed by contact stress components, may require a correction by introducing the
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