PSI - Issue 61

Ahmet Arda Akay et al. / Procedia Structural Integrity 61 (2024) 138–147 A.A. Akay et al. / Structural Integrity Procedia 00 (2024) 000–000

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dimensions of inclusions in a matrix phase such as polymer nanocomposite materials, FEM analyses of such a struc ture will be computationally ine ffi cient and expensive. Since the FEM mesh size should be smaller than the size of the filler in the neighborhood of the inclusion and should macroscopically cover all the material, the transition of the mesh from small-scale to macro-scale will be di ffi cult. Hence, the number of finite elements required in such a mesh will be extremely high. One of the most important parameters determining the strength of heterogeneous domains is the strength of the reinforcement-matrix interface. Interface modeling plays a crucial role in the mathematical modeling of Representa tive Volume Elements (RVEs) with reinforcing phases. The boundary elements where the matrix and the reinforce ment material at the interface intersect should be defined in a way that separation is allowed. Unlike the continuous medium of finite elements, the mechanical behavior of these elements can not be described by a constitutive equa tion between the stress tensor-strain tensor. Instead, linear or nonlinear constitutive equations between the stress vector-displacement jump (traction-displacement jump) must be introduced. In the finite element method, traditional interface elements in three-dimensional problems are two-dimensional surface elements. 8-node rectangular interface elements are utilized between 8-node trilinear rectangular brick elements, while 6-node linear triangle interface ele ments are defined for 4-node linear tetrahedron. Similarly, 10-node quadratic triangle interface elements are employed between 10-node quadratic tetrahedron. In two-dimensional finite elements, one-dimensional interface elements with zero thickness are introduced. In the boundary element method, since the elements are already defined in the boundary regions, a separate element definition is not required, as opposed to the finite element method. Classical interface models have been presented in many studies in the literature. To address the relationship between nodes on two di ff erent faces of an interface, we first need to define the relative displacement ( u ) and the stress vector ( R ) between these nodes. The normal and tangential components of these variables are defined as ( u n , u t ) and ( R n , R t ), respectively. In the literature, various laws are used to represent the relationship between the stress vector R and the relative displacement u . Some of these models are presented in Figure 1.

(a) Barenblatt et al. (1962)

(b) Dugdale (1960)

(c) Needleman (1987)

(d) Tvergaard and Hutchinson (1992)

(e) Xu and Needleman (1994)

(f) Tvergaard (1990)

(g) RCMM Raous et al. (1999) (h) Chaboche et al. (2001)

Fig. 1: A selection of interface models used in the literature

Adhesive interface models for the normal stress vector under monotonic loading conditions are mainly used for the numerical simulation of the propagation of cracks in Mode-I fracture, and therefore only the displacements in the normal direction are taken into account. The models of Barenblatt et al. (1962), Dugdale (1960), and Needleman (1987), which are presented in Figure 1, can be considered as representative examples of such numerical methods. The interface models that take the friction / adhesion e ff ects into account were first introduced in the 1970s by Palmer and Rice (1973). In the 1980s, Fre´mond (1988) introduced the concept of the intensity of adhesion. Some authors in the literature have not taken friction into account while modeling the interface (i.e. Tvergaard and Hutchinson (1992)