PSI - Issue 39

Fabrizio Greco et al. / Procedia Structural Integrity 39 (2022) 638–648 Author name / Structural Integrity Procedia 00 (2019) 000–000

643

6

purely mathematical interfaces (comprised in a single phase), inserted to capture the diffuse damage phenomena occurring inside the mortar joint. The creation of the numerical model is conducted by means of a pre-processing stage, which entails the following three steps (also depicted in Figure 2): • Creation of the initial 2D volumetric mesh according to either a structured (i.e., cross-triangle equilateral) or unstructured ( i.e. , Delaunay-type triangulation scheme) mesh arrangement (Figure 2-a). • Separation of the bulk finite elements (Figure 2-b) • Insertion of four-node zero-thickness cohesive interface elements between adjacent volumetric elements (Figure 2-c).

Figure 2. Schematics of the pre-processing stages for the construction of the enriched cohesive/volumetric finite element mesh: (a) Generation of the initial 2D mesh; (b) separation of the bulk FE elements; (c) Insertion of four-node zero-thickness cohesive interface elements.

Both brick/mortar and mortar/mortar interface elements are equipped with the intrinsic traction-separation law described in Section 2.1. As described in (Tomar et al. (2004)), the presence of inactive diffuse interface elements affects negatively the mechanical behavior of the entire bulk/cohesive system. More precisely, since cohesive stiffnesses must assume a finite value also for undamaged states, the inserting of several interface elements along all the boundaries of the computational mesh produces an artificial stiffness reduction of the entire material. Such a reduction inversely depends on the mesh size, so that the numerical solution suffers from mesh dependency issues. This is the commonly known mesh-induced artificial compliance effect. To address such drawbacks, the cohesive stiffness of the embedded interface must be properly calibrated. Some of the present authors have already proposed an effective micromechanics-based stiffness calibration procedure, involving a numerical homogenization technique applied to a cohesive/volumetric element assembly (De Maio et al. (2020b)). In particular, the calibration procedure consists of controlling the reduction factor hom E R E E = ( i.e. , the ratio between the homogenized and the bulk elastic moduli of the assembly), after assuming no reduction for the Poisson’s ratio ( i.e., hom 1 R ν ν ν = = ). The main outputs where two charts for the calibration of the dimensionless normal and tangential stiffnesses, expressed as follows:

0 K L

0

K K

;

(7)

κ

=

ξ

=

n mesh

s

0

E

n

where, E is the Young’s modulus of the material embedding interface elements, L mesh is the mesh size adopted in the numerical model, and 0 n K and 0 s K are the normal and tangential cohesive stiffnesses. As highlighted in (Klein et al. (2001)), κ appears as the key dimensionless parameter in controlling the mesh dependency of the cohesive finite element approach. Specifically, the stiffness reduction reduces as the parameter κ assumes a large value. In the present study, ξ is fixed to the unity and κ is assumed equal to 239 and 171 for structured and unstructured mesh configurations, respectively. Such values ensure that Young’s modulus reduction is of about 1%.