Finite‐volume stress analysis in multi‐material linear elastic body

Abstract

Correct calculation of stresses at the interface of bonded or otherwise joined materials plays a significant role in many applications. It is therefore, important that traction at the material interface is calculated as accurately as possible. This paper describes procedures that can be employed to achieve this goal by using centre-based finite volume method. Total traction at the interface is calculated by decomposing it into normal and tangential components, both being calculated at each side of the interface, and applying the continuity assumption. The way in which the traction approximation is achieved depends on calculation of tangential gradient of displacement at the interface. To this end, three different methods are proposed and validated against problems with known solutions. It was shown than all methods can be successfully used to simulate problems with multi-material domains, with the procedure based on finite area method being most accurate.

Analysis of two-phase ceramic composites using micromechanical models

“…When the critical normal separation, δ c , is reached, fracture is assumed to have taken place and the cohesive faces are thereafter treated as traction-free faces. in Carolan et al [9] and Tukovic et al [37].…”

Arbitrary crack propagation in multi-phase materials using the finite volume method

“…As shown in [12], the normal and tangential components of the traction vector t = n · σ can be expressed in terms of displacement vector u using constitutive equation (5) as follows:…”

“…Equations (6) and (7) are valid up to the interface but not across the interface due to discontinuity of displacement gradient across the interface. The derivation of the correction traction at the interface can be found in Tuković et al [12].…”

“…Details of FV discretization of the considered mathematical model can be found in [12], where special attention is paid to discretization of traction force at the multi-material interface.…”

“…Recently, Tuković et al [12] have developed a finite-volume based method to accurately calculate tractions at the interface of two or more dissimilar solid materials. Due to the difference in elastic properties of the constituent material they showed that the interface can be a potential source of the onset of damage.…”