Browsing by Subject "Weighted average"
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Item Open Access Generalized interfaces via weighted averages for application to graded interphases at large deformations(Elsevier Ltd, 2021-04) Saeb, S.; Firooz, S.; Steinmann, P.; Javili, AliFinite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zero-thickness interface model. Commonly accepted interface models intuitively assume that the interface layer is situated exactly in the middle of its associated interphase. Furthermore, it has been reported in the literature that this assumption is necessary to guarantee the balance of angular momentum on the interface. While the interface coincides with the mid-layer of a uniform interphase, we argue that this assumption fails to sufficiently capture the behavior of graded or inhomogeneous interphases. This contribution extends the formulation of the general interface model to account for arbitrary interface positions. The issue of angular momentum balance on general interfaces is critically revisited. It is proven that the interface position does not necessarily have to coincide with the mid-layer in order to satisfy the angular momentum balance. The analysis here leads to a unique definition of the controversially discussed interface configuration. The presented general interface model is essentially based upon the weighted average operator instead of the commonly accepted classical average operator. The framework is geometrically exact and suitable for finite deformations. The significance of the interface position is demonstrated via a series of examples where the interface position is identified based on a full resolution interphase.Item Open Access Homogenization of composites with extended general interfaces: comprehensive review and unified modeling(ASME, 2021-08-03) Javili, Ali; Steinmann, P.; Firooz, S.Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well-established strategy to capture a finite thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. This paper revisits this assumption and introduces an extended general interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed within the framework of linear elasticity. Through utilizing a weighted average operator, we demonstrate that the assumption of enforcing the interface to coincide with the midlayer is not required and thereby develop a new class of interfaces where the interface is allowed to take any arbitrary position between its bulk neighbors. The proposed novel interface model can recover any of the classical interface models. Next, via incorporating this extended general interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio, and interface parameters on the overall properties of composites. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nanocomposites due to their pronounced interface effects at small scales.