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. We revisit this assumption and introduce a universal interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed. The proposed novel interface model is universal in the sense that it can recover any of the classical interface models. Next, via incorporating this universal 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. Furthermore, we elaborate on the computational implications of this interface model. 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, where an excellent agreement between the analytical and computational results is observed. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nano-composites due their pronounced interface effects at small scales.

Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.

Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks.

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Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zerothickness 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.