The zeroth-order multiphysics finite-volume micromechanics has been proposed to model coupled thermo-electro-mechanical behaviors of unidirectional composites embedded with piezoelectric phases. Parametric mapping is implemented within the multiphysics finite-volume theory’s framework, facilitating modeling of multiphase piezoelectric materials with complex microstructures with relatively coarse unit cell discretization. The resulting theory admits piezoelectric materials with complete anisotropy and arbitrary poling direction and enables rapid generation of the entire set of coupled thermo-mechanical, piezoelectric properties, figures of merits, as well as the local fluctuations of fields within the composite microstructures with greater fidelity than its predecessor. The proposed method is verified extensively by comparison with the finite-element homogenization technique, which produces an excellent agreement in a wide range of volume fractions but offers much better stability and efficiency. The contrast with the rectangular theory is also presented and discussed, demonstrating the advantage and the need for the development of parametric formulation. This extension further increases the finite-volume direct averaging micromechanics theory’s range of applicability, providing an attractive standard for investigating multiphase and multiphysics problems with different microstructural architectures and scales against which other approaches may be compared.
The zeroth-order parametric finite-volume direct averaging micromechanics (FVDAM) theory is further extended in order to model the evolution of damage in periodic heterogeneous materials. Toward this end, displacement discontinuity functions are introduced into the formulation, which may represent cracks or traction-interfacial separation laws within a unified framework. The cohesive zone model (CZM) is then implemented to simulate progressive separation of adjacent phases or subdomains. The new capability is verified in the linear region upon comparison with an exact elasticity solution for an inclusion surrounded by a linear interface of zero thickness in an infinite matrix that obeys the same law as CZM before the onset of degradation. The extended theory's utility is then demonstrated by revisiting the classical fiber/matrix debonding phenomenon observed in SiC/Ti composites, illustrating its ability to accurately capture the mechanics of progressive interfacial degradation.
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