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Eigenstrain based reduced order homogenization for polycrystalline materials. Comput. Methods
- F 〉q−1 ∂ 〈F 〉 ∂f ∂f ∂σ ⊗ a ] = γ 〈F 〉q [ ∂a ∂σ + q [sign(F
"... In this manuscript, an eigenstrain based reduced order homogenization method is devel-oped for polycrystalline materials. A two-scale asymptotic analysis is used to decompose the original equations of polycrystal plasticity into micro- and macroscale problems. Eigenstrain based representation of the ..."
Abstract
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In this manuscript, an eigenstrain based reduced order homogenization method is devel-oped for polycrystalline materials. A two-scale asymptotic analysis is used to decompose the original equations of polycrystal plasticity into micro- and macroscale problems. Eigenstrain based representation of the inelastic response field is employed to approximate the microscale boundary value problem using an approximation basis of much smaller order. The reduced or-der model takes into account the grain-to-grain interactions through influence functions that are numerically computed over the polycrystalline microstructure. The proposed approach is also endowed with a hierarchical model improvement capability that allows accurate rep-resentation of stress and deformation state within subgrains. The proposed approach was implemented and its performance was assessed against crystal plasticity finite element simula-tions. Numerical studies point to the capability to efficiently compute the mechanical response of the polycrystal RVEs with good accuracy and the ability to capture stress risers near grain boundaries.
Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media
"... This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal ..."
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This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.
