This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the anal...This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the analytical solutions for the stress and displacement fields are derived with the Stroh formalism,Green's function method,and polygonal mapping functions.Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution.The results show that the polygonal hole shapes significantly influence the generalized hoop stress,with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects.The stress concentrations at hole corners reach their maximum values at specific sharpness parameters,depending on the polygon type.The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs,and provide theoretical guidance for their structural design and optimization.展开更多
Lattice materials have demonstrated promising potential in engineering applications owing to their exceptional lightweight,high specific strength,and tunable mechanical properties.However,the traditional homogenizatio...Lattice materials have demonstrated promising potential in engineering applications owing to their exceptional lightweight,high specific strength,and tunable mechanical properties.However,the traditional homogenization methods based on the classical elasticity theory struggle to accurately describe the non-classical mechanical behaviors of lattice materials,especially when dealing with complex unit-cell geometries featured by non-symmetric configurations or non-single central node connections.In response to this limitation,this study establishes a generalized homogenization model based on the micropolar theory framework,employing Hill's boundary conditions to precisely predict the equivalent moduli of complex lattice materials.By introducing the independent rotational degree of freedom(DOF)characteristic of the micropolar theory,the proposed model successfully overcomes the limitation of conventional methods in accurately describing the asymmetric deformation and scale effects.We initially calculate the constitutive relations of two-dimensional(2D)cross-shaped multi-node chiral lattices and subsequently extend the method to three-dimensional(3D)lattices,successfully predicting the mechanical properties of both traditional and eccentric body-centered cubic(BCC)lattices.The theoretical model is validated through the finite element numerical verification which shows excellent consistency with the theoretical predictions.A further parametric study investigates the influence of geometric parameters,revealing the underlying size-effect mechanism.This paper provides a reliable theoretical tool for the design and property optimization of complex lattice materials.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12272402 and12102458)the Chinese Universities Scientific Fund(No.2025TC014)the China Agricultural University Education Foundation(No.1101-240001)。
文摘This paper investigates the mechanical behavior of two-dimensional(2D)piezoelectric quasicrystals(PQCs)containing polygonal holes under external forces.Based on the linear elastic theory of quasicrystals(QCs),the analytical solutions for the stress and displacement fields are derived with the Stroh formalism,Green's function method,and polygonal mapping functions.Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution.The results show that the polygonal hole shapes significantly influence the generalized hoop stress,with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects.The stress concentrations at hole corners reach their maximum values at specific sharpness parameters,depending on the polygon type.The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs,and provide theoretical guidance for their structural design and optimization.
基金Project supported by the National Natural Science Foundation of China(No.12472077)the supports from Shanghai Gaofeng Project for University Academic Program Development,Fundamental Research Funds for the Central Universities(No.22120240353).
文摘Lattice materials have demonstrated promising potential in engineering applications owing to their exceptional lightweight,high specific strength,and tunable mechanical properties.However,the traditional homogenization methods based on the classical elasticity theory struggle to accurately describe the non-classical mechanical behaviors of lattice materials,especially when dealing with complex unit-cell geometries featured by non-symmetric configurations or non-single central node connections.In response to this limitation,this study establishes a generalized homogenization model based on the micropolar theory framework,employing Hill's boundary conditions to precisely predict the equivalent moduli of complex lattice materials.By introducing the independent rotational degree of freedom(DOF)characteristic of the micropolar theory,the proposed model successfully overcomes the limitation of conventional methods in accurately describing the asymmetric deformation and scale effects.We initially calculate the constitutive relations of two-dimensional(2D)cross-shaped multi-node chiral lattices and subsequently extend the method to three-dimensional(3D)lattices,successfully predicting the mechanical properties of both traditional and eccentric body-centered cubic(BCC)lattices.The theoretical model is validated through the finite element numerical verification which shows excellent consistency with the theoretical predictions.A further parametric study investigates the influence of geometric parameters,revealing the underlying size-effect mechanism.This paper provides a reliable theoretical tool for the design and property optimization of complex lattice materials.
