Research On Nonlinear Mechanical Properties Of Bimodular Material Microbeams

A large number of experiments and studies show that the elastic moduli of tension and compression are unequal for many existing engineering materials such as concrete,ceramics,rubber,porous metal,shape memory alloy,graphite,and some traditional composite materials,as well as many new materials developed now.The structural materials of micro-nano electromechanical actuators(silicon,ceramics,shape memory alloys,graphene,polymers,functional materials,etc.)generally have bimodular characteristics with different elastic moduli of tension and compression.Micro-nano electromechanical technology has penetrated many fields of the national economy,people’s livelihood,and national high and new technology,and is becoming an emerging industry.Current micro-nano electromechanical technology by using the classical elasticity theory is generally based on the material tensile and compression modulus of elasticity as an equal amount of single-mode based on the constitutive model,if the amount of these materials continues single-mode constitutive relation,will give its macro engineering application,and the application of micro-nano mechanical and electrical reliability and security problems.The construction of a more accurate nonlinear dynamic model based on the twomodulus constitutive relation will make the conventional engineering design and the design of micro-nano actuators more reliable and safer.There are two main problems in the engineering application of bimodular materials:(1)The geometric mid-plane and neutral layer positions of the small deformation and large deformation dual-modulus beams do not coincide,and the neutral layer position jumps symmetrically up and down on the geometric mid-plane when the structure vibrates.The traditional mechanical models are based on the coincidence of the geometric midplane and the neutral layer.(2)Mathematical derivation shows that the neutral layer position of a beam of its dualmodulus material will be a function of deflection w when geometric nonlinearity of large deformation is considered.For these problems,the existing research literature has not given positive treatment,and this problem is unavoidable for all nonlinear static and dynamic response problems except frequency response.In view of above reasons,this paper mainly carries out the following research work:First,a universal nonlinear dynamic model is constructed,which considers the bimodular constitutive relation of different elastic moduli in tension and compression,the geometric nonlinearity of large deformation of the structure,and the scale effect.For the problem that the position of the neutral layer of the dual-modulus material beam is a function of the deflection w when the deformation is large,an appropriate approximate solution is sought to make the problem more reasonable.Then,based on the model,some linear and nonlinear mechanical problems are discussed,and it is concluded that the bimodular properties of the material,the increase of the size effect and the geometric nonlinearity will increase the effective bending stiffness of the microbeam.Finally,the necessity and importance of applying the dual-modulus material model to engineering practice are explained by numerical results,which proves that the engineering application and design of dual-modulus materials using this model will be more secure and reliable.It provides a reliable theoretical basis and method reference for introducing the dual-modulus model into conventional engineering design and micro-nano electromechanical structure engineering design.