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Theoretical analysis of the deformation of SMP sandwich beam in flexure

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Abstract

Shape memory polymers (SMPs) can have a large frozen strain but with a very small recovery stiffness in comparison with shape memory metals or ceramics. To provide more deployable stresses for the application of actuators, sandwich beams consisting of a SMP core and two thin metallic skins were considered. The packaging behaviors of two types of SMP sandwich beams, aluminum/SMP/aluminum and steel/SMP/steel, were discussed. Due to the high compliance of SMP core on packaging condition that the testing temperature is above the activation temperature of the material, buckling and post-buckling are the essential deformation mechanisms of SMP sandwich beams under bending. Theoretical solutions were derived in studying such non-linear behaviors, including the initiation of critical buckling, post-buckling response, and final failure modes. Systematic parameter’s analyses, e.g., buckling half-wavelength, amplitude, location of the neutral-strain surface in different packaging curvatures, were also presented.

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Abbreviations

z m :

thickness of metallic skin

z e :

thickness of SMP epoxy core

z t :

thickness of tensioned SMP core

z c :

thickness of compressed SMP core

z′ t :

thickness of tensioned metallic skin

z′ c :

thickness of compressed metallic skin

ε eff :

effective strain

E eff :

effective modulus of buckled skin

ε z :

strain of SMP core

γ xoz :

shear strain of SMP core

w :

buckling displacement of metallic skin

w e :

displacement of SMP core

E m :

Young’s modulus of metallic skin

E e :

Young’s modulus of SMP epoxy core

G m :

shear modulus of metallic skin

G e :

shear modulus of SMP epoxy core

l :

length of SMP sandwich beam

b :

width of SMP sandwich beam

a :

buckling magnitude of metallic skin

λ:

buckling wavelength of metallic skin

m :

buckling mode number of metallic skin

EI :

flexural stiffness of metallic skin

ρ :

curvature radius

M :

applied bending moment

z ns :

distance from geometric midplane to neutral-strain surface

T :

virtual work applied on the compressed region

\({U_c^m}\) :

compressed strain energy in unbuckled metallic skin

\({U_b^m}\) :

strain energy in buckled metallic skin

U e :

strain energy in SMP epoxy core

\({U_{\rm xoz}^S}\) :

shear strain energy of SMP core in the x − z plane

\({U_z^T}\) :

tensioned/compressed strain energy of SMP core along length direction

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  1. Department of Mechanics, School of Civil Engineering, Beijing Jiao-Tong University, 100044, Beijing, China

    Z. D. Wang & Z. F. Li

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  1. Z. D. Wang
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  2. Z. F. Li
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Wang, Z.D., Li, Z.F. Theoretical analysis of the deformation of SMP sandwich beam in flexure. Arch Appl Mech 81, 1667–1678 (2011). https://doi.org/10.1007/s00419-011-0510-7

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