Large Deformation Constitutive Laws for Isotropic Thermoelastic Materials

Plohr, Bradley J.¹  Plohr, Jeeyeon N.¹ 

[1] Los Alamos National Laboratory

关键词: APPROXIMATIONS;    DEFORMATION;    DIFFERENTIAL EQUATIONS;    ELASTICITY;    ENTROPY;    FREE ENERGY;    SHEAR;    SPECIFIC HEAT;    STRAINS;   

DOI  :  10.2172/1047120
RP-ID  :  LA-UR-12-23451
PID  :  OSTI ID: 1047120
Others  :  TRN: US201216%%354

学科分类：材料科学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

We examine the approximations made in using Hooke's law as a constitutive relation for an isotropic thermoelastic material subjected to large deformation by calculating the stress evolution equation from the free energy. For a general thermoelastic material, we employ the volume-preserving part of the deformation gradient to facilitate volumetric/shear strain decompositions of the free energy, its first derivatives (the Cauchy stress and entropy), and its second derivatives (the specific heat, Grueneisen tensor, and elasticity tensor). Specializing to isotropic materials, we calculate these constitutive quantities more explicitly. For deformations with limited shear strain, but possibly large changes in volume, we show that the differential equations for the stress components involve new terms in addition to the traditional Hooke's law terms. These new terms are of the same order in the shear strain as the objective derivative terms needed for frame indifference; unless the latter terms are negligible, the former cannot be neglected. We also demonstrate that accounting for the new terms requires that the deformation gradient be included as a field variable