TAILIEUCHUNG - Mechanics of Materials 2010 Part 14

Tham khảo tài liệu 'mechanics of materials 2010 part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | format of damage mechanics 3 Multiplying Eq. by Cs 1 from the right side and introducing this relation into Eq. results in the expression for the degrading strain in terms of the compliance evolution d Cs Es Cs Ơ This expression may be attributed to Ortiz Ortiz and Popov 1985 Neilsen and Schreyer and Carol et al. . It relates the change of compliance to the change of degrading strain. Thus the damage flow rule may be determined if the evolution of the secant compliance is known. Since the damage flow rule is now derived from the secant compliance evolution law the compliance evolution law must be defined. Fortunately it can be defined in a similar manner as the damage strain flow rule such that C s XdMd where Ád is still the damage multiplier and Md is defined as the direction of the rate of change of the secant compliance a fourth order tensor. Substituting this new relation into Eq. results in a relation between Md and the damage flow direction md md Md Es Md a Thus by defining the fourth order tensor Md the evolution of both the secant compliance Cs and the degrading strains ed may be determined. The previous relations provide a general framework for material degradation based on a failure surface. This surface can take many forms resulting in damage formulations ranging from simple 1 D scalar damage to fully anisotropic damage. Before discussing anisotropic damage however concepts from the simpler isotropic damage will be presented. Scalar damage Before considering anisotropic damage where material degradation is based on the direction of loading first consider the case of simple isotropic damage in which material degradation is expressed through a scalar parameter D. In scalar damage the reduction of the elastic stiffness Eo to the secant stiffness Es due to material damage is defined by Es 1 D Eo where the damage parameter D provides a measure of the reduction of the stiffness due to the formation of .

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