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Contact of Elastoplastic and Inhomogeneous Materials
Published in Q. Jane Wang, Dong Zhu, Interfacial Mechanics, 2019
In a more general sense, plastic strain belongs to the category of eigenstrain. Eigenstrain means the strain under zero applied stress, but they induce stresses. Mura (1993) defined eigenstrain as a generic term for various non-elastic strains, such as thermal strain, plastic strain, fit-induced strain, phase transformation-induced strain, residual strain, and so on.
Unknown polynomial eigenstrains reconstruction with distributed dislocation technique for crack–inclusion interaction
Published in Applied Mathematics in Science and Engineering, 2022
To mathematically represent the stress field inside an inclusion, Eshelby’s EIM replaces inhomogeneous inclusion with homogeneous inclusion plus an equivalent eigenstrain [26,27]. Eigenstrain is a generic term for fictitious stress-free strain inside an inclusion when the surrounding matrix is absent, for example, thermal strain or phase-transformation strain; and eigenstrain is considered zero in the matrix. Due to the inclusion eigenstrain, there is displacement incompatibility at the boundary with the matrix. In the EIM context, when inclusion is bonded to the surrounding matrix to maintain stress and displacement continuity at the inclusion boundary, the induced elastic disturbance inside the inclusion is termed disturbation strain (or stress) field. Based on standard inclusion mechanics for the inclusion region, eigenstrain ε*, elastic strain εe, and disturbation strain εd are related as follows. where is the total strain field, is the strain due to applied loads.
Reconstruction of eigenstrains and residual stresses in thin plates from modal sensitivity analysis
Published in Nondestructive Testing and Evaluation, 2023
Ce Huang, Li Wang, Tong Liu, Ke Wang
Consider an elastic isotropic thin plate with thickness . The whole volume of the plate is denoted by , where is the middle plane of the plate and the boundary contains the clamped part and the free part , i.e. . The material properties are: the Young’s modulus , Poisson ratio and mass density . Assume that inhomogeneous two-dimensional inelastic/eigenstrain field exists in the plate, which is uniform in the thickness (or -) direction. Such an eigenstrain distribution may arise as a result of various inelastic deformation or processing histories of the structure, including creep, plasticity, thermal treatment and phase transformation and so on. Let denote the in-plane displacements of the plate and under the small strain assumption, the total strain existing in the plate can be expressed via the sum of eigenstrain and resulting elastic strain parts [24]: