A Multiresolution Transformation Rule of Material Defects

Abstract

The ability to quantify the material damage at different length scales is critical in the multiscale analysis of material behavior from nanoscale to macroscale. In this article, on the basis of the equivalence of complementary elastic energy we propose a multiresolution rule that transforms different levels of material defects to the equivalent degradation of material properties. It facilitates a sequential memory-efficient processing of massive material defects in a multiresolution framework, and also supports a functionality of partial damage conversion to serve different needs in subsequent numerical analyses. Numerical simulation was conducted with different settings of material defects. The analysis results indicate the efficacy of the proposed method, offering a potential (i) to interface between multiscale material defects and (ii) as an effective method of homogenization for the determination of the damage variable in continuum damage mechanics.

Experimental and numerical investigation of the effect of key joint variables on the static and fatigue performance of bonded metallic single-lap joints

“…This fatigue data is converted using Morrow's method to account for the mean stress in Figure 12 for comparison. Compared with the prediction results using strain equivalence and energy equivalence methods, [20][21][22][23] a reasonable agreement is observed in the test range from 10 to 10 4 cycle; the energy equivalence prediction is closer to the experimental data. In the range of less than 10 cycles, the higher shear stress in adhesive causes yielding of the adherend material, which delays damage accumulation in the adhesive.…”

“…Another postulate, known as energy equivalence, [20][21][22][23] would relate the damage to the change of the elastic modulus but now through the equation…”

“…The postulate of strain equivalence [20][21][22] states that a constitutive equation for a damaged material can be obtained by replacing the stress in a virgin material by an effective stress value. Thus, the damage may be represented by an elastic modulus change…”

“…Under a continuum damage mechanics model, [6,20,21] the effective stress r adhr ij in the adherends is given by (14) where D A is the adherend damage variable and r adhr ij is the effective stress component. Before damage initiation, D A is 0, while D A ¼ 1 signifies that the adhesive material has totally failed.…”

Finite element method implementation of a nonlocal viscoplastic model with consideration of temperature dependence

“…where ∂(Dp)=∂(De kl ) can be determined from equation Using equation (10), equation (25) can be rewritten as…”