Dissipation inequality-based periodic homogenization of wavy materials

Abstract

In this paper we present an internal variable-based homogenization of a composite made of wavy elastic-perfectly plastic layers. In the context of a strain-driven process, the macrostress and the effective yield surface are expressed in terms of the residual stresses, which act as hardening parameters in the effective behavior of the composite. Moreover, an approximate two-steps homogenization scheme useful for composites made of matrix with wavy inclusions is proposed and a comparison with one computational and one semi-analytical homogenization method is presented.International audienceIn this paper we present an internal variable-based homogenization of a composite made of wavy elastic-perfectly plastic layers. In the context of a strain-driven process, the macrostress and the effective yield surface are expressed in terms of the residual stresses, which act as hardening parameters in the effective behavior of the composite. Moreover, an approximate two-steps homogenization scheme useful for composites made of matrix with wavy inclusions is proposed and a comparison with one computational and one semi-analytical homogenization method is presented

Effective properties of multiphase composites made of elastic materials with hierarchical structure

“…The results of the first step of homogenization are depicted in Tables 4 and 5, while the effective elastic matrix for the whole unit cell is depicted in Table 6. Comparing Table 6 with Table 7, we conclude that the results of the present approach are in very good agreement with the results of the DIPH (see [53]).…”

“…In Figure 7 we compare the effective stresses obtained by the two methods. Recalling the results for the shearing in [53], it seems that the present method gives a more realistic effective behavior for the simple shearing.…”

“…The coefficients from the second step of homogenization are depicted in Table 10 and correspond to an orthotropic material. We can compare them with the results of DIPH in Table 11 (see [53]) and we observe that the second method overestimates the shear coefficients by 8 % , responsible for the shear stress in the x 1 – x 2 plane. In Figure 7 we compare the effective stresses obtained by the two methods.…”

“…In Section 4, three examples are presented, namely a “chevron” pattern, a composite with wavy layers and a matrix reinforced by wavy fibers in two directions. The results are compared with the results from the dissipation-inequality-based periodic homogenization (DIPH) (see [53]) showing excellent agreement.…”

Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials

“…The averaged term of (33) 2 (or (33) 4 ) cannot be decomposed into a macroscopic variables product, like the rest of the terms. Only the average of γ (0) loc can be identified as the macroscopic γ loc (a discussion about the implications that arise from this product can be found in Tsalis et al, 2015). Thus, in the general case, the mechanical dissipation in the macroscale can be obtained only by averaging the microscale mechanical dissipation over the unit cell.…”