Modeling deformation and failure of viscoelastic composites at finite strains
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ORIGINAL PAPER
Modeling deformation and failure of viscoelastic composites at finite strains Jacob Aboudi1 · Konstantin Y. Volokh2 Received: 19 May 2020 / Accepted: 17 August 2020 © Springer Nature Switzerland AG 2020
Abstract A micromechanical analysis is proposed for the establishment of the macroscopic constitutive relations for viscoelastic composite materials undergoing large deformations. The composites are assumed to possess a triply periodic microstructure and their viscoelastic constituents are modeled by the incorporation of the viscoelastic effects with an arbitrary chosen hyperelastic strain energy function. Furthermore, an energy limiter is introduced which enforces the saturation of the viscoelastic strain energy function. The value of the strain energy at the saturation corresponds to the failure energy of the viscoelastic constituent. In conjunction with the derived micromechanical analysis, the occurrence of the energy saturation of the viscoelastic constituent predicts the composite failure. Applications are given for the determination of the macroscopic (overall) response and creep of a viscoelastic unidirectional composite, and the behavior of viscoelastic porous materials. In all cases, failure occurrences of the unidirectional composite and porous materials are predicted. Keywords Finite viscoelasticity · Strain energy limiters · Failure · Softening · Composite materials · Porous materials · Micromechanics · High-fidelity generalized method of cells
1 Introduction Materials can exhibit time-dependent behavior such as creep under constant stress, relaxation under constant deformation, and the dependence of their response to different rates of applied loading. These viscoelastic effects can be modeled in the framework of infinitesimal or finite strain theories. For the latter theory, see the monographs by [8, 10, 13] and [21], for example. There are several approaches for the incorporation of viscoelastic effects in the constitutive equations of elasticity at finite strain; see [7] for a list of references and for these authors’ approach to model viscoelasticity at high rates. In the present investigation, the three-dimensional finite viscoelastic constitutive relations that were presented by [14] are adopted. This model, which is motivated by the linear theory of viscoelasticity, is based on an appropriately chosen hyperelastic strain energy function. It is very general since the convolution integral that appears in the equations may involve several relaxation times, a continuous spectrum of relaxation times or fractional derivatives. The resulting constitutive relations recover this strain energy of finite elasticity for a very fast or very slow process. The various strain energy functions that have been developed describe the behavior of isotropic hyperelastic materials subjected to large deformations do not predict failure. The stresses which are derived from these strain energy functions increase monotonously as the applied deformations increase. This behavior is not realistic since a rea
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