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An anisotropic model of the Mullins effect. (English) Zbl 1115.74009
Summary: The Mullins effect in rubber-like materials is inherently anisotropic. However, most constitutive models developed in the past are isotropic. These models cannot describe the anisotropic stress-softening effect, often called the Mullins effect. In this paper we develop a phenomenological three-dimensional anisotropic model for the Mullins effect in incompressible rubber-like materials. The terms, damage function and damage point are introduced to facilitate the analysis of anisotropic stress softening in rubber-like materials. A material parametric energy function is postulated which depends on the right stretch tensor and written explicitly in terms of principal stretches and directions. The material parameters in the energy function are symmetric second-order damage and shear-history tensors. A class of energy functions and a specific form of constitutive equation are proposed which appear to simplify both the analysis of the three-dimensional model and the calculation of material constants from experimental data. The behaviour of tensional and compressive ground-state Young’s moduli in uniaxial deformations is discussed. To further justify our model, we show that the proposed model produces a transversely anisotropic non-virgin material in a stress-free state after a simple tension deformation. The proposed anisotropic theory is applied to several types of homogeneous deformations, and the theoretical results obtained are consistent with expected behaviour and compare well with several experimental data.

MSC:
74B20 Nonlinear elasticity
74E10 Anisotropy in solid mechanics
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