New Approaches to Modeling Failure and Fracture of Rubberlike Materials
In this chapter we review some recent approaches to modeling failure and fracture of soft materials. By failure we mean the onset of damage via material instability. By fracture we mean further localization of damage into cracks with their subsequent prop
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New Approaches to Modeling Failure and Fracture of Rubberlike Materials K. Y. Volokh
Contents 1 Introduction 2 Failure as Onset of Damage 2.1 Elasticity with Energy Limiters 2.2 Cavitation 2.3 Strength of Soft Composites 2.4 Prediction of Crack Direction 3 Fracture as Damage Localization 3.1 Material Sink Formulation 3.2 Dynamic Crack Propagation 4 Final Remarks References
Abstract In this chapter we review some recent approaches to modeling failure and fracture of soft materials. By failure we mean the onset of damage via material instability. By fracture we mean further localization of damage into cracks with their subsequent propagation. Mathematical description of failure is simple and it only requires some bounding of the strain energy density. The bounded strain energy automatically implies the bounded achievable stress, which is an indicator of material failure. By bounding the strain energy via energy limiters we show, for instance, how to explain cavitation, analyze strength of soft composites, and predict direction of possible cracks. Mathematical description of fracture is more involved because it requires regularized formulations suppressing the so-called pathological mesh sensitivity. Most existing approaches utilize purely formal regularization schemes that lack physical grounds. We discuss a more physically based approach rooted in the idea that bulk K. Y. Volokh (*) Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa, Israel e-mail: [email protected]
K. Y. Volokh
cracks are not a peaceful unzipping of adjacent atomic layers but rather a catastrophic explosion of bonds localized within a finite characteristic area.
1 Introduction Failure and fracture are the central unsolved problems in solid mechanics generally and in mechanics of soft materials particularly. In this chapter we present some recent developments towards the solution of the problem. We emphasize the distinction between the concept of failure, which we interpret as the onset of material instability and damage, and the concept of fracture, which we interpret as the localization of damage into cracks and their dynamic propagation. We strongly believe that the only consistent description of failure and fracture should be the one incorporated in constitutive equations. For the general theoretical background and notation we refer to [1].
2 Failure as Onset of Damage Traditional strength-of-materials approach defines material strength as the maximum stress achievable in uniaxial tension experiments. Various other criteria can be imposed on stresses or strains to define the state of failure. Importantly, such criteria are not a part of the constitutive laws. Rather, they are extra conditions or constraints that should be obeyed in analysis and design in order to provide reliable mechanical behavior of materials and structures. The strength-of-materials approach is seemingly simple yet it can be dangerous. For example, the critical strains of highly stretchable elastomers are much lower in eq
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