page_title: Fracture of soft materials
section_title: J-integral in the pure-shear experiment
hierarchical_section_title: Fracture of soft materials / J-integral / J-integral in the pure-shear experiment
caption_attribution_description: Calculations of J integral in a pure shear experiment
context_page_description: Soft materials consist of a type of material that e.g. includes soft biological tissues as well as synthetic elastomers, and that is very sensitive to thermal variations. Hence, soft materials can become highly deformed before crack propagation. Consequently, the stress field close to the crack tip is significantly different from the traditional formulation encountered in the Linear elastic fracture mechanics. Therefore, fracture analysis for these applications requires a special attention.
  The Linear Elastic Fracture Mechanics and K-field are based on the assumption of infinitesimal deformation, and as a result are not suitable to describe the fracture of soft materials. The reason for this is that soft materials usually become highly deformed and blunted before crack propagation. However, LEFM general approach can be applied to understand the basics of fracture on soft materials.
  Alternatively to the linear approach of fracture in LEFM, the solution for the deformation and crack stress field in soft materials considers large deformation and is derived from the finite strain elastostatics framework and hyperelastic material models.
context_section_description: The J-integral can be determined by experiments. One common experiment is the pure-shear in an infinite long strip, as shown in Fig. 2. The upper and bottom edges are clamped by grips and the loading is applied by pulling the grips vertically apart by ± ∆. This set generates a condition of plane stress. 
  Under these conditions, the J-integral is evaluated, therefore, as
  where   ,
  and is the high of the strip undeformed state. The function is determined by measuring the nominal stress acting on the strip stretched by :
  .
  Therefore, from the imposed displacement of each grip, ± ∆, it is possible to determine the J-integral for the corresponding nominal stress. With the J-integral, the amplitude (parameter a) of some true stress components can be found. Some other stress components amplitudes, however, depend on other parameters such as c (e.g.   under plane stress condition) and cannot be determined by the pure shear experiment. Nevertheless, the pure shear experiment is very important because it allows the characterization of fracture toughness of soft materials.
caption: Figure 2: Pure-shear experiment.
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