Consider a square plate subjected to an in-plane biaxial stretching. The plate is made of an...

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Consider a square plate subjected to an in-plane biaxial stretching. The plate is made of an incompressible material that can be modeled by the following Gent constitutive relation: o=-pl+ μJ m (Jm-1₁+3) -B, where p is the constraint of incompressibility, and Jm are the material constants, the first invariant of stretch is I₁ = tr(B), the left Cauchy stretch tensor is B = FF, and the deformation gradient is F. a) For the in-plane stretch A₁ = A; A₂=2A determine the corresponding stresses. b) For the in-plane stretch A₁ = A2 = A, determine the corresponding stresses. c) Ifu=17kPa; Jm = 27, plot the response for 011-A₁ in problem a) for 1≤A≤5. d) Now compare the response in problem c) when the Neo-Hookean model with μ=17kPa is considered. Consider a square plate subjected to an in-plane biaxial stretching. The plate is made of an incompressible material that can be modeled by the following Gent constitutive relation: o=-pl+ μJ m (Jm-1₁+3) -B, where p is the constraint of incompressibility, and Jm are the material constants, the first invariant of stretch is I₁ = tr(B), the left Cauchy stretch tensor is B = FF, and the deformation gradient is F. a) For the in-plane stretch A₁ = A; A₂=2A determine the corresponding stresses. b) For the in-plane stretch A₁ = A2 = A, determine the corresponding stresses. c) Ifu=17kPa; Jm = 27, plot the response for 011-A₁ in problem a) for 1≤A≤5. d) Now compare the response in problem c) when the Neo-Hookean model with μ=17kPa is considered.

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