Concept Question Which of the following statements is correct? Uo=U for ALL elastic materials(1 Uo=OijEij-U0 ONLY for linear elastic materials Jo=-ijEii for a nonlinear elastic material Statements(1) and 3)
The change in volume or shape of an object that results from stress is called strain. The response of rocks to stress can be divided into - elastic response: rock returns to original shape - ductile or plastic response: permanent deformation without fracture; occurs above the so-called elastic limit
Which of the following statements is correct? 1. The PVD only applies to linear elastic materials 2. The PVD applies only to elastic materials, but they can be linear or non-linear 3. The PVD applies regardless of the constitutive behavior of the material
which generalizes to the statement. This reduces the number of material constants from 81 to 54. In a similar fashion we can make use of the symmetry of the strain tensor This further reduces the number of material constants to 36. To further reduce the number of material constants consider the conclusion from the first law for elastic materials, equation
3.064 Quiz 3- Sample Questions 1. Consider a unidirectionally reinforced fiber-matrix composite a)What elastic constants(relative to the fiber and transverse directions )are needed to describe this material?
Brannon-Peppas theory of swelling in ionic hydrogels Original theory for elastic networks developed by Flory and Mehrer, refined for treatment of ionic hydrogels by Brannon-Peppas and Peppas Other theoretical treatments Derivation of ionic hydrogel swelling Model structure of the system
1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension
