An Introduction to the Theory of Elasticity

Deformation of a Peridynamic Bar

“…This makes it much less straightforward to derive the constitutive model for a bar from a three-dimensional constitutive model in the peridynamic theory than in the classical theory, e.g., Atkin and Fox [2]. Instead, we formulate the constitutive law for a peridynamic bar directly in the one-dimensional setting, omitting the calculations that would be required by (4).…”

“…Therefore the peridynamic equation of motion (2) reduces to the classical equation of motion in the limit → 0:…”

Element-free Galerkin methods in combination with finite element approaches

“…Stationarity of J(a) with respect to Q results in a set of linear equations for u(x) PW(x)P'u(x) = P W(X)U, (2.6) with the entries of the matrices P and W given by P,,=JI,(R.,) j=l...., m, iE{l,.... +,(x)X)} (2. 7) w,l = w,w,,, i, j E ( I, . , II 1 W,(X) > 0).…”

“…For both a regular and a radial pattern in the EFG-part of the domain, the radii Y, of the weight functions are set equal to where in case of a regular pattern h is the grid size of this pattern and in case of a radial pattern h is the grid size in the radial direction. Eight volume cells are used in the EFG-part with in each cell (7,7) Gauss quadrature. For the evaluation of J, the closed contour depicted in Fig.…”

A Biomechanical Model of the Liver for Reality-Based Haptic Feedback

“…We have not included stress history in our modeling. Therefore, the stress of the liver tissue is only determined by the strain and the strain energy function can be obtained through the deformation tensor [10].…”