Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

A new peridynamic formulation with shear deformation for elastic solid

Abstract: We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.

Numerical study of the hydromechanical behavior of two rough fracture surfaces in contact

Abstract: Flow in fractures is traditionally modeled by characterizing the aperture distribution with some deterministic function or set of stochastic parameters. Other models generate the aperture distribution by the closure of two stochastic surfaces. The objective of this research is to develop a model where the aperture distribution is determined during the closure of two random elastic surfaces with complete hydromechanical interaction. Because stress and strain conditions required to generate a given aperture distribution are calculated during closure, the model is used to couple the mechanical and hydraulic characteristics of the fracture. Stochastic realizations of clay fracture surfaces are generated by measuring one-dimensional profiles of a fracture surface. Next, the spectral representation of the profile is related to the fractal dimension of the fracture. Using the fractal dimension determined from one-dimensional clay profiles, an equivalent two-dimensional fractal surface is generated. Conceptually, each surface consists of linear elastic rectangular asperities resting upon a linear elastic half-space. During closure, asperities that come into contact deform and punch into the half space creating mechanical interaction between all the asperities on the grid. Once we determine the aperture distribution at an applied stress level, a hydraulic gradient is applied across the fracture and fluid flow is determined. Nodal pressures created by flow deform the aperture distribution coupling hydraulic to mechanical behavior. Stress versus relative closure results indicate that stress increases nonlinearly with relative closure. Fluid pressures in the aperture distribution exert a significant influence on the mechanical characteristics of a fracture. Fluid discharge through the fracture decreases exponentially with an increase in relative closure. Flow calculated in the rough walled aperture distribution deviates increasingly from the parallel plate model with the geometric mean aperture as the percent contact area increases. The deviation results from an increase in tortuosity and channelling of the flow field in the aperture distribution. We can use this model to develop stress and flow versus relative closure constitutive relationships for a single fracture as a function of fracture surface geometry.

Mathematical vs. Experimental Stress Analysis of Inhomogeneities in Solids

Abstract: The intent of this paper is to apply the discrete Fourier transform to the computation of eigenstress and eigenstrain fields around heterogeneities in composite materials. To this end the discrete Fourier transform is first briefly reviewed and then used to solve the basic equations of linear elasticity as pertinent to eigenstrained bodies under external loads. The results of this procedure are then used to discuss a few typical geometries such as an hexagonal two-dimensional array of thermally as well as elastically mismatched fibers in a composite matrix and a spherical Zirconia inclusion after a phase transformation. The resulting stress-strain fields are finally compared to experimental observations of eigenstress fields. The experimental techniques considered include photoelastic analyses as well as electron diffusion contrast techniques. It will be shown that the discrete Fourier transform as applied to eigenstress problems is capable of simulating the outcome of such experiments.