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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: The constitutive model was found to successfully quantitatively predict the loading behavior and its dependence on biaxiality of the loading conditions and to underestimate the gradual nature of both the forward and reverse plastic deformation processes as well as the strain recovery at zero load.
63 citations
TL;DR: In this paper, the Simple Asymptotic Body (SAB) model was used to simulate the elasticity of geomaterials at small strain levels, and the model showed that the peak-to-peak secant modulus has maximum and minimum values at very high and low loading frequencies where the damping value is zero, while damping has the maximum value at an intermediate loading frequency.
63 citations
TL;DR: In this paper, the a priori error analysis of finite element methods for Biot's consolidation model is studied, and the analysis does not need a uniformly positive storage coefficient and the error estimates are robust for nearly incompressible materials.
Abstract: We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed finite elements, one for linear elasticity and the other for mixed Poisson problems are coupled for spatial discretization, and we show that any pair of stable mixed finite elements is available. The novelty of our analysis is that the error estimates of all the unknowns are robust for material parameters. Specifically, the analysis does not need a uniformly positive storage coefficient, and the error estimates are robust for nearly incompressible materials. Numerical experiments illustrating our theoretical analysis are included.
63 citations
01 Jan 2006
TL;DR: In this article, the free vibration of conical shell structures is studied using the generalized differential quadrature (GDQ) method, and the treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic.
Abstract: This paper is focused on the Generalized Differential Quadrature (GDQ) Method to study the free vibration of conical shell structures. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion are expressed as functions of five kinematic parameters. Numerical solutions are obtained.
63 citations
TL;DR: In this paper, a variational formulation is applied to the nonlinear field equations in order to find a weak form, which can be solved numerically by using open-source codes.
Abstract: The theory of linear elasticity is insufficient at small length scales, e.g., when dealing with micro-devices. In particular, it cannot predict the “size effect” observed at the micro- and nanometer scales. In order to design at such small scales an improvement of the theory of elasticity is necessary, which is referred to as strain gradient elasticity. There are various approaches in literature, especially for small deformations. In order to include geometric nonlinearities we start by discussing the necessary balance equations. Then we present a generic approach for obtaining adequate constitutive equations. By combining balance equations and constitutive relations nonlinear field equations result. We apply a variational formulation to the nonlinear field equations in order to find a weak form, which can be solved numerically by using open-source codes. By using balances of linear and angular momentum we obtain the so-called stress and couple stress as tensors of rank two and three, respectively. Since dealing with tensors an adequate representation theorem can be applied. We propose for an isotropic material a stress with two and a couple stress with three material parameters. For understanding their impact during deformation the numerical solution procedure is performed. By successfully simulating the size effect known from experiments, we verify the proposed theory and its numerical implementation. Based on representation theorems a self consistent strain gradient theory is presented, discussed, and implemented into a computational reality.
63 citations