Topic
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: This work disentangle mutual contributions of cell size and cell stiffness to cell deformation by a theoretical analysis in terms of hydrodynamics and linear elasticity theory and demonstrates that the analytical model not only predicts deformed shapes inside the channel but also allows for quantification of cell mechanical parameters.
190 citations
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TL;DR: In this paper, the free vibration problem of a homogeneous isotropic thick cylindrical shell or panel subjected to a certain type of simply supported edge boundary conditions is considered, and the governing equations of three-dimensional linear elasticity are employed and solved by using a new iterative approach which, in practice, leads to the prediction of the exact frequencies of vibration.
190 citations
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TL;DR: In this paper, the structural, electronic and mechanical properties of zigzag graphene nanoribbons were investigated by applying density functional theory within the generalized gradient approximation-Perdew-Burke-Ernzerhof (GGA-PBE) approximation.
Abstract: Herein, we investigate the structural, electronic and mechanical properties of zigzag graphene nanoribbons in the presence of stress by applying density functional theory within the GGA-PBE (generalized gradient approximation-Perdew–Burke–Ernzerhof) approximation. The uniaxial stress is applied along the periodic direction, allowing a unitary deformation in the range of ± 0.02%. The mechanical properties show a linear response within that range while a nonlinear dependence is found for higher strain. The most relevant results indicate that Young's modulus is considerable higher than those determined for graphene and carbon nanotubes. The geometrical reconstruction of the C–C bonds at the edges hardens the nanostructure. The features of the electronic structure are not sensitive to strain in this linear elastic regime, suggesting the potential for using carbon nanostructures in nano-electronic devices in the near future.
189 citations
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25 Nov 2009
TL;DR: In this article, Lemaitre et al. introduce the concept of constitutive equations in nonlinear models and apply them to linear elastic heterogeneous materials, such as brittle materials.
Abstract: Preface by Jean Lemaitre Chapter 1 Introduction 1.1. Model construction 1.2. Applications to models Chapter 2 General concepts 2.1. Formulation of the constitutive equations 2.2. Principle of virtual power 2.3. Thermodyna~nicso f irreversible processes 2.4. Main class of constitutive equations 2.5. Yield criteria 2.6. Numerical methods for nonlinear equations 2.7. Numerical solution of differential equations 2.8. Finite element Chapter 3 Plasticity and 3D viscoplasticity 3.1. Generality 3.2. Formulation of the constitutive equations 3.3. Flow direction associated to the classical criteria 3.4. Expression of some particular constitutive equations in plasticity 3.5. Flow under prescribed strain rate 3.6. Non-associated plasticity 3.7. Nonlinear hardening 3.8. Some classical extensions 3.9. Hardening and recovery in viscoplasticity 3.10. Multimechanism models 3.1 1. Behaviour of porous materials Chapter 4 Introduction to damage mechanics 4.1. Introduction 4.2. Notions and general concepts 4.3. Damage variables and state laws 4.4. State and dissipative couplings 4.5. Damage deactivation 4.6. Damage evolution laws 4.7. Examples of damage models in brittle materials Chapter 5 Microstructural mechanics 5.1. Characteristic lengths and scales in microstructural mechanics 5.2. Some homogenization techniques 5.3. Application to linear elastic heterogeneous materials 5.4. Some examples. applications and extensions 5.5. Homogenization in thermoelasticity 5.6. Nonlinear homogenization 5.7. Computation of RVE 5.8. Homogenization of coarse grain structures Chapter 6 Finite deformations 6.1. Geometry and kinematics of continuum 6.2. Sthenics and statics of the continuum 6.3. Constitutive laws 6.4. Application: Simple glide 6.5. Finite deformations of generalized continua Chapter 7 Nonlinear structural analysis 7.1. The material object 7.2. Examples of implementations of particular models 7.3. Specificities related to finite elements Chapter 8 Strain localization 8.1. Bifurcation modes in elastoplasticity 8.2. Regularization methods Appendix Notation used A.1. Tensors A.2. Vectors, Matrices A.3. Voigt notation
189 citations
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TL;DR: In this paper, the basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described and a stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution.
189 citations