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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: In this article, a novel conjugated bond linear elastic model is proposed and implemented into the bond-based peridynamic (BB-PD) framework, which can overcome the limitation of Poisson's ratio in the standard BB-PD.

65 citations

Journal ArticleDOI
TL;DR: In this paper, a new stabilized mixed finite element method for the linear elasticity problem in R 2 is presented, based on the introduction of Galerkin least-squares terms arising from the constitutive and equilibrium equations, and from the relation defining the rotation in terms of the dis- placement.
Abstract: We present a new stabilized mixed finite element method for the linear elasticity problem in R 2 . The approach is based on the introduction of Galerkin least-squares terms arising from the constitutive and equilibrium equations, and from the relation defining the rotation in terms of the dis- placement. We show that the resulting augmented variational formulation and the associated Galerkin scheme are well posed, and that the latter becomes locking-free and asymptotically locking-free for Dirichlet and mixed boundary conditions, respectively. In particular, the discrete scheme allows the utilization of Raviart-Thomas spaces of lowest order for the stress tensor, piecewise linear elements for the displacement, and piecewise constants for the rotation. In the case of mixed boundary con- ditions, the essential one (Neumann) is imposed weakly, which yields the introduction of the trace of the displacement as a suitable Lagrange multiplier. This trace is then approximated by piecewise linear elements on an independent partition of the Neumann boundary whose mesh size needs to satisfy a compatibility condition with the mesh size associated to the triangulation of the domain. Several numerical results illustrating the good performance of the augmented mixed finite element scheme in the case of Dirichlet boundary conditions are also reported.

65 citations

Journal ArticleDOI
TL;DR: In this article, the tensor cross product is used to model the elasticity of polyconvex elasticity and the area and volume maps between reference and final configurations, together with the fiber map, which make up the fundamental kinematic variables in elasticity, leading to new formulas for the spatial and material stress and their corresponding elasticity tensors.

65 citations

Journal ArticleDOI
TL;DR: In this paper, a sampling method for the shape reconstruction of a penetrable scatterer in three-dimensional linear elasticity is examined, where the governing differential equations of the problem in dyadic form are formulated in order to acquire a symmetric and uniform representation for the underlying elastic fields.
Abstract: In this paper the sampling method for the shape reconstruction of a penetrable scatterer in three-dimensional linear elasticity is examined. We formulate the governing differential equations of the problem in dyadic form in order to acquire a symmetric and uniform representation for the underlying elastic fields. The corresponding far-field operator is defined in the appropriate space setting. We establish the interior transmission problem in the weak sense and consider the case where the nonhomogeneous boundary data are generated by a dyadic source point located in the interior domain. Assuming that the inclusion has absorbing behaviour, we prove the existence and uniqueness of the weak solution of the interior transmission problem. In this framework the main theorem for the shape reconstruction for the transmission case is established. As for the cases of the rigid body and the cavity an approximate far-field equation is derived with the known dyadic Green function term with the source point an interior point of the inclusion. The inversion scheme which is proposed is based on the unboundedness for the solution of an equation of the first kind. More precisely, the support of the body can be found by noting that the solution of the integral equation is not bounded as the point of the location of the fundamental solution approaches the boundary of the scatterer from interior points.

65 citations

Journal ArticleDOI
TL;DR: In this paper, a servo-controlled double-direct shear configuration was used to investigate the frictional response of creeping faults to sudden changes in normal stress, which resulted in a linear elastic response of shear stress followed by a transient evolution of friction over a characteristic displacement.
Abstract: [1] We report on laboratory experiments to investigate the frictional response of creeping faults to sudden changes in normal stress. Experiments were conducted on layers of quartz powder, bare surfaces of Westerly granite, and layers of a 50/50 mixture of quartz powder and smectite clay powder. The tests were carried out at room temperature and controlled humidity using a servo-controlled double-direct shear configuration. Normal stress perturbations, corresponding to loading and unloading of tectonic fault zones, were applied during steady sliding at constant loading rate from 3 to 1000 μm/s (shear strain rates of 1.5 × 10−3 to 0.5 s−1). Sudden changes in normal stress resulted in a linear elastic response of shear stress followed by a transient evolution of friction over a characteristic displacement. The transient, inelastic response is quantified as α = (Δτα/σ)/ln(σ/σ0), where Δτα is the transient change in shear stress following a step change from initial normal stress σ0 to final normal stress σ. We find that α is independent of sliding velocity and varies with ambient relative humidity and shear loading history. For unloading, we document a transition from stable to unstable behavior as a function of net slip in the range 3 to 30 mm (shear strains of 1.5 to 15). Increased humidity led to higher values of α for pure quartz gouge, but smaller α for the quartz-clay gouge. The effects of shear displacement and humidity are discussed in the context of particle characteristics and gouge fabric development. The extended rate- and state-dependent friction laws, using one state variable and the Ruina evolution law with normal stress variation, describe our observations.

65 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335