T-shape inclusion in elastic body with a damage parameter

2021 ◽  
Vol 393 ◽  
pp. 113540
Author(s):  
Alexander Khludnev
Keyword(s):  
Elastic Body ◽  
Damage Parameter

Inverse problem for elastic body with thin elastic inclusion

2020 ◽  
Vol 28 (2) ◽  
pp. 195-209
Author(s):  
Alexander M. Khludnev
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Elastic Body ◽  
Elastic Inclusion ◽  
Sufficient Conditions ◽  
Damage Parameter ◽  
External Boundary ◽  
Thin Elastic Inclusion ◽  
Limit Models

AbstractAn inverse problem for an elastic body with a thin elastic inclusion is investigated. It is assumed that the inclusion crosses the external boundary of the elastic body. A connection between the inclusion and the elastic body is characterized by the damage parameter. We study a dependence of the solutions on the damage parameter. In particular, passages to infinity and to zero of the damage parameter are investigated. Limit models are analyzed. Assuming that the damage and rigidity parameters of the model are unknown, inverse problems are formulated. Sufficient conditions for the inverse problems to have solutions are found. Estimates concerning solutions of the inverse problem are established.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Identification of a plane crack in an elastic body by invariant integrals

2008 ◽  
Vol 43 (3) ◽  
pp. 437-452 ◽  
Author(s):  
A. V. Kaptsov ◽  
E. I. Shifrin
Keyword(s):  
Elastic Body ◽  
Plane Crack ◽  
Invariant Integrals

scholarly journals 6-Axis Stress Tensor Sensor Using Multifaceted Silicon Piezoresistors

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 279
Author(s):  
Kentaro Noda ◽  
Jian Sun ◽  
Isao Shimoyama
Keyword(s):  
Stress Tensor ◽  
Elastic Body ◽  
Building Materials ◽  
Sensor Response ◽  
Stress Change ◽  
Sensor Chip ◽  
Naked Eye ◽  
Highly Sensitive ◽  
Wide Range

A tensor sensor can be used to measure deformations in an object that are not visible to the naked eye by detecting the stress change inside the object. Such sensors have a wide range of application. For example, a tensor sensor can be used to predict fatigue in building materials by detecting the stress change inside the materials, thereby preventing accidents. In this case, a sensor of small size that can measure all nine components of the tensor is required. In this study, a tensor sensor consisting of highly sensitive piezoresistive beams and a cantilever to measure all of the tensor components was developed using MEMS processes. The designed sensor had dimensions of 2.0 mm by 2.0 mm by 0.3 mm (length by width by thickness). The sensor chip was embedded in a 15 mm3 cubic polydimethylsiloxane (PDMS) (polydimethylsiloxane) elastic body and then calibrated to verify the sensor response to the stress tensor. We demonstrated that 6-axis normal and shear Cauchy stresses with 5 kPa in magnitudes can be measured by using the fabricated sensor.

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

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