Moving Morphable Inclusion Approach: An Explicit Framework to Solve Inverse Problem in Elasticity

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Yue Mei ◽  
Zongliang Du ◽  
Dongmei Zhao ◽  
Weisheng Zhang ◽  
Chang Liu ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Shear Modulus ◽  
New Paradigm ◽  
Elastic Solids ◽  
Shear Moduli ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Inverse Approach ◽  
Optimization Parameters ◽  
Very High

Abstract In this work, we present a novel inverse approach to characterize the nonhomogeneous mechanical behavior of linear elastic solids. In this approach, we optimize the geometric parameters and shear modulus values of the predefined moving morphable inclusions (MMIs) to solve the inverse problem. Thereby, the total number of the optimization parameters is remarkably reduced compared with the conventional iterative inverse algorithms to identify the nonhomogeneous shear modulus distribution of solids. The proposed inverse approach is tested by multiple numerical examples, and we observe that this approach is capable of preserving the shape and the shear moduli of the inclusions well. In particular, this inverse approach performs well even without any regularization when the noise level is not very high. Overall, the proposed approach provides a new paradigm to solve the inverse problem in elasticity and has potential of addressing the issue of computational inefficacy existing in the conventional inverse approaches.

A Comparative Study of Direct and Iterative Inversion Approaches to Determine the Spatial Shear Modulus Distribution of Elastic Solids

2019 ◽  
Vol 11 (10) ◽  
pp. 1950097 ◽  
Author(s):  
Zhi Liu ◽  
Yanli Sun ◽  
Jianwei Deng ◽  
Dongmei Zhao ◽  
Yue Mei ◽  
...  
Keyword(s):  
Shear Modulus ◽  
Comparative Study ◽  
Inversion Method ◽  
Noise Levels ◽  
Elastic Solids ◽  
Direct Inversion ◽  
Advantages And Disadvantages ◽  
Iterative Inversion ◽  
Very High ◽  
Selection Of

This paper presents a comparative study of two typical inverse algorithms, i.e., direct and iterative inversion methods, to reconstruct the shear modulus distribution of linearly elastic solids. Both approaches are based on the finite element framework and compared utilizing both the simulated and experimental data. The reconstruction results demonstrate that both approaches are capable of identifying the nonhomogeneous shear modulus distribution of solids well. It can also be found that the direct inversion method is much faster than the iterative inversion method, whereas the iterative inversion method is capable of yielding better shear modulus ratio between the stiff inclusion and the soft background even with very high noise levels. Afterwards, a thorough comparison on the advantages and disadvantages of these two approaches has been performed. This comparative study provides useful information on the selection of the proper inverse scheme in estimating nonhomogeneous elastic property distribution of soft solids nondestructively.

Effects of gravel content on liquefaction resistance and its assessment considering deformation characteristics in gravel – mixed sand

2019 ◽  
Vol 56 (12) ◽  
pp. 1743-1755
Author(s):  
Hirofumi Toyota ◽  
Susumu Takada
Keyword(s):  
Shear Modulus ◽  
Small Strain ◽  
Bender Element ◽  
Liquefaction Resistance ◽  
Liquefaction Potential ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Undisturbed Samples ◽  
Strong Relation ◽  
Secant Shear Modulus

Many reports describe overestimation of liquefaction resistance based on sounding data related to ground materials containing coarse particles such as gravel and cobbles. Better methods of liquefaction potential estimation must be developed using investigation data other than those from sounding. Gathering perfect and undisturbed samples is difficult, but using seismic methods such as PS logging might be effective for assessing liquefaction potential. For this study, bender element (BE) tests and local small strain (LSS) tests were conducted, respectively, to measure the dynamic and static shear moduli of gravel – mixed sand specimens. Subsequently, relations between liquefaction strength and secant shear moduli were examined to provide reliable estimation of liquefaction in gravel – mixed sand. Although the liquefaction resistance increased considerably with overconsolidation, the initial shear modulus exhibited only a slight change with the same overconsolidation. The experimentally obtained results elucidated that the important shear strain level, for which secant shear modulus has a strong relation with liquefaction strength, was not a linear elastic region of 0.001%: it was about 0.01%.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

scholarly journals Estimation of quadriceps femoris muscle dysfunction in the early period after surgery of the knee joint using shear-wave elastography

2018 ◽  
Vol 4 (1) ◽  
pp. e000381 ◽  
Author(s):  
Makoto Kawai ◽  
Keigo Taniguchi ◽  
Tomoyuki Suzuki ◽  
Masaki Katayose
Keyword(s):  
Shear Modulus ◽  
Knee Joint ◽  
Patient Group ◽  
Quadriceps Femoris ◽  
Control Group ◽  
Muscle Dysfunction ◽  
Shear Moduli ◽  
Quadriceps Femoris Muscle ◽  
Contraction Ratio ◽  
Femoris Muscle

ObjectivesOrthopaedic surgery of the knee joint results in functional deterioration of the quadriceps femoris muscle. However, little is known about quadriceps femoris muscle dysfunction in the early postsurgical period. Therefore, we examined the stiffness of the quadriceps femoris muscle in the early postsurgical period.MethodsSeven patients and seven healthy controls performed quadriceps contraction exercises. In resting and contraction conditions, the shear modulus, muscle thickness and pennation angle were measured for the vastus medialis (VM), vastus lateralis (VL) and the rectus femoris (RF) using ultrasound elastography.ResultsThe shear moduli of the VM, VL and RF in the control group did not significantly interact, while the shear moduli in the patient group did show a significant interaction. In the resting condition, there was no difference between the unaffected and affected sides in the patient group, but the shear moduli of the VM and VL in the contraction condition was significantly lower on the affected side than the unaffected side.The contraction ratios between muscles by limbs did not significantly interact. However, there were main effects due to muscle and limb factors. The VM and VL had a significantly higher contraction ratio than the RF, and the control and unaffected limbs had a higher contraction ratio than the affected limb.ConclusionThe results demonstrated a decrease in muscle stiffness during contraction in patients with quadriceps femoris dysfunction. Measurement of the shear modulus has potential as a new evaluation index and with high sensitivity to decreases in muscle contraction.

Comparative study of destructive, nondestructive, and numerical procedures for the determination of moisture dependent shear moduli in Scots pine wood

2021 ◽  
Vol 63 (11) ◽  
pp. 1063-1069
Author(s):  
Murat Aydın ◽  
Hasan Hüseyin Ciritcioğlu
Keyword(s):  
Finite Element ◽  
Relative Humidity ◽  
Shear Modulus ◽  
Scots Pine ◽  
Constant Temperature ◽  
Transverse Wave ◽  
Element Analysis ◽  
Shear Moduli ◽  
Principal Axes ◽  
Static Shear

Abstract In this study, moisture dependent shear moduli in Scots pine (Pinus sylvestris L.) wood were determined by a 45° off-axis (longitudinal, radial, and tangential) compression test and ultrasonic transverse wave propagation. Finite element modeling was performed to ascertain how the results agree with the numerical method. Ultrasonic transverse wave velocities on the LR, LT, and RT planes were decreased from 1347, 1323, and 589 m × s-1 to 1286, 1269, and 561 m × s-1 when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. The dynamic and static shear modulus on the LR, LT, and RT planes were decreased from 988, 953, and 189, and 966, 914, and 182 MPa to 927, 903, and 176, and 845, 784, and 154 MPa when relative humidity increased from 45 % to 85 % at a constant temperature of 20 ± 1 °C, respectively. Therefore, both velocity and modulus values at all principal axes and planes were decreased with an increase in moisture. Maximum (15.2 %) and minimum (2.3 %) differences between dynamic and the static shear modulus were observed for GLT at 85 % and GLR at 45 % relative humidity, respectively. Coefficients of determinations between the dynamic and static shear moduli were ranged from 0.68 (GLR at 65 % RH) to 0.97 (GLR at 85 % RH). Finite element analysis, only for 65 % RH values, was performed using Solid 45 element, and, according to results, load-deformation curves created by linear orthotropic material properties, are well-matched with the static curves.

Hashin–Shtrikman bounds of periodic linear elastic media with cubic symmetry

2020 ◽  
Vol 25 (5) ◽  
pp. 1182-1198 ◽  
Author(s):  
George Mejak
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Elastic Media ◽  
Macroscopic Strain ◽  
Two Phase ◽  
Cubic Symmetry ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Periodic Linear ◽  
Periodic Composite

Based on the Hashin–Shtrikman variational principle, novel bounds on the effective shear moduli of a two-phase periodic composite are derived. The composite constituents are assumed to be isotropic, while the microstructure is assumed to exhibit cubic symmetry. A solution of the subsidiary boundary value problem is expressed as a double contraction of a fourth-order cubic tensor with the applied macroscopic strain. The bounds for cubic shear moduli are new, while the bounds for the bulk modulus are equal to the classical ones. The new bounds are verified for composites with the cubic, frame, octet and cubic + octet structures. It is shown that they are nearly attained for the cubic, octet and cubic + octet structures.

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