# Introduction to Isotropic Material

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## Isotropic Material sentence examples within finite element method

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In engineering practice, a given space is first described using the finite element method and, subsequently, density-based method with solid isotropic material with penalty.

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The formula for the model I fracture toughness of the transversely isotropic material is obtained on the basis of the finite element method (FEM) together with the J-integral.

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## Isotropic Material sentence examples within topology optimization method

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This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method.

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The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional Evolutionary Structural Optimization (BESO), and the Variational Topology Optimization (VARTOP) methods.

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## Isotropic Material sentence examples within Solid Isotropic Material

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1007/s00158-020-02545-z
), that is based on DBNs and the solid isotropic material with penalization (SIMP) approach.

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The solid isotropic material with penalization method is employed to obtain the material distribution.

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## Isotropic Material sentence examples within Transversely Isotropic Material

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It indicates that the MAE behaves as a transversely isotropic material in the presence of an external magnetic field.

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Exact solution of axisymmetric wave propagation problem in radially and functionally graded circular cylinder made from combination of isotropic and transversely isotropic materials is obtained.

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## Isotropic Material sentence examples within Homogeneou Isotropic Material

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While geometry, mass and stiffness can often be characterised quite accurately, at least for homogeneous isotropic materials, the experimental quantification of structural damping is a time consuming endeavour.

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A new peridynamic bond failure model is proposed for mixed-mode crack fracture analysis in material interface and homogeneous isotropic materials, which utilize bond failure criteria presented for mixed-mode peridynamic bonds using the angle-dependent formations of critical stretch (CS) or critical energy density (CED).

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## Isotropic Material sentence examples within Elastic Isotropic Material

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Constitutive relations of two classes are proposed for nonlinear elastic isotropic materials, which, in case of purely volumetric deformation, are reduced to the Murnaghan’s equation of state.

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The problem lies in the fact that when one is solving applied problems of ice engineering, ice is often considered as an elastic isotropic material, and its stress-strain state (SSS) is studied in terms of the theory of bending of elastic plates.

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## Isotropic Material sentence examples within Transverse Isotropic Material

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We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials.

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However, when it comes to transverse isotropic material, this approach has a natural limitation due to the isotropic radial stresses; particular attention to the boundary conditions and the proper design of pressurization steps is warranted.

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## Isotropic Material sentence examples within Nonlinear Isotropic Material

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It can accommodate nonlinear isotropic materials described by a Young’s modulus and any Poisson ratio value by enforcing a volumetric constitutive law.

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Inverse numerical simulation was used to simulate the indentation tests to determine and verify the parameters of a nonlinear isotropic material model for the weldment of LBW.

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## Isotropic Material sentence examples within Virtual Isotropic Material

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This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites.

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A newly proposed concept, called the Virtual Isotropic Material Concept (VIMC), accompanying with two well-known brittle failure models, namely the maximum tangential stress (MTS) and the mean stress (MS) criteria, is utilized for the first time for theoretical LPF load prediction under mixed mode I/II loading.

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## Isotropic Material sentence examples within Thin Isotropic Material

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Therefore, in the present work a 3D hexahedral solid-shell element, based on the initial work of Schwarze and Reese [2,3], which has shown promising results for the forming of thin isotropic materials [1], is extended for highly anisotropic materials.

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In the present investigation, free vibration analysis of thin isotropic materials of bonded metallic plates under various boundary conditions is found using finite element method.

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## Isotropic Material sentence examples within Conventional Isotropic Material

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Conventional joining elements like rivets and screws or simple clamping are designed for an application in conventional isotropic materials such as steel or aluminum.

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Three types of material are tested: conventional isotropic materials (like XPS), compressible anisotropic materials (like wood fiber insulation) and heterogeneous anisotropic materials (like light-earth biobased concrete).

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## Isotropic Material sentence examples within isotropic material property

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Its dual-responsiveness allows the independent control of different DoFs for complex shape-morphing behaviors with anisotropic material properties.

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Future composite aircraft wing designs will exploit anisotropic material properties by aeroelastic tailoring and include active control methods for manoeuvre and gust load alleviation.

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## Isotropic Material sentence examples within isotropic material model

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This cubic model also enables us to compare the differences between system behaviour when using isotropic and anisotropic material models for the skeleton.

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Due to the unique processing conditions in PBF-LB/M, materials often develop a dominating microstructure that leads to anisotropic mechanical properties, and thus isotropic material models fail to account for the orientation-dependent mechanical properties.

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## Isotropic Material sentence examples within isotropic material behavior

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This paper presents a multicomponent topology optimization method for designing structures assembled from additively manufactured components, considering anisotropic material behavior for each component due to its build orientation, distinct material behavior, and stress constraints at component interfaces (i.

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The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult.

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## Isotropic Material sentence examples within isotropic material concept

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This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites.

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A newly proposed concept, called the Virtual Isotropic Material Concept (VIMC), accompanying with two well-known brittle failure models, namely the maximum tangential stress (MTS) and the mean stress (MS) criteria, is utilized for the first time for theoretical LPF load prediction under mixed mode I/II loading.

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## Isotropic Material sentence examples within isotropic material parameter

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Tensile tests for different sheet orientations are conducted both experimentally and numerically to adjust the anisotropic material parameters by inverse parameter identification for aluminium EN AW-6014 and steel HCT590X.

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We utilize the finite-element method with unstructured tetrahedral meshes for the spatial discretization supporting irregular survey geometries and anisotropic material parameters.

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## Isotropic Material sentence examples within isotropic material characteristic

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In this research, mechanical characterisation procedures that experimentally evaluate the anisotropic material characteristics of a fibre-reinforced printable concrete (FRPC) are presented.

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We calculated 3 × 3 Mueller matrix elements, which can be used to described an intuitive overview of the anisotropic material characteristics.

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## Isotropic Material sentence examples within isotropic material penalization

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The optimization model was built on the basis of the solid isotropic material penalization method with the introduction of additional restrictions in the model of searching for pseudo-densities of the material, taking into account the duration of the force action on the stamp under multicyclic loading.

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This interpolation scheme, unlike the traditional Solid Isotropic Material Penalization (SIMP) interpolation, is observed to perform better in terms of approximating the structure’s load-bearing capacity, primarily due to its formulation on the lattice’s stiffness matrices.

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Thin-walled corrugated structures have been widely used in engineering applications for centuries, because corrugation enables engineers to tailor directional dependent properties despite the structures being made of isotropic materials.

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For the description of yielding, an isotropic yield criterion which allows to differentiate between isotropic materials was used.

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Conventional techniques, suitable for the typical design of the strips made from anisotropic material such as steel, are not useful for СFRP strips.

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Almost all earlier mechanical analysis of implants presumed bone as an isotropic material while the bone is anisotropic.

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We introduce an FFT-based method to compute the effective crack energy of heterogeneous, locally anisotropic materials.

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However, 3DCP has many challenges such as competing rheological requirements, weak interlayer bonding, difficulty in integrating reinforcement, and anisotropic material behaviour.

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1 Technical challenge: earing prediction for an anisotropic material Most sheet forming benchmarks include information such as: the hardening law parameters, based on limited experimental data (generally, r-values, yield stresses and ultimate strengths for 3 loading directions) extracted from uniaxial tension tests the coefficients for certain yield functions, available in the material libraries of most commercial software.

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However, high f r are obtainable only along the easy axis direction of the magnetic anisotropic materials.

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Consequently, the initial systems of governing equations for vibration analysis of sandwich structures made of isotropic materials are derived.

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Its dual-responsiveness allows the independent control of different DoFs for complex shape-morphing behaviors with anisotropic material properties.

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17 at 808 nm), superior to most 2D anisotropic materials.

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Future composite aircraft wing designs will exploit anisotropic material properties by aeroelastic tailoring and include active control methods for manoeuvre and gust load alleviation.

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This paper presents a 3D model of a terahertz photoconductive antenna (PCA) using black phosphorus, an emerging 2D anisotropic material, as the semiconductor layer.

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Using the 3D microstructure of a real cathode, the stresses inside a free-standing electrode and model cells with a thin and a thick LLZO separator are calculated for the charging cycle considering isotropic and anisotropic material properties of LCO as well as non-textured and textured crystallographic alignment.

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Once corrected stresses of homogenous layers satisfy von Mises criterion, Ramberg-Osgood curve is used to update elastic constants of isotropic materials.

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By extending the conventional scattering canceling theory, we propose a new design method for thermal cloaks based on isotropic materials.

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In addition, we demonstrate how the use of anisotropic materials enables us to set this optimum state at smaller wavelengths, even close to ultraviolet (UV), as compared to isotropic dielectrics, and we reveal the key role of the incident field's polarization in achieving optimized operation for both prolate and oblate configurations.

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In this study, finite-element simulations of seven shear test geometries were evaluated for an isotropic material in a series of virtual experiments by varying the input hardening response.

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This cubic model also enables us to compare the differences between system behaviour when using isotropic and anisotropic material models for the skeleton.

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The isotropic and anisotropic materials with damping effects are also considered.

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In this work, a technique of how to detect the presence of a crack-like defect and estimate its orientation in an anisotropic material by means of two orthogonal shear waves is presented.

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All bones and external fixators were assigned with isotropic material properties while the cartilages were simulated with hyper-elastic.

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In this work, the virtual crack closure-integral technique is implemented to a mixed finite element, in addition with the stiffness derivative procedure, to evaluate the energy release rate of crack extension in anisotropic materials.

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The ductile fracture behavior of anisotropic materials was investigated and modeled by the uncoupled ductile fracture criterion for aluminum alloys 6016-AC200.

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The stress state of hollow cylinders with oval cross-section made of orthotropic and isotropic materials is analyzed using spatial problem statement and analytical methods of separation of variables, approximation of functions by discrete Fourier series, and numerical discrete-orthogonalization method.

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The main focus of this work is to predict the effective thermal conductivity of anisotropic materials based on the three-dimensional reconstruction of their fibrous structure, obtained from X-ray micro-tomography.

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The stress field is also obtained from Hooke’s law for isotropic materials.

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The proposed PIL method has the following advantages: (a) it can be applied to isotropic/anisotropic plate structures; (b) it doesn’t require any signal interpretation, making it attractive for active impact monitoring systems; (c) for anisotropic materials it doesn’t require the accurate knowledge of the wave velocity in all directions of propagation; (d) it doesn’t need a reference database; and (e) it remains effective even in the presence of noise.

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A graphene layer, with isotropic surface conductivity of σ, has been sandwiched between two adjacent anisotropic materials.

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They require only a low-to-moderate amount of training data and training time to learn without human guidance the constitutive behavior also of complex nonlinear and anisotropic materials.

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