Materials with prescribed constitutive parameters: An inverse homogenization problem

PurposeThe purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.Design/methodology/approachThe optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.FindingsThe optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.Originality/valueThe proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

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Interaction of Lactoferrin with Unsaturated Fatty Acids: In Vitro and In Vivo Study of Human Lactoferrin/Oleic Acid Complex Cytotoxicity

Materials ◽

10.3390/ma14071602 ◽

2021 ◽

Vol 14 (7) ◽

pp. 1602

Author(s):

Anna Elizarova ◽

Alexey Sokolov ◽

Valeria Kostevich ◽

Ekaterina Kisseleva ◽

Evgeny Zelenskiy ◽

...

Keyword(s):

Oleic Acid ◽

Structural Changes ◽

Unsaturated Fatty Acids ◽

Structural Features ◽

Control Group ◽

Acid Complex ◽

Hepatoma 22A ◽

Constitutive Parameters

As shown recently, oleic acid (OA) in complex with lactoferrin (LF) causes the death of cancer cells, but no mechanism(s) of that toxicity have been disclosed. In this study, constitutive parameters of the antitumor effect of LF/OA complex were explored. Complex LF/OA was prepared by titrating recombinant human LF with OA. Spectral analysis was used to assess possible structural changes of LF within its complex with OA. Structural features of apo-LF did not change within the complex LF:OA = 1:8, which was toxic for hepatoma 22a cells. Cytotoxicity of the complex LF:OA = 1:8 was tested in cultured hepatoma 22a cells and in fresh erythrocytes. Its anticancer activity was tested in mice carrying hepatoma 22a. In mice injected daily with LF-8OA, the same tumor grew significantly slower. In 20% of animals, the tumors completely resolved. LF alone was less efficient, i.e., the tumor growth index was 0.14 for LF-8OA and 0.63 for LF as compared with 1.0 in the control animals. The results of testing from 48 days after the tumor inoculation showed that the survival rate among LF-8OA-treated animals was 70%, contrary to 0% rate in the control group and among the LF-treated mice. Our data allow us to regard the complex of LF and OA as a promising tool for cancer treatment.

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Thermodynamic compatibility conditions of a new class of hysteretic materials

Continuum Mechanics and Thermodynamics ◽

10.1007/s00161-021-01044-w ◽

2021 ◽

Author(s):

Salvatore Sessa

Keyword(s):

Constitutive Model ◽

Dynamic Analysis ◽

Closed Form ◽

Iterative Procedure ◽

Displacement Amplitude ◽

Compatibility Conditions ◽

Algebraic Functions ◽

New Class ◽

Thermodynamic Compatibility ◽

Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

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Modelling the elastic mechanical properties of bioactive glass-derived scaffolds

Biomedical glasses ◽

10.1515/bglass-2020-0005 ◽

2020 ◽

Vol 6 (1) ◽

pp. 50-56

Author(s):

Francesco Baino ◽

Elisa Fiume

Keyword(s):

Elastic Properties ◽

Poisson’S Ratio ◽

Mechanical Performance ◽

Solid Material ◽

Poisson's Ratio ◽

Predictive Capability ◽

Shear Moduli ◽

Wide Range ◽

Constitutive Parameters ◽

The Relationship

AbstractPorosity is known to play a pivotal role in dictating the functional properties of biomedical scaffolds, with special reference to mechanical performance. While compressive strength is relatively easy to be experimentally assessed even for brittle ceramic and glass foams, elastic properties are much more difficult to be reliably estimated. Therefore, describing and, hence, predicting the relationship between porosity and elastic properties based only on the constitutive parameters of the solid material is still a challenge. In this work, we quantitatively compare the predictive capability of a set of different models in describing, over a wide range of porosity, the elastic modulus (7 models), shear modulus (3 models) and Poisson’s ratio (7 models) of bioactive silicate glass-derived scaffolds produced by foam replication. For these types of biomedical materials, the porosity dependence of elastic and shear moduli follows a second-order power-law approximation, whereas the relationship between porosity and Poisson’s ratio is well fitted by a linear equation.

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An Improved Lagrangian-Inverse Method for Evaluating the Dynamic Constitutive Parameters of Concrete

Materials ◽

10.3390/ma13081871 ◽

2020 ◽

Vol 13 (8) ◽

pp. 1871

Author(s):

Xinlu Yu ◽

Yingqian Fu ◽

Xinlong Dong ◽

Fenghua Zhou ◽

Jianguo Ning

Keyword(s):

High Speed ◽

Inverse Method ◽

Image Correlation ◽

Analysis Method ◽

Stress Strain ◽

Optical Techniques ◽

Element Simulation ◽

Non Linear ◽

Constitutive Parameters ◽

Inverse Analysis Method

The dynamic constitutive behaviors of concrete-like materials are of vital importance for structure designing under impact loading conditions. This study proposes a new method to evaluate the constitutive behaviors of ordinary concrete at high strain rates. The proposed method combines the Lagrangian-inverse analysis method with optical techniques (ultra-high-speed camera and digital image correlation techniques). The proposed method is validated against finite-element simulation. Spalling tests were conducted on concretes where optical techniques were employed to obtain the high-frequency spatial and temporal displacement data. We then obtained stress–strain curves of concrete by applying the proposed method on the results of spalling tests. The results show non-linear constitutive behaviors in these stress–strain curves. These non-linear constitutive behaviors can be possibly explained by local heterogeneity of concrete. The proposed method provides an alternative mean to access the dynamic constitutive behaviors which can help future structure designing of concrete-like materials.

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