Study on evaluation method for strain energy in second order homogenization method

2014 ◽  
Vol 2014.27 (0) ◽  
pp. 509-510
Author(s):  
Makoto UCHIDA ◽  
Yoshihisa KANEKO
2021 ◽  
pp. 108128652110216
Author(s):  
Victor A. Eremeyev

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.


Coatings ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 440
Author(s):  
Chunguang Xu ◽  
Lei He ◽  
Shiyuan Zhou ◽  
Dingguo Xiao ◽  
Pengzhi Ma

During the service or external loading of the surface coating, the damage accumulation may develop in the coating or at the interface between the substrate and the coating, but it is difficult to measure directly in the early stage, so the acoustic nonlinear parameters are used as the early damage index of the coating. In this paper, the nonlinear wave motion equation is solved by the perturbation method and the new relationship between the relative ratio of second-order parameter and third-order parameter was derived. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing of for the specimen with Al2O3 coatings. It is found that when the stress is less than 260 MPa, the appearance of the coating has no obvious change, but the nonlinear coefficients measured by the experiment increase with the increase of the tensile stress. By comparing the curves of nonlinear coefficients and stress respectively, the fluctuation of curves the second-order nonlinear coefficient A2 and the relative nonlinear coefficient β′ to stress is relatively small, and close to the linear relationship with the tensile stress, which indicates that the two parameters of the specimen with Al2O3 coatings are more sensitive to the bonding conditions, and can be used as an evaluation method to track the coating damage.


2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xiong Liu ◽  
Wenming He

In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂ / ∂ x i a i j x / ε , x ∂ u ε x / ∂ x j = f x . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u 0 , we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u 0 satisfies than the classical homogenization theory needs.


2021 ◽  
Vol 1034 ◽  
pp. 193-198
Author(s):  
Pana Suttakul ◽  
Thongchai Fongsamootr ◽  
Duy Vo ◽  
Pruettha Nanakorn

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.


2010 ◽  
Vol 26-28 ◽  
pp. 1184-1189 ◽  
Author(s):  
Ying Zi Zhang ◽  
Ying Fang Fan ◽  
Hong Nan Li ◽  
Xue Nan Wu

Corrosion ratio is an important index to study the mechanical deteriorates of the steel bars, which has a significant effect to evaluate the residual bearing capacity of reinforced concrete structures. To investigate the mechanical properties of the corroded steel bars, Strain energy loss as corrosion ratio is firstly proposed. Tensile test are conducted on ribbed and plain steels, which are corroded by acceleration corrosion method. Comparing with the weight loss and cross-section loss to describe the effect of corrosion of reinforcing bar, the strain energy loss of reinforcing bars is calculated by Simpson quadrature. Results from this paper and other researchers’ test suggest that the strain energy loss may be a better parameter than weight loss or section loss which to assess the corroded steel bars.


2019 ◽  
Vol 7 (2) ◽  
pp. T363-T372
Author(s):  
Cheng Huang ◽  
Chao Yang ◽  
Feng Shen

Rock brittleness and fracture toughness are important parameters for evaluating rock fracability. The stress-strain curves indicate that the lacustrine shale is strongly brittle. Brittle failure occurs rapidly when the stress of the lacustrine shale reaches its peak value. In addition, the lacustrine shale has different plastic strains before and after peak stress; this can relax the stress concentration of the crack tips. Therefore, the plastic strain that occurs before and after the peak stress can cause decreasing brittleness, which can be used to distinguish the brittleness and fracability in the formation of the lacustrine shale clearly. Moreover, this further enlarges the difference in the brittleness index. Based on the influence of plastic strain on brittleness, we have developed a new brittleness evaluation method that uses the ratio of linear elastic strain energy to the total strain energy before complete rock failure, which can indicate the difference of the lacustrine shale clearly. Fracture toughness is another important parameter that impacts the fracture extension and influences fracability. Based on the impact of brittleness and fracture toughness on the fracability, we have developed a new fracability evaluation method. The brittleness index increases with increases in the quartz content, and it decreases with increases in the albite feldspar and calcite contents. The fracture toughness decreases with increases in the quartz and clay contents, and it increases with increases in the siderite content. In addition, we established an empirical formula that can evaluate the brittleness index and the fracture toughness using mineral contents obtained from elemental logging. Using the new fracability evaluation method to optimize the fracturing stage, the preliminary field test indicates that the new approach was effective in the lacustrine shale formation.


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