M. Gattu | National Institute of Technology Rourkela (original) (raw)
Papers by M. Gattu
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
Most commercial finite element programs use the Jaumann (or co-rotational) rate of Cauchy stress ... more Most commercial finite element programs use the Jaumann (or co-rotational) rate of Cauchy stress in their incremental (Riks') updated Lagrangian loading procedure. This rate has long ago been shown not to be work-conjugate with the Hencky (logarithmic) finite strain tensor used in these programs, nor with any other finite strain tensor. The lack of work-conjugacy has been either overlooked or believed to cause only negligible errors.
Journal of Structural Engineering, 2014
The typical cause of flexural failure of prestressed beams is compression crushing of concrete, 5... more The typical cause of flexural failure of prestressed beams is compression crushing of concrete, 5 which is a progressive softening damage. Therefore, according to the amply validated theory of 6 deterministic (or energetic) size effect in quasibrittle materials, a size effect must be expected. 7 A commercial finite element code, ATENA, with embedded constitutive equation for softening 8 damage and a localization limiter in the form of the crack band model, is calibrated by the 9 existing data on the load-deflection curves and failure modes of prestressed beams of one size. 10 Then this code is applied to beams scaled up and down by factors 4 and 1/2. It is found that 11 the size effect indeed takes place. Within the size range of beam depths approximately from 12 152 mm to 1220 mm (6 in. to 48 in.), the size effect represents a nominal strength reduction 13 of about 30% to 35%. In the interest of design economy and efficiency, a size effect correction 14 factor could easily be introduced into the current code design equation. However, for safety 15 this is not really necessary since the safety margin required by the code is exceeded for the 16 practical size range if the hidden safety margins are taken into account. The mildness of size 17 effect is explained by the fact that the compression softening zone occupies a large portion of 18 the beam and that, at peak load, the normal stress profiles across the softening zone exhibit 19
Journal of Engineering Materials and Technology, 2008
The finite-volume direct averaging micromechanics (FVDAM) theory for periodic heterogeneous mater... more The finite-volume direct averaging micromechanics (FVDAM) theory for periodic heterogeneous materials is extended by incorporating parametric mapping into the theory's analytical framework. The parametric mapping enables modeling of heterogeneous microstructures using quadrilateral subvolume discretization, in contrast with the standard version based on rectangular subdomains. Thus arbitrarily shaped inclusions or porosities can be efficiently rendered without the artificially induced stress concentrations at fiber/matrix interfaces caused by staircase approximations of curved boundaries. Relatively coarse unit cell discretizations yield effective moduli with comparable accuracy of the finite-element method. The local stress fields require greater, but not exceedingly fine, unit cell refinement to generate results comparable with exact elasticity solutions. The FVDAM theory's parametric formulation produces a paradigm shift in the continuing evolution of this approach, enabling high-resolution simulation of local fields with much greater efficiency and confidence than the standard theory.
Journal of Applied Mechanics, 2013
Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NAS-TRAN, use as the obj... more Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NAS-TRAN, use as the objective stress rate the Jaumann rate of Cauchy (or true) stress, which has two flaws: It does not conserve energy since it is not work-conjugate to any finite strain tensor and, as previously shown for the case of sandwich columns, does not give a correct expression for the work of in-plane forces during buckling. This causes no appreciable errors when the skins and the core are subdivided by several layers of finite elements. However, in spite of a linear elastic behavior of the core and skins, the errors are found to be large when either the sandwich plate theory with the normals of the core remaining straight or the classical equivalent homogenization as an orthotropic plate with the normals remaining straight is used. Numerical analysis of a plate intended for the cladding of the hull of a light long ship shows errors up to 40%. It is shown that a previously derived stress-dependent transformation of the tangential moduli eliminates the energy error caused by Jaumann rate of Cauchy stress and yields the correct critical buckling load. This load corresponds to the Truesdell objective stress rate, which is work-conjugate to the Green-Lagrangian finite strain tensor. The commercial codes should switch to this rate. The classical differential equations for buckling of elastic softcore sandwich plates with a constant shear modulus of the core are shown to have a form that corresponds to the Truesdell rate and Green-Lagrangian tensor. The critical inplane load is solved analytically from these differential equations with typical boundary conditions, and is found to agree perfectly with the finite element solution based on the Truesdell rate. Comparisons of the errors of various approaches are tabulated.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
Most commercial finite element programs use the Jaumann (or co-rotational) rate of Cauchy stress ... more Most commercial finite element programs use the Jaumann (or co-rotational) rate of Cauchy stress in their incremental (Riks') updated Lagrangian loading procedure. This rate has long ago been shown not to be work-conjugate with the Hencky (logarithmic) finite strain tensor used in these programs, nor with any other finite strain tensor. The lack of work-conjugacy has been either overlooked or believed to cause only negligible errors.
Journal of Structural Engineering, 2014
The typical cause of flexural failure of prestressed beams is compression crushing of concrete, 5... more The typical cause of flexural failure of prestressed beams is compression crushing of concrete, 5 which is a progressive softening damage. Therefore, according to the amply validated theory of 6 deterministic (or energetic) size effect in quasibrittle materials, a size effect must be expected. 7 A commercial finite element code, ATENA, with embedded constitutive equation for softening 8 damage and a localization limiter in the form of the crack band model, is calibrated by the 9 existing data on the load-deflection curves and failure modes of prestressed beams of one size. 10 Then this code is applied to beams scaled up and down by factors 4 and 1/2. It is found that 11 the size effect indeed takes place. Within the size range of beam depths approximately from 12 152 mm to 1220 mm (6 in. to 48 in.), the size effect represents a nominal strength reduction 13 of about 30% to 35%. In the interest of design economy and efficiency, a size effect correction 14 factor could easily be introduced into the current code design equation. However, for safety 15 this is not really necessary since the safety margin required by the code is exceeded for the 16 practical size range if the hidden safety margins are taken into account. The mildness of size 17 effect is explained by the fact that the compression softening zone occupies a large portion of 18 the beam and that, at peak load, the normal stress profiles across the softening zone exhibit 19
Journal of Engineering Materials and Technology, 2008
The finite-volume direct averaging micromechanics (FVDAM) theory for periodic heterogeneous mater... more The finite-volume direct averaging micromechanics (FVDAM) theory for periodic heterogeneous materials is extended by incorporating parametric mapping into the theory's analytical framework. The parametric mapping enables modeling of heterogeneous microstructures using quadrilateral subvolume discretization, in contrast with the standard version based on rectangular subdomains. Thus arbitrarily shaped inclusions or porosities can be efficiently rendered without the artificially induced stress concentrations at fiber/matrix interfaces caused by staircase approximations of curved boundaries. Relatively coarse unit cell discretizations yield effective moduli with comparable accuracy of the finite-element method. The local stress fields require greater, but not exceedingly fine, unit cell refinement to generate results comparable with exact elasticity solutions. The FVDAM theory's parametric formulation produces a paradigm shift in the continuing evolution of this approach, enabling high-resolution simulation of local fields with much greater efficiency and confidence than the standard theory.
Journal of Applied Mechanics, 2013
Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NAS-TRAN, use as the obj... more Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NAS-TRAN, use as the objective stress rate the Jaumann rate of Cauchy (or true) stress, which has two flaws: It does not conserve energy since it is not work-conjugate to any finite strain tensor and, as previously shown for the case of sandwich columns, does not give a correct expression for the work of in-plane forces during buckling. This causes no appreciable errors when the skins and the core are subdivided by several layers of finite elements. However, in spite of a linear elastic behavior of the core and skins, the errors are found to be large when either the sandwich plate theory with the normals of the core remaining straight or the classical equivalent homogenization as an orthotropic plate with the normals remaining straight is used. Numerical analysis of a plate intended for the cladding of the hull of a light long ship shows errors up to 40%. It is shown that a previously derived stress-dependent transformation of the tangential moduli eliminates the energy error caused by Jaumann rate of Cauchy stress and yields the correct critical buckling load. This load corresponds to the Truesdell objective stress rate, which is work-conjugate to the Green-Lagrangian finite strain tensor. The commercial codes should switch to this rate. The classical differential equations for buckling of elastic softcore sandwich plates with a constant shear modulus of the core are shown to have a form that corresponds to the Truesdell rate and Green-Lagrangian tensor. The critical inplane load is solved analytically from these differential equations with typical boundary conditions, and is found to agree perfectly with the finite element solution based on the Truesdell rate. Comparisons of the errors of various approaches are tabulated.