Jan Vorel

Analysis of coupled heat and moisture transfer in masonry structures

Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem with an emphasis on various types of boundary conditions applied to the representative volume element—a periodic unit cell. Since the results essentially suggest no superiority of any type of boundary conditions, the paper proceeds with the coupled nonlinear heat and moisture problem subjecting the selected representative volume element to the prescribed macroscopically uniform heat flux. This allows for a direct use of the academic or commercially available codes. Here, the presented results are derived with the help of the SIFEL (More information available at http://mech.fsv.cvut.cz/web/?page=software) (SImple Finite Elements) system.

Mori-Tanaka Based Estimates of Effective Thermal Conductivity of Various Engineering Materials

The purpose of this paper is to present a simple micromechanics-based model to estimate the effective thermal conductivity of macroscopically isotropic materials of matrix-inclusion type. The methodology is based on the well-established Mori-Tanaka method for composite media reinforced with ellipsoidal inclusions, extended to account for imperfect thermal contact at the matrix-inclusion interface, random orientation of particles and particle size distribution. Using simple ensemble averaging arguments, we show that the Mori-Tanaka relations are still applicable for these complex systems, provided that the inclusion conductivity is appropriately modified. Such conclusion is supported by the verification of the model against a detailed finite-element study as well as its validation against experimental data for a wide range of engineering material systems.

Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it

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 was shown long ago 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. Presented are examples of indentation of a naval-type sandwich plate with a polymeric foam core, in which the error can reach 28.8 per cent in the load and 15.3 per cent in the work of load (relative to uncorrected results). Generally, similar errors must be expected for all highly compressible materials, such as metallic and ceramic foams, honeycomb, loess, silt, organic soils, pumice, tuff, osteoporotic bone, light wood, carton and various biological tissues. It is shown that a previously derived equation relating the tangential moduli tensors associated with the Jaumann rates of Cauchy and Kirchhoff stresses can be used in the user’s material subroutine of a black-box commercial program to cancel the error due to the lack of work-conjugacy and make the program perform exactly as if the Jaumann rate of Kirchhoff stress, which is work-conjugate, were used.

Multiscale simulations of concrete mechanical tests

In civil engineering, computational modeling is widely used in the design process at the structural level. In contrast to that, an automated support for the selection or design of construction materials is currently not available. Specification of material properties and model parameters has a strong influence on the results. Therefore, an uncoupled two-step approach is employed to provide relatively quick and reliable simulations of concrete (mortar) tests. First, the Mori-Tanaka method is utilized to include the majority of small aggregates and air voids. The strain incremental form of MT approach serves for the prediction of material properties subsequently used in the finite element simulations of mechanical tests.

HOMOGENIZATION OF PLAIN WEAVE COMPOSITES WITH IMPERFECT MICROSTRUCTURE. PART II. ANALYSIS OF REAL-WORLD MATERIALS

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.

Elastic Soft-Core Sandwich Plates: Critical Loads and Energy Errors in Commercial Codes Due to Choice of Objective Stress Rate

Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NASTRAN, use as the objective stress rate the Jaumann rate of Cauchy (or true) stress, which has two flaws: It does not conserve energy since 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 the Truesdell objective stress rate, which is work-conjugate to the GreenLagrangian finite strain tensor. The commercial codes should switch to this rate. The classical differential equations for buckling of elastic soft-core 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 in-plane 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. 1 Motivation and Nature of Problem This paper is motivated by the design of large foam-core sandwich panels, intended for the cladding of a ribbed hull of light long ships with superior maneuverability and fuel-efficiency. In a laboratory test, one such panel failed at one third of the axial compressive load predicted by a standard commercial finite element program. Although the main cause of this gross underestimation of strength is probably the neglect of size effect due to cohesive delamination fracture, which was previously identified for cylindrical buckling of sandwich plates [7] and is the subject of a separate study, an important additional cause to be studied here appears to lie in two long-ignored flaws [2, 5] in the handling of finite strain by standard commercial codes [1, 15, 16, e.g.]: 1) One flaw of these code is the use of objective stress rates that are not work-conjugate to any finite strain tensor [2]. In the implicit updated Lagrangian analysis, it is the Jaumann rate Visiting Scholar, Northwestern University; Assistant Professor on leave from Czech Technical University in Prague. McCormick Institute Professor and W.P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, Illinois 60208; z-bazant@northwestern.edu (corresponding author) Graduate Research Assistant, Northwestern University. of Cauchy stress and, in the explicit analysis, the use of the Green-Naghdi rate. 2) Another flaw is that the bifurcation analysis uses the Jaumann rate of Kirchhoff stress. Although this rate is work-conjugate to the Hencky (or logarithmic) strain tensor, it cannot correctly capture the work of initial in-plane stresses in soft-in-shear highly orthotropic structures compressed in the strong direction. This work can be captured correctly only by the Truesdell objective stress rate [3, 4]. The former flaw can lead to major errors in volume changes of polymeric, ceramic and metallic foams, fiber-reinforced foams and other highly compressible porous materials such as loess, silt, tuff, snow, under-consolidated granular materials, light wood, honeycomb, osteoporotic bones and various biological tissues. But it is unimportant for elastic buckling of a sandwich, which is the only case to be studied here. The reason is that even though the foam core is highly compressible, its hydrostatic stress is negligible (except for inelastic buckling with delamination, or for indentation [6]). This study will focus on the latter flaw. Its seriousness has already been demonstrated for sandwich columns [3, 4] and for highly orthotropic columns [12, 13], but not for sandwich plates. The energetically correct form of the differential equations of equilibrium of sandwich plates will also be identified, and their solution will be compared to finite element analysis of two kinds–a two-dimensional analysis with sandwich-type elements having a linear strain profile across the core, and three-dimensional analysis in which the core thickness is subdivided into several elements. In contrast to finite elements for the entire cross section of sandwich column, this subdivision has already been shown to yield correct results regardless of the choice of objective stress rate; see [4] (and for elastomeric bearings see [28]). It will be verified whether this is also true for sandwich plates. A salient characteristic of sandwich plates is that the shear strain in a soft core is important for buckling. The shear buckling is a problem with a hundred-year controversial history. It requires using the stability criteria for a three-dimensional continuum, which were for half a century a subject of polemics. Although the polemics were resolved four decades ago, some authors still dispute various aspects. All the historical controversies can be traced to the arbitrariness in choosing the finite strain measure and to inattention to the work-conjugacy requirement, which means that the (doubly contracted) product of the incremental objective stress tensor with the incremental finite strain tensor must give a correct expression for the second-order work [5, ch.11]. How does the choice of strain measure affect the differential equations of equilibrium and the eigenvalues of compressed sandwich plates? And which choice is correct? These questions will be addressed first analytically, and then in the context of finite element analysis, with and without subdividing the core thickness into several layers of elements. The aim is to appraise the magnitude of errors and choose the best practical approach. 2 Review of Objective Stress Rates and Their Energy-Variational Basis A broad class of equally admissible finite strain measures which comprises virtually all of those ever used is represented by the Doyle-Ericksen tensors (m) = (U − I) /m, where m is a real parameter, I = unit tensor and U = right-stretch tensor [5]. The second-order approximation of these tensors is (m) ij = eij + 1 2 uk,iuk,j − αekiekj, eki = 12 (uk,i + ui,k) , α = 1− 1 2 m (1)

Modeling Adhesive Anchors in a Discrete Element Framework

In recent years, post-installed anchors are widely used to connect structural members and to fix appliances to load-bearing elements. A bonded anchor typically denotes a threaded bar placed into a borehole filled with adhesive mortar. The high complexity of the problem, owing to the multiple materials and failure mechanisms involved, requires a numerical support for the experimental investigation. A reliable model able to reproduce a system’s short-term behavior is needed before the development of a more complex framework for the subsequent investigation of the lifetime of fasteners subjected to various deterioration processes can commence. The focus of this contribution is the development and validation of such a model for bonded anchors under pure tension load. Compression, modulus, fracture and splitting tests are performed on standard concrete specimens. These serve for the calibration and validation of the concrete constitutive model. The behavior of the adhesive mortar layer is modeled with a stress-slip law, calibrated on a set of confined pull-out tests. The model validation is performed on tests with different configurations comparing load-displacement curves, crack patterns and concrete cone shapes. A model sensitivity analysis and the evaluation of the bond stress and slippage along the anchor complete the study.

Numerical simulation of ductile fiber-reinforced cement-based composite

Strain Hardening Cement-based Composite (SHCC) is a type of High Performance Concrete (HPC) that was developed to overcome the brittleness of conventional concrete. Even though there is no significant compressive strength increase compared to conventional concrete, it exhibits superior behavior in tension. The primary objective of the presented research is to develop a constitutive model that can be used to simulate structural components with SHCC under different types of loading conditions. In particular, the constitutive model must be efficient and robust for large-scale simulations. The proposed model, based on previous research Vorel and Boshoff (2012), for plane stress is outlined and the further focus of this paper is on the mesh objectivity of the model. It is shown to be mesh size independent.

Energy-Conservation Error Due to Use of Green–Naghdi Objective Stress Rate in Commercial Finite-Element Codes and Its Compensation

The objective stress rates used in most commercial finite element programs are the Jaumann rate of Kirchhoff stress, Jaumann rates of Cauchy stress, or Green–Naghdi rate. The last two were long ago shown not to be associated by work with any finite strain tensor, and the first has often been combined with tangential moduli not associated by work. The error in energy conservation was thought to be negligible, but recently, several papers presented examples of structures with high volume compressibility or a high degree of orthotropy in which the use of commercial software with the Jaumann rate of Cauchy or Kirchhoff stress leads to major errors in energy conservation, on the order of 25–100%. The present paper focuses on the Green–Naghdi rate, which is used in the explicit nonlinear algorithms of commercial software, e.g., in subroutine VUMAT of ABAQUS. This rate can also lead to major violations of energy conservation (or work conjugacy)—not only because of high compressibility or pronounced orthotropy but also because of large material rotations. This fact is first demonstrated analytically. Then an example of a notched steel cylinder made of steel and undergoing compression with the formation of a plastic shear band is simulated numerically by subroutine VUMAT in ABAQUS. It is found that the energy conservation error of the Green–Naghdi rate exceeds 5% or 30% when the specimen shortens by 26% or 38%, respectively. Revisions in commercial software are needed but, even in their absence, correct results can be obtained with the existing software. To this end, the appropriate transformation of tangential moduli, to be implemented in the users material subroutine, is derived.

Review of energy conservation errors in finite element softwares caused by using energy-inconsistent objective stress rates

The paper briefly summarizes the theoretical derivation of the objective stress rates that are work-conjugate to various finite strain tensors, and then briefly reviews several practical examples demonstrating large errors that can be used by energy inconsistent stress rates. It is concluded that the software makers should switch to the Truesdell objective stress rate, which is work-conjugate to Green’s Lagrangian finite strain tensor. The Jaumann rate of Cauchy stress and the Green-Naghdi rate, currently used in most software, should be abandoned since they are not work-conjugate to any finite strain tensor. The Jaumann rate of Kirchhoff stress is work-conjugate to the Hencky logarithmic strain tensor but, because of an energy inconsistency in the work of initial stresses, can lead to severe errors in the cases of high natural orthotropy or strain-induced incremental orthotropy due to material damage. If the commercial softwares are not revised, the user still can make in the user’s implicit or explicit material subroutines (such as UMAT and VUMAT in ABAQUS) a simple transformation of the incremental constitutive relation to the Truesdell rate, and the commercial software then delivers energy consistent results.