Ferhun C. Caner

Microplane model M7 for plain concrete. I: Formulation

AbstractMathematical modeling of the nonlinear triaxial behavior and damage of such a complex material as concrete has been a long-standing challenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit finite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. The microplane models, which use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions among phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which achieves this goal much better than the previous versions M1–M6 developed at Northwestern University since 1985. The basic mathematical structure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the frictional slip regi...

Microplane Model M7 for Plain Concrete. II: Calibration and Verification

AbstractThe microplane material model for concrete, formulated mathematically in the companion paper, is calibrated by material test data from all the typical laboratory tests taken from the literature. Then, the model is verified by finite-element simulations of data for some characteristic tests with highly nonuniform strain fields. The scaling properties of model M7 are determined. With the volumetric stress effect taken from the previous load step, the M7 numerical algorithm is explicit, delivering in each load step the stress tensor from the strain tensor with no iterative loop. This makes the model robust and suitable for large-scale finite-element computations. There are five free, easily adjustable material parameters, which make it possible to match the given compressive strength, the corresponding strain, the given hydrostatic compression curve, and certain triaxial aspects. In addition, there are many fixed, hard-to-adjust parameters, which can be taken to be the same for all concretes. The opt...

Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfels recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.

Size Effect on Strength of Laminate-Foam Sandwich Plates

Experiments on size effect on the failure loads of sandwich beams with PVC foam core and skins made of fiber-polymer composite are reported. Two test series use beams with notches at the ends cut in the foam near the top or bottom interface, and the third series uses beams without notches. The results demonstrate that there is a significant nonstatistical (energetic) size effect on the nominal strength of the beams, whether notched or unnotched. The observed size effect shows that the failure loads can be realistically predicted on the basis of neither the material strength concept nor linear elastic fracture mechanics (LEFM). It follows that nonlinear cohesive (quasi-brittle) fracture mechanics, or its approximation by equivalent LEFM, must be used to predict failure realistically. Based on analogy with the previous asymptotic analysis of energetic size effect in other quasibrittle materials, approximate formulas for the nominal strength of notched or unnotched sandwich beams are derived using the approximation by equivalent LEFM. Different formulas apply to beams with notches simulating pre-existing stress-free (fatigued) cracks, and to unnotched beams failing at crack initiation. Knowledge of these formulas makes it possible to identify from size effect experiments both the fracture energy and the effective size of the fracture process zone.

Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing

Significance Fragmentation, crushing, and pulverization of solids, referred to as comminution, has long been of keen interest for mining, tunneling, explosions, meteorite impact, missile impact, ground shock, terrorist attacks, and various industrial processes. Recently, interest surged in comminution of gas or oil shale as a way to enhance the permeability of shale mass by orders of magnitude. Particularly intriguing is a proposed, environmentally friendlier, alternative to hydraulic fracturing in which the fracturing would be achieved by shock waves from explosions or electrohydraulic pulsed arc in a horizontal borehole. The discharge of contaminated water would, in this case, be negligible. In all these problems the energy dissipation density is a key parameter to predict. Here a theory to do so is outlined. Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of the macroscopic model. Unlike static fracture, in which the driving force is the release of strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of shear strain rate. The density of this energy at strain rates >1,000/s is found to exceed the maximum possible strain energy density by orders of magnitude, making the strain energy irrelevant. It is shown that particle size is proportional to the −2/3 power of the shear strain rate and the 2/3 power of the interface fracture energy or interface shear stress, and that the comminution process is macroscopically equivalent to an apparent shear viscosity that is proportional (at constant interface stress) to the −1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.

Fibre–matrix interaction in the human annulus fibrosus

Although the mechanical behaviour of the human annulus fibrosus has been extensively studied, the interaction between the collagen fibres and the ground matrix has not been well understood and is therefore ignored by most constitutive models. The objective of this study is to identify the significance of the fibre-matrix interaction in the human annulus fibrosus by careful investigation of the experimental data, the theoretical constitutive models, and the numerical simulation results in the literature. Based on the experimental results from biaxial and uniaxial tests, it is shown that the mechanical behaviour of the matrix can be well simulated by an incompressible neo-Hookean type model, but the effective stiffness of the matrix depends on fibre stretch ratio, which can only be explained by fibre-matrix interaction. Furthermore, we find that this interaction takes place anisotropically between the matrix and the fibres distributed in different proportions in different directions. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by this fibre orientation dispersion.

Diffusion-controlled and creep-mitigated asr damage via microplane model. II: Material degradation, drying, and verification

AbstractThe theory for the material and structural damage due to the alkali-silica reaction (ASR) in concrete is calibrated and validated by finite element fitting of the main test results from the...

MECHANICAL BEHAVIOUR OF TRANSVERSELY ISOTROPIC POROUS NEO-HOOKEAN SOLIDS

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i1 – i2 plane, the normal stress in the third axial direction (i3) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

Scaling of Strength of Metal-Composite Joints—Part I: Experimental Investigation

Knowledge of the size effect on the strength of hybrid bimaterial joints of steel and fiber composites is important for new designs of large lightweight ships, large fuel-efficient aircrafts, and lightweight crashworthy automobiles. Three series of scaled geometrically similar specimens of symmetric double-lap joints with a rather broad size range (1:12) are manufactured. The specimens are tested to failure under tensile displacement-controlled loading, and at rates that ensure the peak load to be reached within approximately the same time. Two series, in which the laminate is fiberglass G-10/FR4, are tested at Northwestern University, and the third series, in which the laminate consists of NCT 301 carbon fibers, is tested at the University of Michigan. Except for the smallest specimens in test series I, all the specimens fail by propagation of interface fracture initiating at the bimaterial corner. All the specimens fail dynamically right after reaching the maximum load. This observation confirms high brittleness of the interface failure. Thus, it is not surprising that the experiments reveal a marked size effect, which leads to a 52% reduction in nominal interface shear strength. As far as the inevitable scatter permits it to see, the experimentally observed nominal strength values agree with the theoretical size effect derived in Part II of this study, where the size exponent of the theoretical large-size asymptotic power law is found to be -0.459 for series I and II, and -0.486 for series III.

Vertex Effect and Confinement of Fracturing Concrete via Microplane Model M4

A newly developed powerful version of microplane model, labeled model M4, is used to study two basic phenomena in fracturing concrete: the vertex effect, i.e., the tangential stiffness for loading increments to the side of previous radial loading path in the stress space, and the effect of confinement by a steel tube or a spiral on the suppression of softening response of columns. Comparisons with the tests show the microplane model to predict the initial torsional stiffness very closely, while the classical tensorial models with invariants overpredict this stiffness several times. In the tests performed recently, steel tubes of different thicknesses filled by concrete are squashed to about half of their initial length and very large strains with shear angles up to about 70 degree are achieved. Observations and conclusions from the investigations are provided.