Characterization of heterogeneous solids via wave methods in computational microelasticity

Real solids are inherently heterogeneous bodies. While the resolution at which they are observed may be disparate from one material to the next, heterogeneities heavily affect the dynamic behavior of all microstructured solids. This work introduces a wave propagation simulation methodology, based on Mindlin's microelastic continuum theory, as a tool to dynamically characterize microstructured solids in a way that naturally accounts for their inherent heterogeneities. Wave motion represents a natural benchmark problem to appreciate the full benefits of the microelastic theory, as in high-frequency dynamic regimes do microstructural effects unequivocally elucidate themselves. Through a finite-element implementation of the microelastic continuum and the interpretation of the resulting computational multiscale wavefields, one can estimate the effect of microstructures upon the wave propagation modes, phase and group velocities. By accounting for microstructures without explicitly modeling them, the method allows reducing the computational time with respect to classical methods based on a direct numerical simulation of the heterogeneities. The numerical method put forth in this research implements the microelastic theory through a finite-element scheme with enriched super-elements featuring microstructural degrees of freedom, and implementing constitutive laws obtained by homogenizing the microstructure characteristics over material meso-domains. It is possible to envision the use of this modeling methodology in support of diverse applications, ranging from structural health monitoring in composite materials to the simulation of biological and geomaterials. From an intellectual point of view, this work offers a mathematical explanation of some of the discrepancies often observed between one-scale models and physical experiments by targeting the area of wave propagation, one area where these discrepancies are most pronounced.     

Phase boundaries as agents of structural change in macromolecules

We model long rod-like molecules, such as DNA and coiled-coil proteins, as one-dimensional continua with a multi-well stored energy function. These molecules suffer a structural change in response to large forces, characterized by highly typical force-extension behavior. We assume that the structural change proceeds via a moving folded/unfolded interface, or phase boundary, that represents a jump in strain and is governed by the Abeyaratne–Knowles theory of phase transitions. We solve the governing equations using a finite difference method with moving nodes to represent phase boundaries. Our model can reproduce the experimental observations on the overstretching transition in DNA and coiled-coils and makes predictions for the speed at which the interface moves. We employ different types of kinetic relations to describe the mobility of the interface and show that this leads to different classes of experimentally observed force-extension curves. We make connections with several existing theories, experiments and simulation studies, thus demonstrating the effectiveness of the phase transitions-based approach in a biological setting.     

Mode III fracture of an arbitrary oriented crack in two dimensional functionally graded material

In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared.     

Virtual testing applied to transverse multiple cracking of tows in woven ceramic composites

The present paper proposes a method of virtual testing with a view to investigating the local response of tows within textile ceramic matrix composite (CMC) under various loading conditions. The method was developed on 2D woven SiC/SiC composites. It capitalizes on knowledge on mechanical damage phenomenology and data established in previous works. It is applied to isolated transverse tows subjected to uniaxial loading by parallel longitudinal tows. The transverse tows contain heterogeneities like matrix voids, fibres and interphases. Mesh for finite element analysis is constructed from micrographs of composite cross section. Cracks were introduced into the mesh for simulation of multiple cracking. Transverse tow tensile behavior and data on distributions of flaw populations were derived from finite element computations of stress-state. Results were compared to experimental observations.     

On a novel expression of the field scattered by an arbitrary constant impedance plane

The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an arbitrary impedance, passive or active.     

热荷载作用下Timoshenko功能梯度夹层梁的静态响应

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦...     

Analytical study of the interface in fibre-reinforced 2D composite material

Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures.An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibrereinforced composite materials are proposed.The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems.All solutions are obtained in a closed analytical form.The obtained results can be used for the calculation of pull-out and pushout tests,as well as for the investigation of the fracture of composite materials.     

A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

We present a fully general, three dimensional, constitutive model for Shape Memory Alloys (SMAs), aimed at describing all of the salient features of SMA evolutionary response under complex thermomechanical loading conditions. In this, we utilize the mathematical formulation we have constructed, along with a single set of the model’s material parameters, to demonstrate the capturing of numerous responses that are experimentally observed in the available SMA literature. This includes uniaxial, multi-axial, proportional, non-proportional, monotonic, cyclic, as well as other complex thermomechanical loading conditions, in conjunction with a wide range of temperature variations. The success of the presented model is mainly attributed to the following two main factors. First, we use multiple inelastic mechanisms to organize the exchange between the energy stored and energy dissipated during the deformation history. Second, we adhere strictly to the well established mathematical and thermodynamical requirements of convexity, associativity, normality, etc. in formulating the evolution equations governing the model behavior, written in terms of the generalized internal stress/strain tensorial variables associated with the individual inelastic mechanisms. This has led to two important advantages: (a) it directly enabled us to obtain the limiting/critical transformation surfaces in the spaces of both stress and strain, as importantly required in capturing SMA behavior; (b) as a byproduct, this also led, naturally, to the exhibition of the apparent deviation from normality, when the transformation strain rate vectors are plotted together with the surfaces in the space of external/global stresses, that has been demonstrated in some recent multi-axial, non-proportional experiments.     

Dual-stage nested homogenization for rate-dependent anisotropic elasto-plasticity model of dendritic cast aluminum alloys

This paper proposes a nested dual-stage homogenization method for developing microstructure based continuum elasto-viscoplastic models for large secondary dendrite arm spacing or SDAS cast aluminum alloys. Microstructures of these alloys are characterized by extremely inhomogeneous distribution of inclusions along the dendrite cell boundaries. Traditional single-step homogenization methods are not suitable for this type of microstructure due to the size of the representative volume element (RVE) and the associated computations required for micromechanical analyses. To circumvent this limitation, two distinct RVE’s or statistically equivalent RVE’s are identified, corresponding to the inherent scales of inhomogeneity in the microstructure. The homogenization is performed in multiple stages for each of the RVE’s identified. The macroscopic behavior is described by a rate-dependent, anisotropic homogenization based continuum plasticity (HCP) model. Anisotropy and viscoplastic parameters in the HCP model are calibrated from homogenization of micro-variables for the different RVE’s. These parameters are dependent on microstructural features such as morphology and distribution of different phases. The uniqueness of the nested two-stage homogenization is that it enables evaluation of the overall homogenized model parameters of the cast alloy from limited experimental data, but also material parameters of constituents like inter-dendritic phase and pure aluminum matrix. The capabilities of the HCP model are demonstrated for a cast aluminum alloy AS7GU having a SDAS of 30 μm.