Brian M. Powers's research while affiliated with University of Delaware and other places

A macroscopic numerical material model based on the mesoscopic structure of woven fabrics is developed. A mesoscopic unit cell modeling approach is adopted based on the sawtooth geometry to take into account the mesoscopic length scale deformations involved. Three important woven fabric mechanical responses (Uniaxial, biaxial and shear) are implemented using continuum mechanics and constitutive relations. The material model is implemented as a user-defined-material (UMAT) within an explicit finite element framework and validated under various loading conditions by simulating different experiments (Uniaxial tensile, bias extension and indentation tests). The results show that the developed macroscale material model based on the mesoscopic unit cell is capable of capturing the woven fabric response while simulating the deformation mechanisms involved in the mesoscopic length scale.

This research explores the effects of mesoscale (yarn) material properties on the macroscale mechanical response of various woven fabric architectures. A unit cell finite element modeling for plain, basket, twill and satin weaves is adopted and coupled with a special design-of-experiments approach. To investigate the effects of the yarn material properties and weave architectures, two loading cases are studied: (1) Uniaxial tensile, and (2) Shear. Macroscale response outcomes such as woven fabric modulus, Poisson's ratio, frictional energy dissipation and shear resistance are defined for each loading case and the effects of the mesoscale material properties on these outcomes are studied. The method is capable of identifying significant parameters along with their relative effects and contributions to the outcomes. The results of the study revealed the importance of transverse shear modulus of the yarns. Moreover, the relative effects of the yarn material properties are determined using different weave architectures.

A macroscale non-orthogonal constitutive material model for woven fabrics based on a mesoscale unit cell is developed and implemented in an explicit finite element code. The model utilizes two important deformation mechanisms involved in woven fabrics: (1) Yarn elongation, and (2) Relative yarn rotation due to shear loads. The yarns' uniaxial tensile response is modeled using nonlinear springs within the unit cell formulation while a nonlinear rotational spring is used to define the fabric's shear stiffness. Continuum mechanics are employed to keep track of the yarn orientations at a given unit cell configuration. Material properties/parameters of the model can be easily determined from standard experimental tests. The material model is validated using uniaxial tensile, bias extension, 30° off axis tension and indentation tests for two different plain weave Kevlar fabrics. The results show that the developed model is capable of the mechanical response of the woven fabrics under various loading conditions.

The mechanical response of textiles depends upon various parameters including materials, yarn structure and the architecture of the textile. These factors play an important role in the non-linear mechanical response. In this work, a novel numerical modeling approach is proposed to better capture the effect of the mesoscale structure on the textile's mechanical response. Monofilament textiles exhibiting mesoscale irregularities due to the manufacturing are studied. A novel numerical method is developed to study these effects on the in-plane mechanical response. The in-plane experiments validated the proposed modeling approach. The results show the importance of the meso-scale structure induced by manufacturing.

Advanced woven fabrics can provide a wide range of mechanical properties since the yarns can be arranged in different architectural patterns thus allowing the fabric structure to be tuned based on the specific needs. This adjustable nature makes them an attractive material choice for applications where versatility is highly desired. Hence, there is an increasing interest in woven fabrics in the recent years. They have been used in various applications such as deployable structures, protective garments, medical scaffolds and composites. With the increased interest, there is a need for efficient and accurate computational tools to investigate the mechanical behavior and deformation of woven fabrics for specific applications. Although there are several computational models in the literature that can model uniaxial and biaxial behavior of woven fabrics, there are not any commonly accepted material models for woven fabrics due to the complex interaction of trellising and deformation. Here, we propose an easy to implement constitutive material model based on a mesoscale unit cell of the woven fabrics. The proposed model utilizes the two prominent deformation mechanisms affecting the mechanical response at the mesoscale level: (1) Yarn stretching, and (2) shearing. These mesoscale mechanisms are mechanistically implemented within an unit cell by using truss and rotational springs to generate the mechanical response of the woven fabric. The yarns' nonlinear mechanical behavior is modeled with non-linear trusses and assumed to be pin-jointed at the center of the unit cell. The truss elements are allowed to rotate at the pin-joint reproducing the yarns' relative rotational motion during shearing. The fabric's shear resistance involves two components: yarn-to-yarn relative rotation/sliding and yarn locking due to the yarn transverse compression. These components of the fabric shear resistance are modeled as a nonlinear rotational spring located at the pin-joint which generates a moment resisting the shear deformation. The developed forces and moments from the trusses and rotational spring within the unit cell structure are then used to determine the continuum stress state of the material point. The material properties and parameters defined in the proposed model are easy to obtain from uniaxial tensile and shear tests on fabrics. To validate the material model, plain weave Kevlar KM2 fabric is modeled by replicating the standard uniaxial tensile and bias extension tests. The results obtained show that the material model provides a good description of the in-plane deformation and mechanical response.

In this report, we present the method of integral transforms and the Gauss-Chebyshev quadrature methods to solve the problem of a crack parallel to a rigid boundary under remote tension. We derive a system of singular integral equations of the first kind, specific to the problem at hand, which we numerically solve using Gauss-Chebyshev integration. We specialize our results to the problem of a crack in an infinite plate under remote tension, and show that the relative error in our numerically derived solutions are within machine precision of the closed-form analytical solutions. Stress intensity factors are calculated that are in excellent agreement with those derived by others using different methods. We also demonstrate that both the stress intensity factors and normal �sigmayy(x,y) and shear �sigmaxy(x,y) stress fields derived via numerical solution of the singular integral equations, compare well with those determined using the commercially available Abaqus finite element code where the crack is modeled using the eXtended Finite Element Method.

Direct computational simulations of unidirectional wave propagation through uniaxially prestressed, microcrack-damaged media are conducted to study the interaction between the prestress and stress wave parameters. Tensile and compressive waves, tensile and compressive prestresses and various orientational distributions of microcrack damage are analyzed. The relationships among the input wave amplitude, wavelength and prestress magnitude and the output wave speed and wave attenuation are studied. The results show that wave speed and attenuation depend on the prestress and the wavelength in a complex way. In the cases of compressive waves traveling through tensile prestress and tensile waves passing through compressive prestress, the wave response depends on the ratio of the amplitude of the applied stress pulse to the magnitude of the prestress (defined as R). Specifically, the simulations show that the compressive wave speed through tensile prestressed media increases gradually with an increase in R, while the tensile wave speed in media under compressive prestress, decreases with increase in R, but the change is abrupt at a particular R value. In the cases of sufficiently small R, the wave speeds match the results of Su et al. (Eng Fract Mech 74:1436–1455, 2007) where the cracks are always open or always closed. However, above a certain wavelength (a cut-off wavelength), the wave speed is no longer a function of wavelength and, furthermore, this cut-off wavelength varies with R.

Despite the importance of electromagnetomechanical physics to processes ranging from piezoelectricity to the dynamics of electron beams, confusion abounds in the continuum mechanics literature as to how Maxwell’s equations of electrodynamics should be formulated in the material frame of continuum mechanics. Current formulations in the literature conflict as to the manner in which the authors define fields, derive constitutive relations, and interpret contradictory formulations. The difficulties persist even when the phenomena described are electrostatic. This paper will demonstrate that the perplexity arises from two sources: a misunderstanding of the limitations of material frame descriptions, and the failure to appreciate the centrality of relativity theory to the formulation of electrodynamic equations in the vicinity of mechanical motion. Two new formulations of Maxwell’s equations are provided that avoid the paradoxes of earlier formulations and thus describe the physics clearly and without self-contradiction.