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Paul Steinmann - One of the best experts on this subject based on the ideXlab platform.
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APPLICATION OF THE Material FORCE METHOD TO STRUCTURAL OPTIMIZATION
2020Co-Authors: Swantje Bargmann, Harm Askes, Ellen Kuhl, Paul SteinmannAbstract:Summary The present contribution aims at deriving a variationally consistent strategy to generate truss structures which are optimal in the sense of energy minimization. Accordingly, not only the spatial node point positions of the individual truss members, but also their Material node point positions, i.e. the truss geometry itself, are introduced as primary unknowns. The governing equations follow straightforwardly from the Dirichlet principle for conservative mechanical systems. Thereby, the central idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed Material and at fixed spatial coordinates. The corresponding Euler‐Lagrange equations define the spatial and the Material Motion version of the balance of linear momentum, i.e. the balance of spatial and Material forces, in a consistent dual format. The suggested algorithm is then essentially characterized through the discretization and simultaneous solution of both, the spatial and the Material Motion problem. In this sense, the proposed strategy can be interpreted as a variational ALE formulation which renders not only the deformed truss structure but also an improvement of the node point positions themselves. The suggested algorithm will be discussed by means of illustrative examples.
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on the spatial and Material Motion problems in nonlinear electro elastostatics with consideration of free space
Mathematics and Mechanics of Solids, 2012Co-Authors: D K Vu, Paul SteinmannAbstract:In this work the formulation of spatial and Material Motion problems in nonlinear electro-elastostatics is considered using an energy approach, which takes into account the contribution of the free space surrounding a nonlinearly polarized body undergoing large deformation. The free space can have a huge impact on the electric field and on the deformation field inside a body made of Materials with low electric permittivity such as the so-called electronic electroactive polymers (EEAPs). The contribution of the free space can be taken into account by using the electric flux and the Maxwell's traction acting on the boundary of the body. These two quantities can be expressed in terms of a stored energy density function. By using a stored energy density function for both the Material body and the (finite or infinite) free space, the governing equations of both spatial and Material Motion problems are derived by considering the change of energy with respect to a change in the spatial or Material configuration. In the spatial Motion problem, well-known definitions for electric and mechanical quantities are derived. In the Material Motion problem, in addition to the derivation of configurational forces, this approach reveals the formulas for the part of energy that is released from the system Material body, applied forces in response to a change in the Material configuration, which are particularly useful in the study of defects such as crack propagation. The same approach can be used in the case of nonlinear electro-thermo-mechanical coupling and constitutes the direction for future works.
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Material and spatial Motion problems in nonlinear electro and magneto elastostatics
Mathematics and Mechanics of Solids, 2010Co-Authors: D K Vu, Paul SteinmannAbstract:In this paper, Material and spatial Motion problems of the coupled nonlinear problem of electro-and magneto-elastostatics are discussed in the context of non-potential loading where mechanical loads are not assumed to be derived explicitly from some potential. A virtual work approach is used to derive the corresponding balance equations and boundary conditions of the Material Motion problems.
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Material force method: theoretical and numerical aspects in nonlinear electro‐elastostatics
Pamm, 2008Co-Authors: Duc Khoi Vu, Paul SteinmannAbstract:Formulations of the spatial and Material Motion problem in nonlinear electroelastostatics are considered in this work by a virtual work approach. Based on these formulations, a finite element discretization is realized and a numerical example is presented to demonstrate possible uses of the Material force method in studying the closing process of cracks. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: C. Britta Hirschberger, Ellen Kuhl, Paul SteinmannAbstract:Abstract A micromorphic continuum formulation is presented in the context of both, the spatial- and the Material-Motion problem. For both approaches the kinematics as well as the balance relations together with the various representations of the occurring stress fields are derived. The relations between the spatial-Motion problem and the Material-Motion problem quantities are examined in detail. Upon a hyperelastic constitutive assumption a finite-element approximation is derived and the Material–force method, which is especially suited for defect-mechanics problems, is successfully applied to the present micromorphic continuum theory.
F G Mariam - One of the best experts on this subject based on the ideXlab platform.
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the evolution of solid density within a thermal explosion i proton radiography of pre ignition expansion Material Motion and chemical decomposition
Journal of Applied Physics, 2012Co-Authors: Laura Smilowitz, B F Henson, J J Romero, B W Asay, A Saunders, F E Merrill, C L Morris, K Kwiatkowski, G Grim, F G MariamAbstract:We report proton transmission images obtained during direct heating of a sample of PBX 9501 (a plastic bonded formulation of the explosive nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX)) prior to the ignition of a thermal explosion. We describe the application of proton radiography using the 800 MeV proton accelerator at Los Alamos National Laboratory to obtain transmission images in these thermal explosion experiments. We have obtained images at two spatial magnifications and viewing both the radial and the transverse axes of a solid cylindrical sample encased in aluminum. During heating we observe the slow evolution of proton transmission through the samples, with particular detail during Material flow associated with the HMX β-δ phase transition. We also directly observe the loss of solid density to decomposition associated with elevated temperatures in the volume defining the ignition location in these experiments. We measure a diameter associated with this volume of 1–2 mm, in agree...
M. Campbell - One of the best experts on this subject based on the ideXlab platform.
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Parametric investigation of solar panel hypervelocity impact damage
Advances in Space Research, 2001Co-Authors: D. F. Medina, L Wright, M. CampbellAbstract:Individual hypervelocity impacts on satellite solar panel surfaces generally pose less of a threat to critical system functioning than impacts on critical components located on the satellite body. However, accumulation of impacts over the large surface area of the solar panels leads, in some cases, to a degradation of efficiency. Since this degradation depends both on the number of impacts and the extent of the individual localized damage, we have conducted a suite of calculations designed to understand the dependence of localized surface damage on mass and velocity of the impactor. The calculations varied mass (10 -12 to 10 -3 g) and velocity (1 to 12 km/s) to reveal a distinct threshold for penetration damage. In addition, the effect of including voids in the impactor Material was considered. The solar panel was modeled, using the CTH hydrocode, as three layers -- glass, silicon and aluminum. CTH is designed to treat a wide range of shock wave propagation and Material Motion phenomena. Physically based numerical models are relied on due to the limited laboratory data available over the mass and velocity range covered. This paper presents and analyzes more than 40 calculations; most are 2D, but some are 3D. Published by Elsevier Science Ltd on behalf of COSPAR.
R. Mueller - One of the best experts on this subject based on the ideXlab platform.
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On configurational forces in short-time dynamics and their computation with an explicit solver
Computational Mechanics, 2005Co-Authors: S. Kolling, R. MuellerAbstract:A theoretical description and a computational method to calculate configurational forces in the context of the finite element (FE) method is presented. With respect to problems in short-time dynamics, the fully 3D-case and large deformations in hyper-elastic Materials are taken into account. The FE implementation and numerical analysis of different structures demonstrates the applicability of this field of mechanics. In the chosen derivation, the Lagrangian depends on the deformation gradient and on the position (in the reference configuration) explicitly, which accounts for inhomogeneous Materials, e.g. Materials with phase boundaries, voids or cracks. Analogous to the local balance of linear momentum, the so-called Eshelby stress satisfies a configurational force balance (balance of momentum for the Material Motion problem), where configurational (or Material) forces appear as volume forces in the physical space. A consistent FE description is obtained by formulating the weak form of the configurational force balance. Thus, the configurational forces acting on the finite element nodes may be computed after the physical boundary value problem is solved. For the static case and small deformations, the configurational force is strongly related to the well known J-integral in fracture mechanics.
Ellen Kuhl - One of the best experts on this subject based on the ideXlab platform.
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APPLICATION OF THE Material FORCE METHOD TO STRUCTURAL OPTIMIZATION
2020Co-Authors: Swantje Bargmann, Harm Askes, Ellen Kuhl, Paul SteinmannAbstract:Summary The present contribution aims at deriving a variationally consistent strategy to generate truss structures which are optimal in the sense of energy minimization. Accordingly, not only the spatial node point positions of the individual truss members, but also their Material node point positions, i.e. the truss geometry itself, are introduced as primary unknowns. The governing equations follow straightforwardly from the Dirichlet principle for conservative mechanical systems. Thereby, the central idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed Material and at fixed spatial coordinates. The corresponding Euler‐Lagrange equations define the spatial and the Material Motion version of the balance of linear momentum, i.e. the balance of spatial and Material forces, in a consistent dual format. The suggested algorithm is then essentially characterized through the discretization and simultaneous solution of both, the spatial and the Material Motion problem. In this sense, the proposed strategy can be interpreted as a variational ALE formulation which renders not only the deformed truss structure but also an improvement of the node point positions themselves. The suggested algorithm will be discussed by means of illustrative examples.
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On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: C. Britta Hirschberger, Ellen Kuhl, Paul SteinmannAbstract:Abstract A micromorphic continuum formulation is presented in the context of both, the spatial- and the Material-Motion problem. For both approaches the kinematics as well as the balance relations together with the various representations of the occurring stress fields are derived. The relations between the spatial-Motion problem and the Material-Motion problem quantities are examined in detail. Upon a hyperelastic constitutive assumption a finite-element approximation is derived and the Material–force method, which is especially suited for defect-mechanics problems, is successfully applied to the present micromorphic continuum theory.
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An illustration of the equivalence of the loss of ellipticity conditions in spatial and Material settings of hyperelasticity
European Journal of Mechanics A-solids, 2006Co-Authors: Ellen Kuhl, Harm Askes, Paul SteinmannAbstract:The loss of ellipticity indicated through the rank-one-convexity condition is elaborated for the spatial and Material Motion problem of continuum mechanics. While the spatial Motion problem is characterized through the classical equilibrium equations parametrised in terms of the deformation gradient, the Material Motion problem is driven by the inverse deformation gradient. As such, it deals with Material forces of configurational mechanics that are energetically conjugated to variations of Material placements at fixed spatial points. The duality between the two problems is highlighted in terms of balance laws, linearizations including the consistent tangent operators, and the acoustic tensors. Issues of rank-one-convexity are discussed in both settings. In particular, it is demonstrated that if the rank-one-convexity condition is violated, the loss of well-posedness of the governing equations occurs simultaneously in the spatial and in the Material Motion context. Thus, the Material Motion problem, i.e. the configurational force balance, does not lead to additional requirements to ensure ellipticity. This duality of the spatial and the Material Motion approach is illustrated for the hyperelastic case in general and exemplified analytically and numerically for a hyperelastic Material of Neo-Hookean type. Special emphasis is dedicated to the geometrical representation of the ellipticity condition in both settings.
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Application of the Material force method to thermo-hyperelasticity
Computer Methods in Applied Mechanics and Engineering, 2004Co-Authors: Ellen Kuhl, Ralf Denzer, Franz Josef Barth, Paul SteinmannAbstract:The numerical analysis of Material forces in the context of thermo-hyperelasticity constitutes the central topic of the present paper. In contrast to classical spatial forces in the sense of Newton, Material forces in the sense of Eshelby indicate the tendency of Material inhomogeneities to move relative to their surrounding Material. Material forces are thus considered of particular importance in the context of thermo-elasticity where thermal effects can be understood as a potential source of inhomogeneity. The relevant balance equations of thermo-elasticity, i.e. the balance of momentum and energy, which essentially govern the evolution of the deformation and the temperature field are thus illustrated for both, the classical spatial and the Material Motion context. Guided by arguments of duality, the corresponding weak forms are derived. Next, we carry out the finite element discretization of both problems. While the numerical solution of the spatial Motion problem renders the discrete spatial deformation map and the temperature as nodal degrees of freedom, the solution of the Material Motion problem provides the discrete Material node point forces. The former typically relies on the solution of a global system of equations whereas the latter is introduced as a mere post-processing procedure. Since we apply a simultaneous solution of the mechanical and the thermal problem with the deformation and the temperature interpolated in a -continuous way, all the relevant information for the Material force method is readily available once the spatial Motion problem has been solved. Selected examples from the field of fracture mechanics illustrate the additional insight that is provided by the results of the Material force method.
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Material forces in open system mechanics
Computer Methods in Applied Mechanics and Engineering, 2004Co-Authors: Ellen Kuhl, Paul SteinmannAbstract:The basic concern of the present work is the exploitation of the notion of Material forces in the theoretical and computational analysis of open systems with particular application to biomechanical problems. Based on a completely dual framework for the spatial and the Material Motion problem, we introduce the balance equations for open system thermodynamics. In combination with the appropriate constitutive equations, they constitute the basis of the finite element formulation derived thereafter. For the spatial Motion problem, the solution of the governing equations, basically the balance of mass and momentum, renders the discrete nodal values of the density and the deformation as primary unknowns. For the Material Motion problem, the computational analysis of the balance of momentum yields the discrete Material node point forces which can be interpreted as driving forces for the local rearrangement of Material inhomogeneities. Once the spatial Motion problem has been solved, the Material force method is nothing but a mere post-processing step from an algorithmic point of view. As a convincing benefit of the proposed strategy, the computation of the Material forces is extremely cheap and requires no additional finite element data structure. In the context of biomechanics, Material forces give further insight into complex biomechanically induced processes, such as functional adaption, morphogenesis, healing or growth. For example, Material forces on the boundary can be considered as a measure of shape sensitivity and thus indicate morphological changes while Material forces in the interior indicate the tendency to create new mass locally or to equilibrate local density inhomogeneities.