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Lawrence E. Malvern

Bio: Lawrence E. Malvern is an academic researcher. The author has contributed to research in topics: Constitutive equation & Geometric mechanics. The author has an hindex of 1, co-authored 1 publications receiving 3606 citations.

Papers
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Book
01 Jan 1969
TL;DR: In this article, the authors propose a linearized theory of elasticity for tensors, which they call Linearized Theory of Elasticity (LTHE), which is based on tensors and elasticity.
Abstract: 1. Vectors and Tensors. 2. Strain and Deformation. 3. General Principles. 4. Constitutive Equations. 5. Fluid Mechanics. 6. Linearized Theory of Elasticity. Appendix I: Tensors. Appendix II: Orthogonal Curvilinear.

3,658 citations


Cited by
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Book
28 Sep 1997
TL;DR: Bonet and Wood as discussed by the authors provide a complete, clear, and unified treatment of nonlinear continuum analysis and finite element techniques under one roof, providing an essential resource for postgraduates studying non-linear continuum mechanics and ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
Abstract: Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.

1,859 citations

Journal ArticleDOI
TL;DR: In this article, a generalization of the original peridynamic framework for solid mechanics is proposed, which allows the response of a material at a point to depend collectively on the deformation of all bonds connected to the point.
Abstract: A generalization of the original peridynamic framework for solid mechanics is proposed. This generalization permits the response of a material at a point to depend collectively on the deformation of all bonds connected to the point. This extends the types of material response that can be reproduced by peridynamic theory to include an explicit dependence on such collectively determined quantities as volume change or shear angle. To accomplish this generalization, a mathematical object called a deformation state is defined, a function that maps any bond onto its image under the deformation. A similar object called a force state is defined, which contains the forces within bonds of all lengths and orientation. The relation between the deformation state and force state is the constitutive model for the material. In addition to providing a more general capability for reproducing material response, the new framework provides a means to incorporate a constitutive model from the conventional theory of solid mechanics directly into a peridynamic model. It also allows the condition of plastic incompressibility to be enforced in a peridynamic material model for permanent deformation analogous to conventional plasticity theory.

1,591 citations

Journal ArticleDOI
TL;DR: In this paper, the Ehrenfest force acting on an element of ρ(r) and the virial field that determines its potential energy are obtained from equations of motion for the electronic momentum and virial operators, respectively.
Abstract: The quantum mechanics of proper open systems yields the physics that governs the local behavior of the electron density, ρ(r). The Ehrenfest force F(r) acting on an element of ρ(r) and the virial field ν(r) that determine its potential energy are obtained from equations of motion for the electronic momentum and virial operators, respectively. Each is represented by a “dressed” density, a distribution in real space that results from replacing the property in question for a single electron with a corresponding density that describes its average interaction with all of the remaining particles in the system. All bond paths, lines of maximum density linking neighboring nuclei in a system in stable electrostatic equilibrium, have a common physical origin in terms of F(r) and ν(r), regardless of the nature of the interaction. Each is homeomorphically mirrored by a virial path, a line of maximally negative potential energy density linking the same nuclei. The presence of a bond path and its associated virial path...

1,403 citations

Journal ArticleDOI
TL;DR: In this paper, a 3D asymmetric fracture locus, in the space of equivalent fracture strain, stress triaxiality and the Lode angle parameter, is proposed.

1,351 citations

Journal ArticleDOI
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Abstract: Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.

1,218 citations