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  • 1
    Electronic Resource
    Electronic Resource
    A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials (1993)
    Springer
    Computational mechanics 11 (1993), S. 253-278 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A recently proposed methodology for computational plasticity at finite strains is re-examined within the context of geomechanical applications and cast in the general format of multi-surface plasticity. This approach provides an extension to finite strains of any infinitesimal model of classical plasticity that retains both the form of the yield criterion and the hyperelastic character of the stress-strain relations. Remarkably, the actual algorithmic implementation reduces to a reformulation of the standard return maps in principal axis with algorithmic elastoplastic moduli identical to those of the infinitesimal theory. New results in the area of geomechanics included a fully implicit return map for the modified Cam-Clay model, extended here to the finite deformation regime, and a new semi-explicit scheme that restores symmetry of the algorithmic moduli while retaining the unconditional stability property. In addition, a new phenomenological plasticity model for soils is presented which includes a number of widely used models as special cases. The general applicability of the proposed methodology is illustrated in several geomechanical examples that exhibit localization and finite deformations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00371865
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  • 2
    Electronic Resource
    Electronic Resource
    The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics (1992)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 757-792 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In the absence of external loads or in the presence of symmetries (i.e., translational and rotational invariance) the nonlinear dynamics of continuum systems preserves the total linear and the total angular momentum. Furthermore, under assumption met by all classical models, the internal dissipation in the system is non-negative. The goal of this work is the systematic design of conserving algorithms that preserve exactly the conservation laws of momentum and inherit the property of positive dissipation forany step-size. In particular, within the specific context of elastodynamics, a second order accurate algorithm is presented that exhibits exact conservation of both total (linear and angular) momentum and total energy. This scheme is shown to be amenable to a completely straightforward (Galerkin) finite element implementation and ideally suited for long-term/large-scale simulations. The excellent performance of the method relative to conventional time-integrators is conclusively demonstrated in numerical simulations exhibiting large strains coupled with a large overall rigid motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00913408
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  • 3
    Electronic Resource
    Electronic Resource
    An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids (1993)
    Springer
    Computational mechanics 12 (1993), S. 277-296 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Ket qualitative features of solutions exhibiting strong discontinuities in rate-independent inelastic solids are identified and exploited in the design of a new class of finite element approximations. The analysis shows that the softening law must be re-interpreted in a distributional sense for the continuum solutions to make mathematical sense and provides a precise physical interpretation to the softening modulus. These results are verified by numerical simulations employing a regularized discontinuous finite element method which circumvent the strong mesh-dependence exhibited by conventional methods, without resorting to viscosity or introducing additional ad-hoc parameters. The analysis is extended to a new class of anisotropic rate-independent damage models for brittle materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00372173
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  • 4
    Electronic Resource
    Electronic Resource
    On continuum damage-elastoplasticity at finite strains (1989)
    Springer
    Computational mechanics 5 (1989), S. 375-400 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A strain-based continuum damage-elastoplasticity formulation at finite strains is proposed based on an additive split of thestress tensor. Within the proposed framework, a hyperelastic extension of the classicalJ 2-flow theory is developed as a model problem, with a rate-free formulation of the (linear) kinematic hardening law that is free from spurious stress oscillation in the simple shear test. The algorithmic implementation of the coupled damage-elastoplasticity model is shown to reduce to a trivial modification of the classical radial return which is amenable toexact linearization. This results in a closed form expression for theconsistent elastoplastic-damage modulus. The algorithmic treatment of the damage model with no restrictions on the functional forms governing the plastic response is considered subsequently. It is emphasized that objective rates and incrementally objective algorithms play no role in the present approach. A number of numerical experiments are presented that illustrate the performance of the proposed formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01047053
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Conserving algorithms for the dynamics of Hamiltonian systems on lie groups (1994)
    Springer
    Journal of nonlinear science 4 (1994), S. 253-299 
    Details
    ISSN: 1432-1467
    Keywords: Hamilton's equations ; symmetry groups ; canonical transformations ; rigid bodies ; homogeneous elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary Three conservation laws are associated with the dynamics of Hamiltonian systems with symmetry: The total energy, the momentum map associated with the symmetry group, and the symplectic structure are invariant under the flow. Discrete time approximations of Hamiltonian flows typically do not share these properties unless specifically designed to do so. We develop explicit conservation conditions for a general class of algorithms on Lie groups. For the rigid body these conditions lead to a single-step algorithm that exactly preserves the energy, spatial momentum, and symplectic form. For homogeneous nonlinear elasticity, we find algorithms that conserve angular momentum and either the energy or the symplectic form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02430634
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  • 6
    Electronic Resource
    Electronic Resource
    Stability of relative equilibria. Part II: Application to nonlinear elasticity (1991)
    Springer
    Archive for rational mechanics and analysis 115 (1991), S. 61-100 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881679
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A justification of nonlinear properly invariant plate theories (1993)
    Springer
    Archive for rational mechanics and analysis 124 (1993), S. 157-199 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame-invariance properties of three-dimensional finite elasticity. By a successive scaling of the external loading on the three-dimensional body, the nonlinear membrane theory, the nonlinear inextensional theory and the von Kármán equations are derived as the leading-order terms in the asymptotic expansion of finite elasticity. The governing equations of the nonlinear inextensional theory are of particular interest where 1) plane-strain kinematics and plane-stress constitutive equations are derived simultaneously from the asymptotic analysis, 2) the theory can be phrased as a minimization problem over the space of isometric deformations of a surface, and 3) the local equilibrium equations are identical to those arising in the one-director Cosserat shell model. Furthermore, it can be concluded that with a regular, single-scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading-order term of an asymptotic analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00375134
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  • 8
    Electronic Resource
    Electronic Resource
    Stability of relative equilibria. Part I: The reduced energy-momentum method (1991)
    Springer
    Archive for rational mechanics and analysis 115 (1991), S. 15-59 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881678
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  • 9
    Electronic Resource
    Electronic Resource
    Fracture parameter for thermoinelasticity (1992)
    Springer
    International journal of fracture 56 (1992), S. 159-187 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A path domain independent integral, S, that equals the energy release rate for an extending crack in a thermoinelastic field is presented. This paper develops the new parameter from its theoretical foundations in continuum mechanics, demonstrates that S can be calculated from finite element results and describes how S can be obtained from experiments. The S-integral is developed for simple uncoupled and linearized fully coupled quasi static thermoinelastic cases. Invoking thermoinelastic continuum mechanics linearized for small strain and small temperature changes, S emanates from a discrete Lagrangian describing the thermoinelastic system and Noether's theorem from classical field theory. S defines the force acting on an extending crack and represents a conservation law for a crack free body analogous to the Budiansky and Rice interpretation of the J-integral. The conservation law nature of S for a singularity free region is demonstrated by both computational and physical experiments. S can be calculated from finite element results via a two step postprocessing algorithm. Furthermore, S can be obtained from physical experiments. The S-integral offers a parameter to improve the understanding of the strength and reliability of materials subjected to thermomechanical loadings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00015598
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  • 10
    Electronic Resource
    Electronic Resource
    Numerical simulation of equilibrium shocks in maximally dissipative elastic systems. Part I: The one-dimensional case (1994)
    Springer
    Journal of elasticity 35 (1994), S. 175-211 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract An algorithm designed for the determination of equilibrium shocks that appear in quasi-static evolution problems associated to elastic nonmonotonous stress-strain laws is presented in the context of one-dimensional media. Two basic procedures are involved in the proposed method: (i) enhancement of the finite element in order to describe the weak discontinuities in any point of its interior and (ii) implementation of a return mapping algorithm for the determination of the shocks, which have to satisfy the inequality constraints imposed by a maximally dissipative hypothesis. A rigorous proof of the unconditional stability property of the algorithm is also given. The present study is applied to the theoretical model presented by Abeyaratne and Knowles in the context of one-dimensional extensional deformations of bars. The numerical results are in complete agreement with the analytical ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00115542
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