1.3 Further Reading
17
Elasticity characterising rate-independent, reversible material response is perhaps
the best studied material model in continuum mechanics. Some of the classical references on theoretical and mathematical elasticity are the books by Green and Zerna
[30], Love [31], and Muskhelishvili [32]. A masterly introduction to rational nonlinear elasticity is given by Wang and Truesdell [33]. Emphasizing its geometrical
underpinnings, Marsden and Hughes [34] elaborate a quite challenging, yet frequently cited, tract on the mathematical foundations of elasticity. The monograph by
Ogden [35] is acknowledgedly a must-have introduction to non-linear elastic deformations. A comprehensive exposition of demanding non-linear problems in elasticity
is due to Antmann [36]. The tracts by Ciarlet [37, 38] dwell on analysis-based presentations of non-linear elasticity. Based on quasi-convexity, Pedregal [39] analyses the
non/existence of solutions to variational methods in non-linear elasticity. Lurie [40]
provides a detailed examination of theoretical elasticity. Linear elasticity is covered,
e.g., in the rational treatise by Gurtin [41], the scholarly essay by Podio-Guidugli
[42], and the more recent treatment by Slaughter [43].
Rate-dependent, reversible material response is captured by models from the
realm of Visco-Elasticity. The early monograph by Flügge [44] is a reference survey
on the formulation of visco-elasticity. Likewise, Bland [45] represents a classical
reference on linear visco-elasticity. Drozdov [46] comprehensively reviews various visco-elastic response behaviours and the corresponding continuum modelling.
Cho [47] and Phan-Thien and Mai-Duy [48], e.g., provide introductions to viscoelasticity that emphasize the importance of polymer rheology. A classical account
on visco-elasticity is given in the introductory text by Christensen [49]. Fractional
calculus and waves are considered by Mainardi [50] for mathematical models of
linear visco-elasticity. With an interest in the analytical properties of the solutions
to initial-boundary-value problems, Fabrizio and Morro [51] analyse linear viscoelasticity mathematically. A more engineering-oriented approach to visco-elasticity
is presented by Gutierrez-Lemini [52].
As a framework for rate-independent, irreversible material response, Plasticity
poses severe mathematical challenges to the modeler. In this regard the treatise by
Hill [53] is the key reference on mathematical plasticity. The fundamentals of plasticity are outlined, e.g., in the classical account by Kachanov [54]. Chakrabarty [55]
offers a comprehensive exposition of classical plasticity. The focus of the tract by
Maugin [56] is on the mathematical setting of the thermodynamics of plasticity.
Lubliner [57] presents a benchmark compilation of paradigmatic problems in plasticity. An advanced treatment of finite plasticity is given by Lubarda [58]. Likewise
with a view on finite plasticity, Nemat-Nasser [59] treats the case of heterogeneous
materials. Khan and Huang [60] contribute a lucid exposition of continuum plasticity.
An integrated coverage of continuum mechanics and plasticity is due to Wu [61]. An
up-to-date review of finite plasticity is represented in the monograph by Hashiguchi
and Yamakawa [62]. The convex analysis setting of plasticity relevant to the present
Catalogue of Computational Material Models is covered by Han and Reddy [63].
Visco-Plasticity combines rate-dependent and irreversible material response and
is typically modelled as an extension to an underlying plasticity formulation. The
foundational formulation of overstress-type visco-plasticity is due to Perzyna [64].
17
Elasticity characterising rate-independent, reversible material response is perhaps
the best studied material model in continuum mechanics. Some of the classical references on theoretical and mathematical elasticity are the books by Green and Zerna
[30], Love [31], and Muskhelishvili [32]. A masterly introduction to rational nonlinear elasticity is given by Wang and Truesdell [33]. Emphasizing its geometrical
underpinnings, Marsden and Hughes [34] elaborate a quite challenging, yet frequently cited, tract on the mathematical foundations of elasticity. The monograph by
Ogden [35] is acknowledgedly a must-have introduction to non-linear elastic deformations. A comprehensive exposition of demanding non-linear problems in elasticity
is due to Antmann [36]. The tracts by Ciarlet [37, 38] dwell on analysis-based presentations of non-linear elasticity. Based on quasi-convexity, Pedregal [39] analyses the
non/existence of solutions to variational methods in non-linear elasticity. Lurie [40]
provides a detailed examination of theoretical elasticity. Linear elasticity is covered,
e.g., in the rational treatise by Gurtin [41], the scholarly essay by Podio-Guidugli
[42], and the more recent treatment by Slaughter [43].
Rate-dependent, reversible material response is captured by models from the
realm of Visco-Elasticity. The early monograph by Flügge [44] is a reference survey
on the formulation of visco-elasticity. Likewise, Bland [45] represents a classical
reference on linear visco-elasticity. Drozdov [46] comprehensively reviews various visco-elastic response behaviours and the corresponding continuum modelling.
Cho [47] and Phan-Thien and Mai-Duy [48], e.g., provide introductions to viscoelasticity that emphasize the importance of polymer rheology. A classical account
on visco-elasticity is given in the introductory text by Christensen [49]. Fractional
calculus and waves are considered by Mainardi [50] for mathematical models of
linear visco-elasticity. With an interest in the analytical properties of the solutions
to initial-boundary-value problems, Fabrizio and Morro [51] analyse linear viscoelasticity mathematically. A more engineering-oriented approach to visco-elasticity
is presented by Gutierrez-Lemini [52].
As a framework for rate-independent, irreversible material response, Plasticity
poses severe mathematical challenges to the modeler. In this regard the treatise by
Hill [53] is the key reference on mathematical plasticity. The fundamentals of plasticity are outlined, e.g., in the classical account by Kachanov [54]. Chakrabarty [55]
offers a comprehensive exposition of classical plasticity. The focus of the tract by
Maugin [56] is on the mathematical setting of the thermodynamics of plasticity.
Lubliner [57] presents a benchmark compilation of paradigmatic problems in plasticity. An advanced treatment of finite plasticity is given by Lubarda [58]. Likewise
with a view on finite plasticity, Nemat-Nasser [59] treats the case of heterogeneous
materials. Khan and Huang [60] contribute a lucid exposition of continuum plasticity.
An integrated coverage of continuum mechanics and plasticity is due to Wu [61]. An
up-to-date review of finite plasticity is represented in the monograph by Hashiguchi
and Yamakawa [62]. The convex analysis setting of plasticity relevant to the present
Catalogue of Computational Material Models is covered by Han and Reddy [63].
Visco-Plasticity combines rate-dependent and irreversible material response and
is typically modelled as an extension to an underlying plasticity formulation. The
foundational formulation of overstress-type visco-plasticity is due to Perzyna [64].