Strain gradient elasto-plasticity model: 3D isogeometric implementation and applications to cellular structures

Sergei Khakalo (Corresponding Author), Anssi Laukkanen

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
110 Downloads (Pure)


In the present work, we combine Mindlin's strain gradient elasticity theory and Gudmundson–Gurtin–Anand strain gradient plasticity theory to form a unified framework. The gradient plasticity model is enriched by including the gradient of elastic strains into the expression of the internal virtual work and free energy. This augments the modelling capabilities by incorporating elasticity-related length scales along with plasticity-related energetic and dissipative ones. The strong form governing equations are derived via the principle of virtual work addressing a complete set of boundary conditions. The fourth-order boundary value problem of the gradient elasto-plasticity model is then formulated in a variational form within an H 2 Sobolev space setting. Conforming Galerkin discretizations for numerical results are obtained utilizing an isogeometric approach with NURBS basis functions of degree p≥2 providing C p−1-continuity. The implementation follows a viscoplastic constitutive framework and adopts the backward Euler time integration scheme. A set of benchmark examples is considered to illustrate convergence properties and to accomplish parameter studies. It is shown that the elastic length scale parameter controls the slope of the elastic part and causes an additional hardening in the plastic part of the material response curves. Finally, an illustrative example is considered in order to demonstrate the applicability of both the continuum model and the numerical method in capturing the size-dependent torsion response of cellular structures.

Original languageEnglish
Article number114225
Pages (from-to)1-35
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jan 2022
MoE publication typeA1 Journal article-refereed


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