Institute of Fundamental Technological Research
Polish Academy of Sciences

Former Staff

Prof. Tomasz Wierzbicki, PhD, DSc

Doctoral thesis
1965 Dynamika sztywno-lepko-plastycznych płyt kołowych 
supervisor -- Piotr Perzyna, PhD, DSc, IPPT PAN
Habilitation thesis
1972 Liniowa teoria lepkoplastycznych konstrukcji  
1981 Title of professor
Supervision of doctoral theses
1.  1979 Ploch Jerzy   Oszacowania przemieszczeń w geometrycznie nieliniowych zagadnieniach dynamiki ciał sprężystych i plastycznych 

Recent publications
1.  Fras T., Pawlowski P., Li W., Wierzbicki T., Performance of Li-ion pouch battery under a high-velocity impact: experiment and numerical simulation, INTERNATIONAL JOURNAL OF IMPACT ENGINEERING, ISSN: 0734-743X, DOI: 10.1016/j.ijimpeng.2021.103915, Vol.155, pp.1039152-1-16, 2021

The deformation and failure of a Li-ion pouch battery under a high-velocity impact are studied experimentally and numerically. Ballistic tests were performed with 9 × 19 mm small-caliber projectiles travelling at 360 m/s, using state-of-the-art recording equipment and post-mortem examination under CT scan. The experimental observations are followed by a numerical simulation of the detailed multi-layer battery model. The study provides an insight into mechanisms of the progressive delamination and fracture of subsequent layers. The predicted residual velocity is very close to the measured values, but the impact energy absorption of the battery was found to be relatively low. The presented experimental and numerical analysis may contribute to a design of protection systems, in which rechargeable Li-ion batteries are included.

2D and 3D multilayered FE models, CT scan, delamination, high-velocity projectile impact, large format pouch battery, residual velocity

Fras T. - other affiliation
Pawlowski P. - IPPT PAN
Li W. - other affiliation
Wierzbicki T. - other affiliation
2.  Jones N, Wierzbicki T., A study of the higher modal dynamic plastic response of beams, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/0020-7403(76)90079-5, Vol.18, No.11-12, pp.533-542, 1976

A theoretical and experimental investigation into the higher modal dynamic plastic response of fully clamped beams is reported herein. It is shown that the influence of geometry changes or finite-deflections is important which agrees with previous studies on the dynamic plastic behavior of uniformly loaded beams. It appears that the higher modal response of beams is a more efficient means of absorbing a given magnitude of kinetic energy than a single modal response.

Jones N - Massachusetts Institute of Technology (US)
Wierzbicki T. - IPPT PAN
3.  Wierzbicki T., Extremum principles in the dynamics of rigid-plastic bodies: A critical review of existing applications, NUCLEAR ENGINEERING AND DESIGN, ISSN: 0029-5493, DOI: 10.1016/0029-5493(76)90058-3, Vol.37, No.1, pp.149-160, 1976

In recent years a number of variational or extremum principles have been formulated for bodies deforming beyond the elastic range as a result of dynamic loading. These theorems represent a potential for deriving approximate solutions to the initial-boundary value problems for inelastic continua and structures. However, some of the principle are of much more restrictive character than it is commonly believed and care should be taken in interpreting properly the resulting approximations. The importance of applying a variational technique in deriving approximate solutions has somehow been overemphasized in the literature and some authors tried to demonstrate advantages of the suggested methods while no mention was made of the existing shortcomings. This article aims to discuss some of the limitations and clarify difficulties in applying the extremum principles to dynamic problems for rigid-plastic continua and structures with special reference to the development of analytical methods. In particular, an attempt is to answer the following questions: (1) To what extent the existing methods can be used in the analysis of transient problems for impulsively or pulse loaded structures? (2) Under what conditions stationarity of appropriate functionals can be proved so that use of direct methods of the calculus of variations is well legitimated? (3) Can a formal approximation method be developed for mode form response in which exact solution is approached with any desired degree of accuracy?

These questions are related to the problem of a choice of a class of admissible functions. If the admissible functions contain the true solution, then the extremal theorems are shown to be applicable for deriving solutions to both transient and fixed shape problems. However, such a situation can be regarded as exceptional, and in typical cases the exact solution is either unknown or cannot be expressed in terms of elementary functions. It is pointed out that in these circumstances solutions to transient problems, obtained by means of analytical methods, might not be correct. Examples from the available literature are cited. In contrast, approximate mode form solutions can still be derived from variational principles, but then the question of accuracy arises. Most of the existing solutions were obtained from the kinematic principle by considering very simple admissible fields of velocities or accelerations involving only a few free parameters. Because of the non-linearity of the dissipation function and lack of the property of superposition it becomes very tedious or even impossible to evaluate effectively integrals appearing in the functionals when more terms are considered. Thus, the Rayleigh-Ritz method for finding a stationary point of a functional does not seem to be of great help when an improved accuracy is desired. Two ways of overcoming this difficulty are suggested. In the first, possibilities of using a dynamic rather than kinematic principle is explored, the former being expressed entirely in stresses. As an alternative, a new definition of a set of approximate functions is introduced and its advantages over Ritz's coordinate functions are explained on the plate problem. Finally, conditions are examined for the extrema to be stationary. Various types of extremal behaviour with analytic and non-analytic extrema are demonstrated, depending on the smootheness of the yield conditions and continuity in the slope of the admissible velocity field.

Wierzbicki T. - IPPT PAN
4.  Wierzbicki T., Duże ugięcia dynamiczne obciążonych konstrukcji. Krytyczny przegląd istniejących teorii, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.51, pp.1-52, 1975
5.  Wierzbicki T., On the region of admissible deformations in impulsive-loading problems, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 0022-5096, DOI: 10.1016/0022-5096(71)90031-7, Vol.19, No.1, pp.1-10, 1971

Previous impulsive-loading theorems due to J.B. Martin are reconsidered and further developed to reach a uniform treatment of perfectly-plastic and viscoplastic materials. Starting from the extended form of D.C. Drucker's postulate for stability, and using as a reference state a complete solution of an auxiliary quasi-static problem, a single inequality is derived which provides a relation between permanent deflection and response-time in a given boundary-value problem. It is shown that bounds on the one quantity can be found whenever the other is known. Separate bounds on deflections and response-time can be obtained only in the limiting case of perfectly-plastic material. The theory is illustrated by the example of a clamped circular plate.

Wierzbicki T. - IPPT PAN
6.  Wierzbicki T., Liniowa teoria lepkoplastycznych konstrukcji (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.29, pp.1-116, 1971
7.  Wierzbicki T., Wariacyjna metoda oszacowania ugięć dynamicznie obciążonych konstrukcji, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.2, pp.1-29, 1971
8.  Wierzbicki T., Andrzejewski H., An Experimental and Theoretical Study of Impulsively Loaded Viscoplastic Cylindrical Shells, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.11, pp.1-15, 1969
9.  Wierzbicki T., Viscoplastic Flow of Rotationally Symmetric Shells with Particular Application to Dynamic Loadings, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.1, pp.1-21, 1968
10.  Perzyna P., Wierzbicki T., On temperature dependent and strain rate sensitive plastic materials, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, Vol.12, pp.225-232, 1964
11.  Perzyna P., Wierzbicki T., The propagation of stress waves in a sensitive and work-hardening plastic medium, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.16, pp.1215-1244, 1964
12.  Perzyna P., Wierzbicki T., Temperature dependent and strain rate sensitive plastic materials, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.16, pp.135-143, 1964

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